{"id":27,"date":"2023-01-06T11:53:11","date_gmt":"2023-01-06T16:53:11","guid":{"rendered":"https:\/\/pressbooks.bccampus.ca\/math023\/chapter\/two-and-three-digit-multipliers\/"},"modified":"2025-07-03T22:37:09","modified_gmt":"2025-07-04T02:37:09","slug":"two-and-three-digit-multipliers","status":"publish","type":"chapter","link":"https:\/\/pressbooks.bccampus.ca\/math023\/chapter\/two-and-three-digit-multipliers\/","title":{"raw":"Topic B: Two- and Three-Digit Multipliers","rendered":"Topic B: Two- and Three-Digit Multipliers"},"content":{"raw":"When the multiplier is more than one digit, you use the same process and get partial products. You repeat the steps until you have multiplied by every digit, then add the partial products together.\r\n

Multiplying by Two-Digit Multipliers<\/h1>\r\n
\r\n

Example A<\/p>\r\n\r\n<\/header>\r\n

\r\n\r\n[latex]24\\times23=[\/latex]\r\n\r\nPart 1:<\/strong> Multiply by the ones digit in the multiplier.\r\n

Multiply 3 ones by 24 using the method you already know. The first partial product is 72.<\/p>\r\n

[latex]\\begin{array}{rr}&_1\\hspace{0.5em}\\\\&24\\\\\\times&23\\\\\\hline&72\\end{array}[\/latex]<\/p>\r\nPart 2:<\/strong> Multiply by the tens digit in the multiplier. First, put a 0 to hold the ones place in your partial product. We are multiplying by a ten, so we hold the ones place.\r\n

Step 1:<\/strong> Multiply 2 tens 4 ones = 8 tens Write the 8 tens under the tens in your first partial product. It is very important to keep the columns straight \u2013 ones under one, tens under tens.<\/p>\r\n

Step 2:<\/strong> Multiply 2 tens 2 tens = 4 hundreds Write the 4 hundreds in your partial product. The second partial product is 480.<\/p>\r\n

[latex]\\begin{array}{rr}&_1\\hspace{0.5em}\\\\&24\\\\\\times&23\\\\\\hline&72\\\\&480\\end{array}[\/latex]<\/p>\r\nPart 3:<\/strong> Add the partial products together, being sure to add ones to ones, tens to tens, hundreds to hundreds. The sum is the final product.\r\n

Draw a line under the partial products. Add. Check your addition.<\/p>\r\n

[latex]\\begin{array}{rr}&_1\\hspace{0.5em}\\\\&24\\\\\\times&23\\\\\\hline&72\\\\+&480\\\\\\hline&552\\end{array}[\/latex]<\/p>\r\n\r\n<\/div>\r\n<\/div>\r\n

\r\n

Example B<\/p>\r\n\r\n<\/header>\r\n

\r\n\r\n[latex]36\\times425 =[\/latex]\r\n\r\nPart 1:<\/strong> Multiply by the ones digit in the multiplier. 6 \u00d7 425 = 2550<\/span>\r\n

[latex]\\begin{array}{rr}&_1\\hspace{0.15em}_3\\hspace{0.5em}\\\\&425\\\\\\times&36\\\\\\hline&2550\\end{array}[\/latex]<\/p>\r\nPart 2:<\/strong> Multiply by the tens digit in the multiplier. First put a 0 to hold the ones place in the second partial product.\r\n

    \r\n \t
  • Step 1:<\/strong> 3 tens \u00d7 5 tens = 15 tens = 1 hundred and 5 tens\r\nWrite the 5 tens in the second partial product and carry the 1 hundred. Now you can see why it is best to cross out the numbers you carry as soon as you have added them to the product.<\/li>\r\n \t
  • Step 2:<\/strong> 3 tens \u00d7 2 tens = 6 hundreds\r\n6 hundreds + 1 hundred (carried) = 7 hundreds. There is nothing to carry.<\/li>\r\n \t
  • Step 3:<\/strong> 3 tens \u00d7 4 hundreds = 12 thousands<\/li>\r\n<\/ul>\r\n

    [latex]\\begin{array}{rr}&_1\\hspace{0.5em}\\\\&_1\\hspace{0.15em}_3\\hspace{0.5em}\\\\&425\\\\\\times&36\\\\\\hline&2550\\\\&12750\\end{array}[\/latex]<\/p>\r\nPart 3:<\/strong> Add the partial products together.\r\n

    [latex]\\begin{array}{rr}&_1\\hspace{0.5em}\\\\&_1\\hspace{0.15em}_3\\hspace{0.5em}\\\\&425\\\\\\times&36\\\\\\hline&2550\\\\+&12750\\\\\\hline&15300\\end{array}[\/latex]<\/p>\r\n\r\n<\/div>\r\n<\/div>\r\n

    Tip: Keeping the columns straight with ones under ones, tens under tens, hundreds under hundreds is very important. Working on large-squared graphing paper using one digit per square is often helpful.<\/div>\r\n
    tens \u00d7 tens = hundreds\r\ntens \u00d7 hundreds = thousands<\/div>\r\n
    \r\n

    Exercise 1<\/p>\r\n\r\n<\/header>\r\n

    \r\n\r\nMultiply, being very careful to keep the columns straight when you write your partial products. Check your work using the answer key at the end of the exercise.\r\n

    [latex]\\begin{array}{rr}&84\\\\\\times&12\\\\\\hline&168\\\\+&840\\\\\\hline&1008\\end{array}[\/latex]<\/p>\r\n\r\n

      \r\n \t
    1. [latex]\\begin{array}{rr}&73\\\\\\times&12\\\\\\hline\\\\\\end{array}[\/latex]<\/li>\r\n \t
    2. [latex]\\begin{array}{rr}&50\\\\\\times&42\\\\\\hline\\\\\\end{array}[\/latex]<\/li>\r\n \t
    3. [latex]\\begin{array}{rr}&62\\\\\\times&31\\\\\\hline\\\\\\end{array}[\/latex]<\/li>\r\n \t
    4. [latex]\\begin{array}{rr}&61\\\\\\times&42\\\\\\hline\\\\\\end{array}[\/latex]<\/li>\r\n \t
    5. [latex]\\begin{array}{rr}&91\\\\\\times&53\\\\\\hline\\\\\\end{array}[\/latex]<\/li>\r\n \t
    6. [latex]\\begin{array}{rr}&92\\\\\\times&31\\\\\\hline\\\\\\end{array}[\/latex]<\/li>\r\n \t
    7. [latex]\\begin{array}{rr}&91\\\\\\times&49\\\\\\hline\\\\\\end{array}[\/latex]<\/li>\r\n \t
    8. [latex]\\begin{array}{rr}&72\\\\\\times&48\\\\\\hline\\\\\\end{array}[\/latex]<\/li>\r\n \t
    9. [latex]\\begin{array}{rr}&53\\\\\\times&30\\\\\\hline\\\\\\end{array}[\/latex]<\/li>\r\n \t
    10. [latex]\\begin{array}{rr}&41\\\\\\times&53\\\\\\hline\\\\\\end{array}[\/latex]<\/li>\r\n \t
    11. [latex]\\begin{array}{rr}&42\\\\\\times&94\\\\\\hline\\\\\\end{array}[\/latex]<\/li>\r\n \t
    12. [latex]\\begin{array}{rr}&80\\\\\\times&86\\\\\\hline\\\\\\end{array}[\/latex]<\/li>\r\n \t
    13. [latex]\\begin{array}{rr}&31\\\\\\times&79\\\\\\hline\\\\\\end{array}[\/latex]<\/li>\r\n \t
    14. [latex]\\begin{array}{rr}&54\\\\\\times&40\\\\\\hline\\\\\\end{array}[\/latex]<\/li>\r\n \t
    15. [latex]\\begin{array}{rr}&61\\\\\\times&48\\\\\\hline\\\\\\end{array}[\/latex]<\/li>\r\n \t
    16. [latex]\\begin{array}{rr}&60\\\\\\times&31\\\\\\hline\\\\\\end{array}[\/latex]<\/li>\r\n \t
    17. [latex]\\begin{array}{rr}&55\\\\\\times&73\\\\\\hline\\\\\\end{array}[\/latex]<\/li>\r\n \t
    18. [latex]\\begin{array}{rr}&84\\\\\\times&56\\\\\\hline\\\\\\end{array}[\/latex]<\/li>\r\n \t
    19. [latex]\\begin{array}{rr}&53\\\\\\times&38\\\\\\hline\\\\\\end{array}[\/latex]<\/li>\r\n<\/ol>\r\nAnswers to Exercise 1<\/strong>\r\n
        \r\n \t
      1. 876<\/li>\r\n \t
      2. 2100<\/span><\/li>\r\n \t
      3. 1922<\/span><\/li>\r\n \t
      4. 2562<\/span><\/li>\r\n \t
      5. 4823<\/span><\/li>\r\n \t
      6. 2852<\/span><\/li>\r\n \t
      7. 4459<\/span><\/li>\r\n \t
      8. 3456<\/span><\/li>\r\n \t
      9. 1590<\/span><\/li>\r\n \t
      10. 2173<\/span><\/li>\r\n \t
      11. 3948<\/span><\/li>\r\n \t
      12. 6880<\/span><\/li>\r\n \t
      13. 2449<\/span><\/li>\r\n \t
      14. 2160<\/span><\/li>\r\n \t
      15. 2928<\/span><\/li>\r\n \t
      16. 1860<\/span><\/li>\r\n \t
      17. 4015<\/span><\/li>\r\n \t
      18. 4704<\/span><\/li>\r\n \t
      19. 2014<\/span><\/li>\r\n<\/ol>\r\n<\/div>\r\n<\/div>\r\nWhen the multiplier has a zero in the ones place, use this shortcut.\r\n
        \r\n

        Example C<\/p>\r\n\r\n<\/header>\r\n

        \r\n\r\n[latex]\\begin{array}{rr}&48\\\\\\times&80\\\\\\hline&3840\\end{array}[\/latex]\r\n
          \r\n \t
        • Step 1:<\/strong> 0 ones \u00d7 48 = 0. Place one zero in the product and that will hold the ones place.<\/li>\r\n \t
        • Step 2:<\/strong> Multiply by the tens digit and write the product beside the zero.<\/li>\r\n<\/ul>\r\n<\/div>\r\n<\/div>\r\n
          \r\n

          Example D<\/p>\r\n\r\n<\/header>\r\n

          \r\n\r\n[latex]\\begin{array}{rr}&97\\\\\\times&20\\\\\\hline&1940\\end{array}[\/latex]\r\n\r\n<\/div>\r\n<\/div>\r\n
          \r\n

          Exercise 2<\/p>\r\n\r\n<\/header>\r\n

          \r\n\r\nFind the products. Use the shortcut for multipliers with a zero in them. Check your work using the answer key at the end of the exercise.\r\n\r\n[latex]\\begin{array}{rr}&76\\\\\\times&70\\\\\\hline&5320\\end{array}[\/latex]\r\n
            \r\n \t
          1. [latex]\\begin{array}{rr}&52\\\\\\times&70\\\\\\hline\\\\\\end{array}[\/latex]<\/li>\r\n \t
          2. [latex]\\begin{array}{rr}&91\\\\\\times&70\\\\\\hline\\\\\\end{array}[\/latex]<\/li>\r\n \t
          3. [latex]\\begin{array}{rr}&83\\\\\\times&70\\\\\\hline\\\\\\end{array}[\/latex]<\/li>\r\n \t
          4. [latex]\\begin{array}{rr}&49\\\\\\times&70\\\\\\hline\\\\\\end{array}[\/latex]<\/li>\r\n \t
          5. [latex]\\begin{array}{rr}&61\\\\\\times&70\\\\\\hline\\\\\\end{array}[\/latex]<\/li>\r\n \t
          6. [latex]\\begin{array}{rr}&16\\\\\\times&70\\\\\\hline\\\\\\end{array}[\/latex]<\/li>\r\n \t
          7. [latex]\\begin{array}{rr}&36\\\\\\times&70\\\\\\hline\\\\\\end{array}[\/latex]<\/li>\r\n \t
          8. [latex]\\begin{array}{rr}&398\\\\\\times&70\\\\\\hline\\\\\\end{array}[\/latex]<\/li>\r\n \t
          9. [latex]\\begin{array}{rr}&432\\\\\\times&70\\\\\\hline\\\\\\end{array}[\/latex]<\/li>\r\n \t
          10. [latex]\\begin{array}{rr}&863\\\\\\times&70\\\\\\hline\\\\\\end{array}[\/latex]<\/li>\r\n \t
          11. [latex]\\begin{array}{rr}&907\\\\\\times&70\\\\\\hline\\\\\\end{array}[\/latex]<\/li>\r\n \t
          12. [latex]\\begin{array}{rr}&503\\\\\\times&70\\\\\\hline\\\\\\end{array}[\/latex]<\/li>\r\n \t
          13. [latex]\\begin{array}{rr}&452\\\\\\times&70\\\\\\hline\\\\\\end{array}[\/latex]<\/li>\r\n \t
          14. [latex]\\begin{array}{rr}&943\\\\\\times&70\\\\\\hline\\\\\\end{array}[\/latex]<\/li>\r\n \t
          15. [latex]\\begin{array}{rr}&248\\\\\\times&70\\\\\\hline\\\\\\end{array}[\/latex]<\/li>\r\n \t
          16. [latex]\\begin{array}{rr}&6287\\\\\\times&70\\\\\\hline\\\\\\end{array}[\/latex]<\/li>\r\n \t
          17. [latex]\\begin{array}{rr}&9025\\\\\\times&70\\\\\\hline\\\\\\end{array}[\/latex]<\/li>\r\n \t
          18. [latex]\\begin{array}{rr}&8907\\\\\\times&70\\\\\\hline\\\\\\end{array}[\/latex]<\/li>\r\n \t
          19. [latex]\\begin{array}{rr}&300\\\\\\times&70\\\\\\hline\\\\\\end{array}[\/latex]<\/li>\r\n \t
          20. [latex]\\begin{array}{rr}&9075\\\\\\times&70\\\\\\hline\\\\\\end{array}[\/latex]<\/li>\r\n \t
          21. [latex]\\begin{array}{rr}&3952\\\\\\times&70\\\\\\hline\\\\\\end{array}[\/latex]<\/li>\r\n \t
          22. [latex]\\begin{array}{rr}&1528\\\\\\times&70\\\\\\hline\\\\\\end{array}[\/latex]<\/li>\r\n \t
          23. [latex]\\begin{array}{rr}&7106\\\\\\times&70\\\\\\hline\\\\\\end{array}[\/latex]<\/li>\r\n<\/ol>\r\nAnswers to Exercise 2<\/strong>\r\n
              \r\n \t
            1. 3640<\/span><\/li>\r\n \t
            2. 6370<\/span><\/li>\r\n \t
            3. 5810<\/span><\/li>\r\n \t
            4. 3430<\/span><\/li>\r\n \t
            5. 4270<\/span><\/li>\r\n \t
            6. 1120<\/span><\/li>\r\n \t
            7. 2520<\/span><\/li>\r\n \t
            8. 27860<\/span><\/li>\r\n \t
            9. 30240<\/span><\/li>\r\n \t
            10. 60410<\/span><\/li>\r\n \t
            11. 63490<\/span><\/li>\r\n \t
            12. 35210<\/span><\/li>\r\n \t
            13. 31640<\/span><\/li>\r\n \t
            14. 66010<\/span><\/li>\r\n \t
            15. 17360<\/span><\/li>\r\n \t
            16. 440090<\/span><\/li>\r\n \t
            17. 631750<\/span><\/li>\r\n \t
            18. 623490<\/span><\/li>\r\n \t
            19. 21000<\/span><\/li>\r\n \t
            20. 635250<\/span><\/li>\r\n \t
            21. 276640<\/span><\/li>\r\n \t
            22. 106960<\/span><\/li>\r\n \t
            23. 497420<\/span><\/li>\r\n<\/ol>\r\n<\/div>\r\n<\/div>\r\n
              How are you doing? Ask your instructor for help if you are not comfortable with multiplying.<\/div>\r\n

              Multiplying by Three-Digit Multipliers<\/h1>\r\nTo multiply by three digit multipliers, use the same method with one more part.\r\n
              \r\n

              Example E<\/p>\r\n\r\n<\/header>\r\n

              \r\n\r\n[latex]417\\times368 =[\/latex]\r\n

              [latex]\\begin{array}{rr}&417\\\\\\times&368\\\\\\hline&3336\\\\&25020\\\\+&125100\\\\\\hline&153456\\end{array}[\/latex]<\/p>\r\n\r\n

                \r\n \t
              • Part 1:<\/strong> Multiply by the 8 ones.<\/li>\r\n \t
              • Part 2:<\/strong> Multiply the 6 tens; hold the ones place with 0.<\/li>\r\n \t
              • Part 3:<\/strong> Multiply by the 3 hundreds. Put 00 to hold the ones and tens places in the third partial product.\r\n
                  \r\n \t
                • Step 1:<\/strong> 3 hundreds \u00d7 7 ones = 21 hundreds = 2 thousands and 1 hundred. Write the 1 hundred and carry the 2 thousands.<\/li>\r\n \t
                • Step 2:<\/strong> 3 hundreds \u00d7 1 ten = 3 thousands. 3 thousands + 2 thousands (carried) = 5 thousands.<\/li>\r\n \t
                • Step 3:<\/strong> 3 hundreds \u00d7 4 hundreds = 12 ten thousands.<\/li>\r\n<\/ul>\r\n<\/li>\r\n \t
                • Part 4: <\/strong>Add the partial products.<\/li>\r\n<\/ul>\r\n<\/div>\r\n<\/div>\r\n
                  \r\n

                  Exercise 3<\/p>\r\n\r\n<\/header>\r\n

                  \r\n\r\nFind the products. Check your work using the answer key at the end of the exercise.\r\n
                    \r\n \t
                  1. [latex]\\begin{array}{rr}&416\\\\\\times&213\\\\\\hline\\\\\\end{array}[\/latex]<\/li>\r\n \t
                  2. [latex]\\begin{array}{rr}&375\\\\\\times&291\\\\\\hline\\\\\\end{array}[\/latex]<\/li>\r\n \t
                  3. [latex]\\begin{array}{rr}&361\\\\\\times&475\\\\\\hline\\\\\\end{array}[\/latex]<\/li>\r\n \t
                  4. [latex]\\begin{array}{rr}&275\\\\\\times&863\\\\\\hline\\\\\\end{array}[\/latex]<\/li>\r\n \t
                  5. [latex]\\begin{array}{rr}&984\\\\\\times&469\\\\\\hline\\\\\\end{array}[\/latex]<\/li>\r\n \t
                  6. [latex]\\begin{array}{rr}&489\\\\\\times&578\\\\\\hline\\\\\\end{array}[\/latex]<\/li>\r\n \t
                  7. [latex]\\begin{array}{rr}&498\\\\\\times&123\\\\\\hline\\\\\\end{array}[\/latex]<\/li>\r\n \t
                  8. [latex]\\begin{array}{rr}&267\\\\\\times&854\\\\\\hline\\\\\\end{array}[\/latex]<\/li>\r\n \t
                  9. [latex]\\begin{array}{rr}&613\\\\\\times&368\\\\\\hline\\\\\\end{array}[\/latex]<\/li>\r\n \t
                  10. [latex]\\begin{array}{rr}&725\\\\\\times&547\\\\\\hline\\\\\\end{array}[\/latex]<\/li>\r\n \t
                  11. [latex]\\begin{array}{rr}&269\\\\\\times&912\\\\\\hline\\\\\\end{array}[\/latex]<\/li>\r\n \t
                  12. [latex]\\begin{array}{rr}&752\\\\\\times&697\\\\\\hline\\\\\\end{array}[\/latex]<\/li>\r\n \t
                  13. [latex]\\begin{array}{rr}&983\\\\\\times&357\\\\\\hline\\\\\\end{array}[\/latex]<\/li>\r\n \t
                  14. [latex]\\begin{array}{rr}&835\\\\\\times&148\\\\\\hline\\\\\\end{array}[\/latex]<\/li>\r\n \t
                  15. [latex]\\begin{array}{rr}&386\\\\\\times&296\\\\\\hline\\\\\\end{array}[\/latex]<\/li>\r\n<\/ol>\r\nAnswers to Exercise 3<\/strong>\r\n
                      \r\n \t
                    1. 88608<\/span><\/li>\r\n \t
                    2. 109125<\/span><\/li>\r\n \t
                    3. 171475<\/span><\/li>\r\n \t
                    4. 237325<\/span><\/li>\r\n \t
                    5. 461496<\/span><\/li>\r\n \t
                    6. 282642<\/span><\/li>\r\n \t
                    7. 61254<\/span><\/li>\r\n \t
                    8. 228018<\/span><\/li>\r\n \t
                    9. 225584<\/span><\/li>\r\n \t
                    10. 396575<\/span><\/li>\r\n \t
                    11. 245328<\/span><\/li>\r\n \t
                    12. 524144<\/span><\/li>\r\n \t
                    13. 350931<\/span><\/li>\r\n \t
                    14. 123580<\/span><\/li>\r\n \t
                    15. 114256<\/span><\/li>\r\n<\/ol>\r\n<\/div>\r\n<\/div>\r\nYou know to hold the ones place with a zero if the multiplier has a zero in the ones place. Use the same skill if the multiplier has a zero in the tens place.\r\n
                      \r\n

                      Example F<\/p>\r\n\r\n<\/header>\r\n

                      \r\n\r\n[latex]927\\times405 =[\/latex]\r\n

                      [latex]\\begin{array}{rr}&927\\\\\\times&405\\\\\\hline&4635\\\\+&370800\\\\\\hline&375435\\end{array}[\/latex]<\/p>\r\n\r\n

                        \r\n \t
                      • Part 1:<\/strong> Multiply by the 5 ones.<\/li>\r\n \t
                      • Part 2:<\/strong> Multiply by the 0 tens.\r\nHold the ones place with a 0; 0 \u00d7 927 = 0; Place one zero in the tens place in the second partial product.<\/li>\r\n \t
                      • Part 3:<\/strong> Multiply by the 4 hundreds. The ones and tens places are already held by zeros. Start this partial product in the hundreds place on the same line.<\/li>\r\n \t
                      • Part 4:<\/strong> Add the partial products.<\/li>\r\n<\/ul>\r\n<\/div>\r\n<\/div>\r\n
                        \r\n

                        Exercise 4<\/p>\r\n\r\n<\/header>\r\n

                        \r\n\r\nFind the products. Check your work using the answer key at the end of the exercise.\r\n

                        [latex]\\begin{array}{rr}&_2\\hspace{0.15em}_2\\hspace{0.5em}\\\\&698\\\\\\times&301\\\\\\hline&698\\\\+&209400\\\\\\hline&210098\\end{array}[\/latex]<\/p>\r\n\r\n

                          \r\n \t
                        1. [latex]\\begin{array}{rr}&923\\\\\\times&403\\\\\\hline\\\\\\end{array}[\/latex]<\/li>\r\n \t
                        2. [latex]\\begin{array}{rr}&830\\\\\\times&108\\\\\\hline\\\\\\end{array}[\/latex]<\/li>\r\n \t
                        3. [latex]\\begin{array}{rr}&482\\\\\\times&206\\\\\\hline\\\\\\end{array}[\/latex]<\/li>\r\n \t
                        4. [latex]\\begin{array}{rr}&432\\\\\\times&205\\\\\\hline\\\\\\end{array}[\/latex]<\/li>\r\n \t
                        5. [latex]\\begin{array}{rr}&625\\\\\\times&405\\\\\\hline\\\\\\end{array}[\/latex]<\/li>\r\n \t
                        6. [latex]\\begin{array}{rr}&275\\\\\\times&306\\\\\\hline\\\\\\end{array}[\/latex]<\/li>\r\n \t
                        7. [latex]\\begin{array}{rr}&765\\\\\\times&506\\\\\\hline\\\\\\end{array}[\/latex]<\/li>\r\n \t
                        8. [latex]\\begin{array}{rr}&1576\\\\\\times&702\\\\\\hline\\\\\\end{array}[\/latex]<\/li>\r\n \t
                        9. [latex]\\begin{array}{rr}&432\\\\\\times&405\\\\\\hline\\\\\\end{array}[\/latex]<\/li>\r\n \t
                        10. [latex]\\begin{array}{rr}&625\\\\\\times&409\\\\\\hline\\\\\\end{array}[\/latex]<\/li>\r\n \t
                        11. [latex]\\begin{array}{rr}&175\\\\\\times&306\\\\\\hline\\\\\\end{array}[\/latex]<\/li>\r\n \t
                        12. [latex]\\begin{array}{rr}&5874\\\\\\times&309\\\\\\hline\\\\\\end{array}[\/latex]<\/li>\r\n \t
                        13. [latex]\\begin{array}{rr}&7384\\\\\\times&104\\\\\\hline\\\\\\end{array}[\/latex]<\/li>\r\n \t
                        14. [latex]\\begin{array}{rr}&6538\\\\\\times&603\\\\\\hline\\\\\\end{array}[\/latex]<\/li>\r\n<\/ol>\r\nAnswers to Exercise 4<\/strong>\r\n
                            \r\n \t
                          1. 371969<\/span><\/li>\r\n \t
                          2. 89640<\/span><\/li>\r\n \t
                          3. 99292<\/span><\/li>\r\n \t
                          4. 88560<\/span><\/li>\r\n \t
                          5. 253 125<\/li>\r\n \t
                          6. 84150<\/span><\/li>\r\n \t
                          7. 387090<\/span><\/li>\r\n \t
                          8. 1106<\/span>352<\/span><\/li>\r\n \t
                          9. 174960<\/span><\/li>\r\n \t
                          10. 255625<\/span><\/li>\r\n \t
                          11. 53550<\/span><\/li>\r\n \t
                          12. 1815<\/span>066<\/span><\/li>\r\n \t
                          13. 767936<\/span><\/li>\r\n \t
                          14. 3942<\/span>414<\/span><\/li>\r\n<\/ol>\r\n<\/div>\r\n<\/div>\r\n

                            Multiplying by 10, 100, and 1000<\/span><\/h1>\r\n
                            \r\n

                            Exercise 5<\/p>\r\n\r\n<\/header>\r\n

                            \r\n\r\nDo the following questions and see if you can find the pattern. Check your work using the answer key at the end of the exercise.\r\n
                              \r\n \t
                            1. [latex]\\begin{array}{rr}&83\\\\\\times&10\\\\\\hline&830\\end{array}[\/latex]<\/li>\r\n \t
                            2. [latex]\\begin{array}{rr}&46\\\\\\times&10\\\\\\hline\\\\\\end{array}[\/latex]<\/li>\r\n \t
                            3. [latex]\\begin{array}{rr}&97\\\\\\times&10\\\\\\hline\\\\\\end{array}[\/latex]<\/li>\r\n \t
                            4. [latex]\\begin{array}{rr}&123\\\\\\times&10\\\\\\hline\\\\\\end{array}[\/latex]<\/li>\r\n \t
                            5. [latex]\\begin{array}{rr}&70\\\\\\times&10\\\\\\hline\\\\\\end{array}[\/latex]<\/li>\r\n \t
                            6. [latex]\\begin{array}{rr}&129\\\\\\times&10\\\\\\hline\\\\\\end{array}[\/latex]<\/li>\r\n \t
                            7. [latex]\\begin{array}{rr}&1852\\\\\\times&10\\\\\\hline\\\\\\end{array}[\/latex]<\/li>\r\n \t
                            8. [latex]\\begin{array}{rr}&29871\\\\\\times&10\\\\\\hline\\\\\\end{array}[\/latex]<\/li>\r\n \t
                            9. [latex]\\begin{array}{rr}&45\\\\\\times&100\\\\\\hline\\\\\\end{array}[\/latex]<\/li>\r\n \t
                            10. [latex]\\begin{array}{rr}&26\\\\\\times&100\\\\\\hline\\\\\\end{array}[\/latex]<\/li>\r\n \t
                            11. [latex]\\begin{array}{rr}&432\\\\\\times&100\\\\\\hline\\\\\\end{array}[\/latex]<\/li>\r\n \t
                            12. [latex]\\begin{array}{rr}&679\\\\\\times&100\\\\\\hline\\\\\\end{array}[\/latex]<\/li>\r\n \t
                            13. [latex]\\begin{array}{rr}&2482\\\\\\times&100\\\\\\hline\\\\\\end{array}[\/latex]<\/li>\r\n \t
                            14. [latex]\\begin{array}{rr}&9037\\\\\\times&100\\\\\\hline\\\\\\end{array}[\/latex]<\/li>\r\n \t
                            15. [latex]\\begin{array}{rr}&46207\\\\\\times&100\\\\\\hline\\\\\\end{array}[\/latex]<\/li>\r\n \t
                            16. [latex]\\begin{array}{rr}&97512\\\\\\times&100\\\\\\hline\\\\\\end{array}[\/latex]<\/li>\r\n \t
                            17. [latex]\\begin{array}{rr}&23\\\\\\times&1000\\\\\\hline\\\\\\end{array}[\/latex]<\/li>\r\n \t
                            18. [latex]\\begin{array}{rr}&452\\\\\\times&1000\\\\\\hline\\\\\\end{array}[\/latex]<\/li>\r\n \t
                            19. [latex]\\begin{array}{rr}&207\\\\\\times&1000\\\\\\hline\\\\\\end{array}[\/latex]<\/li>\r\n \t
                            20. [latex]\\begin{array}{rr}&348\\\\\\times&1000\\\\\\hline\\\\\\end{array}[\/latex]<\/li>\r\n \t
                            21. [latex]\\begin{array}{rr}&2118\\\\\\times&1000\\\\\\hline\\\\\\end{array}[\/latex]<\/li>\r\n \t
                            22. [latex]\\begin{array}{rr}&2431\\\\\\times&1000\\\\\\hline\\\\\\end{array}[\/latex]<\/li>\r\n \t
                            23. [latex]\\begin{array}{rr}&23681\\\\\\times&1000\\\\\\hline\\\\\\end{array}[\/latex]<\/li>\r\n \t
                            24. [latex]\\begin{array}{rr}&48203\\\\\\times&1000\\\\\\hline\\\\\\end{array}[\/latex]<\/li>\r\n<\/ol>\r\nAnswers to Exercise 5<\/strong>\r\n
                                \r\n \t
                              1. 830<\/li>\r\n \t
                              2. 460<\/li>\r\n \t
                              3. 970<\/li>\r\n \t
                              4. 1230<\/span><\/li>\r\n \t
                              5. 700<\/li>\r\n \t
                              6. 1290<\/span><\/li>\r\n \t
                              7. 18520<\/span><\/li>\r\n \t
                              8. 298710<\/span><\/li>\r\n \t
                              9. 4500<\/span><\/li>\r\n \t
                              10. 2600<\/span><\/li>\r\n \t
                              11. 43200<\/span><\/li>\r\n \t
                              12. 67900<\/span><\/li>\r\n \t
                              13. 248200<\/span><\/li>\r\n \t
                              14. 903700<\/span><\/li>\r\n \t
                              15. 4620700<\/span><\/span><\/li>\r\n \t
                              16. 9751200<\/span><\/span><\/li>\r\n \t
                              17. 23000<\/span><\/li>\r\n \t
                              18. 452000<\/span><\/li>\r\n \t
                              19. 207000<\/span><\/li>\r\n \t
                              20. 348000<\/span><\/li>\r\n \t
                              21. 2118000<\/span><\/span><\/li>\r\n \t
                              22. 2431000<\/span><\/span><\/li>\r\n \t
                              23. 23681000<\/span><\/span><\/li>\r\n \t
                              24. 48203000<\/span><\/span><\/li>\r\n<\/ol>\r\n<\/div>\r\n<\/div>\r\nAnd the pattern is \u2026\r\n\r\nWhen multiplying by 10, 100, 1000, 10000, etc., place as many zeros to the right of the number as there are zeros in the 10, 100, 1000, etc.<\/span><\/span><\/span>\r\n
                                  \r\n \t
                                • To multiply by 10 put one zero after the number.<\/li>\r\n \t
                                • To multiply by 100 put two zeros after the number.<\/li>\r\n \t
                                • To multiply by 1000 put three zeros after the number.<\/span><\/li>\r\n<\/ul>\r\n
                                  \r\n

                                  Exercise 6<\/p>\r\n\r\n<\/header>\r\n

                                  \r\n\r\nFind the products using the short method.\u00a0 Do not rewrite the questions. Check your work using the answer key at the end of the exercise.\r\n
                                    \r\n \t
                                  1. 12 \u00d7 10 = 120<\/li>\r\n \t
                                  2. 10 \u00d7 3175<\/span> =<\/li>\r\n \t
                                  3. 162 \u00d7 10 =<\/li>\r\n \t
                                  4. 10 \u00d7 53821<\/span> =<\/li>\r\n \t
                                  5. 10 \u00d7 123 =<\/li>\r\n \t
                                  6. 27342<\/span> \u00d7 10 =<\/li>\r\n \t
                                  7. 10 \u00d7 98 =<\/li>\r\n \t
                                  8. 1134<\/span> \u00d7 10 =<\/li>\r\n \t
                                  9. 15 \u00d7 100 =<\/li>\r\n \t
                                  10. 100 \u00d7 278 =<\/li>\r\n \t
                                  11. 9134<\/span> \u00d7 100 =<\/li>\r\n \t
                                  12. 651 \u00d7 100 =<\/li>\r\n \t
                                  13. 100 \u00d7 5169<\/span> =<\/li>\r\n \t
                                  14. 100 \u00d7 24815<\/span> =<\/li>\r\n \t
                                  15. 10 \u00d7 905 =<\/li>\r\n \t
                                  16. 45683<\/span> \u00d7 10 =<\/li>\r\n \t
                                  17. 1000<\/span> \u00d7 87 =<\/li>\r\n \t
                                  18. 521 \u00d7 1000<\/span> =<\/li>\r\n \t
                                  19. 1000<\/span> \u00d7 68935<\/span> =<\/li>\r\n \t
                                  20. 1000<\/span> \u00d7 8902<\/span> =<\/li>\r\n \t
                                  21. 1576<\/span> \u00d7 1000<\/span> =<\/li>\r\n \t
                                  22. 31584<\/span> \u00d7 1000<\/span> =<\/li>\r\n \t
                                  23. 1000<\/span> \u00d7 426 =<\/li>\r\n \t
                                  24. 72 \u00d7 1000<\/span> =<\/li>\r\n<\/ol>\r\nAnswers for Exercise 6<\/strong>\r\n
                                      \r\n \t
                                    1. 120<\/li>\r\n \t
                                    2. 31750<\/span><\/li>\r\n \t
                                    3. 1620<\/span><\/li>\r\n \t
                                    4. 538210<\/span><\/li>\r\n \t
                                    5. 1230<\/span><\/li>\r\n \t
                                    6. 273420<\/span><\/li>\r\n \t
                                    7. 980<\/li>\r\n \t
                                    8. 11340<\/span><\/li>\r\n \t
                                    9. 1500<\/span><\/li>\r\n \t
                                    10. 27800<\/span><\/li>\r\n \t
                                    11. 913400<\/span><\/li>\r\n \t
                                    12. 65100<\/span><\/li>\r\n \t
                                    13. 516900<\/span><\/li>\r\n \t
                                    14. 2481500<\/span><\/span><\/li>\r\n \t
                                    15. 9050<\/span><\/li>\r\n \t
                                    16. 456830<\/span><\/li>\r\n \t
                                    17. 87000<\/span><\/li>\r\n \t
                                    18. 521000<\/span><\/li>\r\n \t
                                    19. 68935000<\/span><\/span><\/li>\r\n \t
                                    20. 8902000<\/span><\/span><\/li>\r\n \t
                                    21. 1576000<\/span><\/span><\/li>\r\n \t
                                    22. 31584000<\/span><\/span><\/li>\r\n \t
                                    23. 426000<\/span><\/li>\r\n \t
                                    24. 72000<\/span><\/li>\r\n<\/ol>\r\n<\/div>\r\n<\/div>\r\n

                                      Topic B: Self-Test<\/h1>\r\nMark\u00a0 \/12 \u00a0\u00a0 Aim\u00a0 10\/12<\/strong>\r\n
                                        \r\n \t
                                      1. Multiply these numbers.\r\n
                                          \r\n \t
                                        1. [latex]\\begin{array}{rr}&47\\\\\\times&39\\\\\\hline\\\\\\end{array}[\/latex]<\/li>\r\n \t
                                        2. [latex]\\begin{array}{rr}&58\\\\\\times&93\\\\\\hline\\\\\\end{array}[\/latex]<\/li>\r\n \t
                                        3. [latex]\\begin{array}{rr}&48\\\\\\times&100\\\\\\hline\\\\\\end{array}[\/latex]<\/li>\r\n \t
                                        4. [latex]\\begin{array}{rr}&982\\\\\\times&1000\\\\\\hline\\\\\\end{array}[\/latex]<\/li>\r\n \t
                                        5. [latex]\\begin{array}{rr}&678\\\\\\times&39\\\\\\hline\\\\\\end{array}[\/latex]<\/li>\r\n \t
                                        6. [latex]\\begin{array}{rr}&4579\\\\\\times&86\\\\\\hline\\\\\\end{array}[\/latex]<\/li>\r\n \t
                                        7. [latex]\\begin{array}{rr}&8703\\\\\\times&93\\\\\\hline\\\\\\end{array}[\/latex]<\/li>\r\n \t
                                        8. [latex]\\begin{array}{rr}&7390\\\\\\times&85\\\\\\hline\\\\\\end{array}[\/latex]<\/li>\r\n \t
                                        9. [latex]\\begin{array}{rr}&8047\\\\\\times&236\\\\\\hline\\\\\\end{array}[\/latex]<\/li>\r\n \t
                                        10. [latex]\\begin{array}{rr}&4238\\\\\\times&197\\\\\\hline\\\\\\end{array}[\/latex]<\/li>\r\n \t
                                        11. [latex]\\begin{array}{rr}&8200\\\\\\times&444\\\\\\hline\\\\\\end{array}[\/latex]<\/li>\r\n \t
                                        12. [latex]\\begin{array}{rr}&7265\\\\\\times&409\\\\\\hline\\\\\\end{array}[\/latex]<\/li>\r\n<\/ol>\r\n<\/li>\r\n<\/ol>\r\n

                                          Answers to Topic B Self-Test<\/h2>\r\n
                                            \r\n \t
                                          1. Multiply these numbers.\r\n
                                              \r\n \t
                                            1. 1833<\/span><\/li>\r\n \t
                                            2. 5394<\/span><\/li>\r\n \t
                                            3. 4800<\/span><\/li>\r\n \t
                                            4. 982000<\/span><\/li>\r\n \t
                                            5. 26442<\/span><\/li>\r\n \t
                                            6. 393794<\/span><\/li>\r\n \t
                                            7. 809379<\/span><\/li>\r\n \t
                                            8. 628150<\/span><\/li>\r\n \t
                                            9. 1899092<\/span><\/span><\/li>\r\n \t
                                            10. 834886<\/span><\/li>\r\n \t
                                            11. 3640800<\/span><\/span><\/li>\r\n \t
                                            12. 2 971 385<\/li>\r\n<\/ol>\r\n<\/li>\r\n<\/ol>","rendered":"

                                              When the multiplier is more than one digit, you use the same process and get partial products. You repeat the steps until you have multiplied by every digit, then add the partial products together.<\/p>\n

                                              Multiplying by Two-Digit Multipliers<\/h1>\n
                                              \n
                                              \n

                                              Example A<\/p>\n<\/header>\n

                                              \n

                                              [latex]24\\times23=[\/latex]<\/p>\n

                                              Part 1:<\/strong> Multiply by the ones digit in the multiplier.<\/p>\n

                                              Multiply 3 ones by 24 using the method you already know. The first partial product is 72.<\/p>\n

                                              [latex]\\begin{array}{rr}&_1\\hspace{0.5em}\\\\&24\\\\\\times&23\\\\\\hline&72\\end{array}[\/latex]<\/p>\n

                                              Part 2:<\/strong> Multiply by the tens digit in the multiplier. First, put a 0 to hold the ones place in your partial product. We are multiplying by a ten, so we hold the ones place.<\/p>\n

                                              Step 1:<\/strong> Multiply 2 tens 4 ones = 8 tens Write the 8 tens under the tens in your first partial product. It is very important to keep the columns straight \u2013 ones under one, tens under tens.<\/p>\n

                                              Step 2:<\/strong> Multiply 2 tens 2 tens = 4 hundreds Write the 4 hundreds in your partial product. The second partial product is 480.<\/p>\n

                                              [latex]\\begin{array}{rr}&_1\\hspace{0.5em}\\\\&24\\\\\\times&23\\\\\\hline&72\\\\&480\\end{array}[\/latex]<\/p>\n

                                              Part 3:<\/strong> Add the partial products together, being sure to add ones to ones, tens to tens, hundreds to hundreds. The sum is the final product.<\/p>\n

                                              Draw a line under the partial products. Add. Check your addition.<\/p>\n

                                              [latex]\\begin{array}{rr}&_1\\hspace{0.5em}\\\\&24\\\\\\times&23\\\\\\hline&72\\\\+&480\\\\\\hline&552\\end{array}[\/latex]<\/p>\n<\/div>\n<\/div>\n

                                              \n
                                              \n

                                              Example B<\/p>\n<\/header>\n

                                              \n

                                              [latex]36\\times425 =[\/latex]<\/p>\n

                                              Part 1:<\/strong> Multiply by the ones digit in the multiplier. 6 \u00d7 425 = 2550<\/span><\/p>\n

                                              [latex]\\begin{array}{rr}&_1\\hspace{0.15em}_3\\hspace{0.5em}\\\\&425\\\\\\times&36\\\\\\hline&2550\\end{array}[\/latex]<\/p>\n

                                              Part 2:<\/strong> Multiply by the tens digit in the multiplier. First put a 0 to hold the ones place in the second partial product.<\/p>\n

                                                \n
                                              • Step 1:<\/strong> 3 tens \u00d7 5 tens = 15 tens = 1 hundred and 5 tens
                                                \nWrite the 5 tens in the second partial product and carry the 1 hundred. Now you can see why it is best to cross out the numbers you carry as soon as you have added them to the product.<\/li>\n
                                              • Step 2:<\/strong> 3 tens \u00d7 2 tens = 6 hundreds
                                                \n6 hundreds + 1 hundred (carried) = 7 hundreds. There is nothing to carry.<\/li>\n
                                              • Step 3:<\/strong> 3 tens \u00d7 4 hundreds = 12 thousands<\/li>\n<\/ul>\n

                                                [latex]\\begin{array}{rr}&_1\\hspace{0.5em}\\\\&_1\\hspace{0.15em}_3\\hspace{0.5em}\\\\&425\\\\\\times&36\\\\\\hline&2550\\\\&12750\\end{array}[\/latex]<\/p>\n

                                                Part 3:<\/strong> Add the partial products together.<\/p>\n

                                                [latex]\\begin{array}{rr}&_1\\hspace{0.5em}\\\\&_1\\hspace{0.15em}_3\\hspace{0.5em}\\\\&425\\\\\\times&36\\\\\\hline&2550\\\\+&12750\\\\\\hline&15300\\end{array}[\/latex]<\/p>\n<\/div>\n<\/div>\n

                                                Tip: Keeping the columns straight with ones under ones, tens under tens, hundreds under hundreds is very important. Working on large-squared graphing paper using one digit per square is often helpful.<\/div>\n
                                                tens \u00d7 tens = hundreds
                                                \ntens \u00d7 hundreds = thousands<\/div>\n
                                                \n
                                                \n

                                                Exercise 1<\/p>\n<\/header>\n

                                                \n

                                                Multiply, being very careful to keep the columns straight when you write your partial products. Check your work using the answer key at the end of the exercise.<\/p>\n

                                                [latex]\\begin{array}{rr}&84\\\\\\times&12\\\\\\hline&168\\\\+&840\\\\\\hline&1008\\end{array}[\/latex]<\/p>\n

                                                  \n
                                                1. [latex]\\begin{array}{rr}&73\\\\\\times&12\\\\\\hline\\\\\\end{array}[\/latex]<\/li>\n
                                                2. [latex]\\begin{array}{rr}&50\\\\\\times&42\\\\\\hline\\\\\\end{array}[\/latex]<\/li>\n
                                                3. [latex]\\begin{array}{rr}&62\\\\\\times&31\\\\\\hline\\\\\\end{array}[\/latex]<\/li>\n
                                                4. [latex]\\begin{array}{rr}&61\\\\\\times&42\\\\\\hline\\\\\\end{array}[\/latex]<\/li>\n
                                                5. [latex]\\begin{array}{rr}&91\\\\\\times&53\\\\\\hline\\\\\\end{array}[\/latex]<\/li>\n
                                                6. [latex]\\begin{array}{rr}&92\\\\\\times&31\\\\\\hline\\\\\\end{array}[\/latex]<\/li>\n
                                                7. [latex]\\begin{array}{rr}&91\\\\\\times&49\\\\\\hline\\\\\\end{array}[\/latex]<\/li>\n
                                                8. [latex]\\begin{array}{rr}&72\\\\\\times&48\\\\\\hline\\\\\\end{array}[\/latex]<\/li>\n
                                                9. [latex]\\begin{array}{rr}&53\\\\\\times&30\\\\\\hline\\\\\\end{array}[\/latex]<\/li>\n
                                                10. [latex]\\begin{array}{rr}&41\\\\\\times&53\\\\\\hline\\\\\\end{array}[\/latex]<\/li>\n
                                                11. [latex]\\begin{array}{rr}&42\\\\\\times&94\\\\\\hline\\\\\\end{array}[\/latex]<\/li>\n
                                                12. [latex]\\begin{array}{rr}&80\\\\\\times&86\\\\\\hline\\\\\\end{array}[\/latex]<\/li>\n
                                                13. [latex]\\begin{array}{rr}&31\\\\\\times&79\\\\\\hline\\\\\\end{array}[\/latex]<\/li>\n
                                                14. [latex]\\begin{array}{rr}&54\\\\\\times&40\\\\\\hline\\\\\\end{array}[\/latex]<\/li>\n
                                                15. [latex]\\begin{array}{rr}&61\\\\\\times&48\\\\\\hline\\\\\\end{array}[\/latex]<\/li>\n
                                                16. [latex]\\begin{array}{rr}&60\\\\\\times&31\\\\\\hline\\\\\\end{array}[\/latex]<\/li>\n
                                                17. [latex]\\begin{array}{rr}&55\\\\\\times&73\\\\\\hline\\\\\\end{array}[\/latex]<\/li>\n
                                                18. [latex]\\begin{array}{rr}&84\\\\\\times&56\\\\\\hline\\\\\\end{array}[\/latex]<\/li>\n
                                                19. [latex]\\begin{array}{rr}&53\\\\\\times&38\\\\\\hline\\\\\\end{array}[\/latex]<\/li>\n<\/ol>\n

                                                  Answers to Exercise 1<\/strong><\/p>\n

                                                    \n
                                                  1. 876<\/li>\n
                                                  2. 2100<\/span><\/li>\n
                                                  3. 1922<\/span><\/li>\n
                                                  4. 2562<\/span><\/li>\n
                                                  5. 4823<\/span><\/li>\n
                                                  6. 2852<\/span><\/li>\n
                                                  7. 4459<\/span><\/li>\n
                                                  8. 3456<\/span><\/li>\n
                                                  9. 1590<\/span><\/li>\n
                                                  10. 2173<\/span><\/li>\n
                                                  11. 3948<\/span><\/li>\n
                                                  12. 6880<\/span><\/li>\n
                                                  13. 2449<\/span><\/li>\n
                                                  14. 2160<\/span><\/li>\n
                                                  15. 2928<\/span><\/li>\n
                                                  16. 1860<\/span><\/li>\n
                                                  17. 4015<\/span><\/li>\n
                                                  18. 4704<\/span><\/li>\n
                                                  19. 2014<\/span><\/li>\n<\/ol>\n<\/div>\n<\/div>\n

                                                    When the multiplier has a zero in the ones place, use this shortcut.<\/p>\n

                                                    \n
                                                    \n

                                                    Example C<\/p>\n<\/header>\n

                                                    \n

                                                    [latex]\\begin{array}{rr}&48\\\\\\times&80\\\\\\hline&3840\\end{array}[\/latex]<\/p>\n

                                                      \n
                                                    • Step 1:<\/strong> 0 ones \u00d7 48 = 0. Place one zero in the product and that will hold the ones place.<\/li>\n
                                                    • Step 2:<\/strong> Multiply by the tens digit and write the product beside the zero.<\/li>\n<\/ul>\n<\/div>\n<\/div>\n
                                                      \n
                                                      \n

                                                      Example D<\/p>\n<\/header>\n

                                                      \n

                                                      [latex]\\begin{array}{rr}&97\\\\\\times&20\\\\\\hline&1940\\end{array}[\/latex]<\/p>\n<\/div>\n<\/div>\n

                                                      \n
                                                      \n

                                                      Exercise 2<\/p>\n<\/header>\n

                                                      \n

                                                      Find the products. Use the shortcut for multipliers with a zero in them. Check your work using the answer key at the end of the exercise.<\/p>\n

                                                      [latex]\\begin{array}{rr}&76\\\\\\times&70\\\\\\hline&5320\\end{array}[\/latex]<\/p>\n

                                                        \n
                                                      1. [latex]\\begin{array}{rr}&52\\\\\\times&70\\\\\\hline\\\\\\end{array}[\/latex]<\/li>\n
                                                      2. [latex]\\begin{array}{rr}&91\\\\\\times&70\\\\\\hline\\\\\\end{array}[\/latex]<\/li>\n
                                                      3. [latex]\\begin{array}{rr}&83\\\\\\times&70\\\\\\hline\\\\\\end{array}[\/latex]<\/li>\n
                                                      4. [latex]\\begin{array}{rr}&49\\\\\\times&70\\\\\\hline\\\\\\end{array}[\/latex]<\/li>\n
                                                      5. [latex]\\begin{array}{rr}&61\\\\\\times&70\\\\\\hline\\\\\\end{array}[\/latex]<\/li>\n
                                                      6. [latex]\\begin{array}{rr}&16\\\\\\times&70\\\\\\hline\\\\\\end{array}[\/latex]<\/li>\n
                                                      7. [latex]\\begin{array}{rr}&36\\\\\\times&70\\\\\\hline\\\\\\end{array}[\/latex]<\/li>\n
                                                      8. [latex]\\begin{array}{rr}&398\\\\\\times&70\\\\\\hline\\\\\\end{array}[\/latex]<\/li>\n
                                                      9. [latex]\\begin{array}{rr}&432\\\\\\times&70\\\\\\hline\\\\\\end{array}[\/latex]<\/li>\n
                                                      10. [latex]\\begin{array}{rr}&863\\\\\\times&70\\\\\\hline\\\\\\end{array}[\/latex]<\/li>\n
                                                      11. [latex]\\begin{array}{rr}&907\\\\\\times&70\\\\\\hline\\\\\\end{array}[\/latex]<\/li>\n
                                                      12. [latex]\\begin{array}{rr}&503\\\\\\times&70\\\\\\hline\\\\\\end{array}[\/latex]<\/li>\n
                                                      13. [latex]\\begin{array}{rr}&452\\\\\\times&70\\\\\\hline\\\\\\end{array}[\/latex]<\/li>\n
                                                      14. [latex]\\begin{array}{rr}&943\\\\\\times&70\\\\\\hline\\\\\\end{array}[\/latex]<\/li>\n
                                                      15. [latex]\\begin{array}{rr}&248\\\\\\times&70\\\\\\hline\\\\\\end{array}[\/latex]<\/li>\n
                                                      16. [latex]\\begin{array}{rr}&6287\\\\\\times&70\\\\\\hline\\\\\\end{array}[\/latex]<\/li>\n
                                                      17. [latex]\\begin{array}{rr}&9025\\\\\\times&70\\\\\\hline\\\\\\end{array}[\/latex]<\/li>\n
                                                      18. [latex]\\begin{array}{rr}&8907\\\\\\times&70\\\\\\hline\\\\\\end{array}[\/latex]<\/li>\n
                                                      19. [latex]\\begin{array}{rr}&300\\\\\\times&70\\\\\\hline\\\\\\end{array}[\/latex]<\/li>\n
                                                      20. [latex]\\begin{array}{rr}&9075\\\\\\times&70\\\\\\hline\\\\\\end{array}[\/latex]<\/li>\n
                                                      21. [latex]\\begin{array}{rr}&3952\\\\\\times&70\\\\\\hline\\\\\\end{array}[\/latex]<\/li>\n
                                                      22. [latex]\\begin{array}{rr}&1528\\\\\\times&70\\\\\\hline\\\\\\end{array}[\/latex]<\/li>\n
                                                      23. [latex]\\begin{array}{rr}&7106\\\\\\times&70\\\\\\hline\\\\\\end{array}[\/latex]<\/li>\n<\/ol>\n

                                                        Answers to Exercise 2<\/strong><\/p>\n

                                                          \n
                                                        1. 3640<\/span><\/li>\n
                                                        2. 6370<\/span><\/li>\n
                                                        3. 5810<\/span><\/li>\n
                                                        4. 3430<\/span><\/li>\n
                                                        5. 4270<\/span><\/li>\n
                                                        6. 1120<\/span><\/li>\n
                                                        7. 2520<\/span><\/li>\n
                                                        8. 27860<\/span><\/li>\n
                                                        9. 30240<\/span><\/li>\n
                                                        10. 60410<\/span><\/li>\n
                                                        11. 63490<\/span><\/li>\n
                                                        12. 35210<\/span><\/li>\n
                                                        13. 31640<\/span><\/li>\n
                                                        14. 66010<\/span><\/li>\n
                                                        15. 17360<\/span><\/li>\n
                                                        16. 440090<\/span><\/li>\n
                                                        17. 631750<\/span><\/li>\n
                                                        18. 623490<\/span><\/li>\n
                                                        19. 21000<\/span><\/li>\n
                                                        20. 635250<\/span><\/li>\n
                                                        21. 276640<\/span><\/li>\n
                                                        22. 106960<\/span><\/li>\n
                                                        23. 497420<\/span><\/li>\n<\/ol>\n<\/div>\n<\/div>\n
                                                          How are you doing? Ask your instructor for help if you are not comfortable with multiplying.<\/div>\n

                                                          Multiplying by Three-Digit Multipliers<\/h1>\n

                                                          To multiply by three digit multipliers, use the same method with one more part.<\/p>\n

                                                          \n
                                                          \n

                                                          Example E<\/p>\n<\/header>\n

                                                          \n

                                                          [latex]417\\times368 =[\/latex]<\/p>\n

                                                          [latex]\\begin{array}{rr}&417\\\\\\times&368\\\\\\hline&3336\\\\&25020\\\\+&125100\\\\\\hline&153456\\end{array}[\/latex]<\/p>\n

                                                            \n
                                                          • Part 1:<\/strong> Multiply by the 8 ones.<\/li>\n
                                                          • Part 2:<\/strong> Multiply the 6 tens; hold the ones place with 0.<\/li>\n
                                                          • Part 3:<\/strong> Multiply by the 3 hundreds. Put 00 to hold the ones and tens places in the third partial product.\n
                                                              \n
                                                            • Step 1:<\/strong> 3 hundreds \u00d7 7 ones = 21 hundreds = 2 thousands and 1 hundred. Write the 1 hundred and carry the 2 thousands.<\/li>\n
                                                            • Step 2:<\/strong> 3 hundreds \u00d7 1 ten = 3 thousands. 3 thousands + 2 thousands (carried) = 5 thousands.<\/li>\n
                                                            • Step 3:<\/strong> 3 hundreds \u00d7 4 hundreds = 12 ten thousands.<\/li>\n<\/ul>\n<\/li>\n
                                                            • Part 4: <\/strong>Add the partial products.<\/li>\n<\/ul>\n<\/div>\n<\/div>\n
                                                              \n
                                                              \n

                                                              Exercise 3<\/p>\n<\/header>\n

                                                              \n

                                                              Find the products. Check your work using the answer key at the end of the exercise.<\/p>\n

                                                                \n
                                                              1. [latex]\\begin{array}{rr}&416\\\\\\times&213\\\\\\hline\\\\\\end{array}[\/latex]<\/li>\n
                                                              2. [latex]\\begin{array}{rr}&375\\\\\\times&291\\\\\\hline\\\\\\end{array}[\/latex]<\/li>\n
                                                              3. [latex]\\begin{array}{rr}&361\\\\\\times&475\\\\\\hline\\\\\\end{array}[\/latex]<\/li>\n
                                                              4. [latex]\\begin{array}{rr}&275\\\\\\times&863\\\\\\hline\\\\\\end{array}[\/latex]<\/li>\n
                                                              5. [latex]\\begin{array}{rr}&984\\\\\\times&469\\\\\\hline\\\\\\end{array}[\/latex]<\/li>\n
                                                              6. [latex]\\begin{array}{rr}&489\\\\\\times&578\\\\\\hline\\\\\\end{array}[\/latex]<\/li>\n
                                                              7. [latex]\\begin{array}{rr}&498\\\\\\times&123\\\\\\hline\\\\\\end{array}[\/latex]<\/li>\n
                                                              8. [latex]\\begin{array}{rr}&267\\\\\\times&854\\\\\\hline\\\\\\end{array}[\/latex]<\/li>\n
                                                              9. [latex]\\begin{array}{rr}&613\\\\\\times&368\\\\\\hline\\\\\\end{array}[\/latex]<\/li>\n
                                                              10. [latex]\\begin{array}{rr}&725\\\\\\times&547\\\\\\hline\\\\\\end{array}[\/latex]<\/li>\n
                                                              11. [latex]\\begin{array}{rr}&269\\\\\\times&912\\\\\\hline\\\\\\end{array}[\/latex]<\/li>\n
                                                              12. [latex]\\begin{array}{rr}&752\\\\\\times&697\\\\\\hline\\\\\\end{array}[\/latex]<\/li>\n
                                                              13. [latex]\\begin{array}{rr}&983\\\\\\times&357\\\\\\hline\\\\\\end{array}[\/latex]<\/li>\n
                                                              14. [latex]\\begin{array}{rr}&835\\\\\\times&148\\\\\\hline\\\\\\end{array}[\/latex]<\/li>\n
                                                              15. [latex]\\begin{array}{rr}&386\\\\\\times&296\\\\\\hline\\\\\\end{array}[\/latex]<\/li>\n<\/ol>\n

                                                                Answers to Exercise 3<\/strong><\/p>\n

                                                                  \n
                                                                1. 88608<\/span><\/li>\n
                                                                2. 109125<\/span><\/li>\n
                                                                3. 171475<\/span><\/li>\n
                                                                4. 237325<\/span><\/li>\n
                                                                5. 461496<\/span><\/li>\n
                                                                6. 282642<\/span><\/li>\n
                                                                7. 61254<\/span><\/li>\n
                                                                8. 228018<\/span><\/li>\n
                                                                9. 225584<\/span><\/li>\n
                                                                10. 396575<\/span><\/li>\n
                                                                11. 245328<\/span><\/li>\n
                                                                12. 524144<\/span><\/li>\n
                                                                13. 350931<\/span><\/li>\n
                                                                14. 123580<\/span><\/li>\n
                                                                15. 114256<\/span><\/li>\n<\/ol>\n<\/div>\n<\/div>\n

                                                                  You know to hold the ones place with a zero if the multiplier has a zero in the ones place. Use the same skill if the multiplier has a zero in the tens place.<\/p>\n

                                                                  \n
                                                                  \n

                                                                  Example F<\/p>\n<\/header>\n

                                                                  \n

                                                                  [latex]927\\times405 =[\/latex]<\/p>\n

                                                                  [latex]\\begin{array}{rr}&927\\\\\\times&405\\\\\\hline&4635\\\\+&370800\\\\\\hline&375435\\end{array}[\/latex]<\/p>\n

                                                                    \n
                                                                  • Part 1:<\/strong> Multiply by the 5 ones.<\/li>\n
                                                                  • Part 2:<\/strong> Multiply by the 0 tens.
                                                                    \nHold the ones place with a 0; 0 \u00d7 927 = 0; Place one zero in the tens place in the second partial product.<\/li>\n
                                                                  • Part 3:<\/strong> Multiply by the 4 hundreds. The ones and tens places are already held by zeros. Start this partial product in the hundreds place on the same line.<\/li>\n
                                                                  • Part 4:<\/strong> Add the partial products.<\/li>\n<\/ul>\n<\/div>\n<\/div>\n
                                                                    \n
                                                                    \n

                                                                    Exercise 4<\/p>\n<\/header>\n

                                                                    \n

                                                                    Find the products. Check your work using the answer key at the end of the exercise.<\/p>\n

                                                                    [latex]\\begin{array}{rr}&_2\\hspace{0.15em}_2\\hspace{0.5em}\\\\&698\\\\\\times&301\\\\\\hline&698\\\\+&209400\\\\\\hline&210098\\end{array}[\/latex]<\/p>\n

                                                                      \n
                                                                    1. [latex]\\begin{array}{rr}&923\\\\\\times&403\\\\\\hline\\\\\\end{array}[\/latex]<\/li>\n
                                                                    2. [latex]\\begin{array}{rr}&830\\\\\\times&108\\\\\\hline\\\\\\end{array}[\/latex]<\/li>\n
                                                                    3. [latex]\\begin{array}{rr}&482\\\\\\times&206\\\\\\hline\\\\\\end{array}[\/latex]<\/li>\n
                                                                    4. [latex]\\begin{array}{rr}&432\\\\\\times&205\\\\\\hline\\\\\\end{array}[\/latex]<\/li>\n
                                                                    5. [latex]\\begin{array}{rr}&625\\\\\\times&405\\\\\\hline\\\\\\end{array}[\/latex]<\/li>\n
                                                                    6. [latex]\\begin{array}{rr}&275\\\\\\times&306\\\\\\hline\\\\\\end{array}[\/latex]<\/li>\n
                                                                    7. [latex]\\begin{array}{rr}&765\\\\\\times&506\\\\\\hline\\\\\\end{array}[\/latex]<\/li>\n
                                                                    8. [latex]\\begin{array}{rr}&1576\\\\\\times&702\\\\\\hline\\\\\\end{array}[\/latex]<\/li>\n
                                                                    9. [latex]\\begin{array}{rr}&432\\\\\\times&405\\\\\\hline\\\\\\end{array}[\/latex]<\/li>\n
                                                                    10. [latex]\\begin{array}{rr}&625\\\\\\times&409\\\\\\hline\\\\\\end{array}[\/latex]<\/li>\n
                                                                    11. [latex]\\begin{array}{rr}&175\\\\\\times&306\\\\\\hline\\\\\\end{array}[\/latex]<\/li>\n
                                                                    12. [latex]\\begin{array}{rr}&5874\\\\\\times&309\\\\\\hline\\\\\\end{array}[\/latex]<\/li>\n
                                                                    13. [latex]\\begin{array}{rr}&7384\\\\\\times&104\\\\\\hline\\\\\\end{array}[\/latex]<\/li>\n
                                                                    14. [latex]\\begin{array}{rr}&6538\\\\\\times&603\\\\\\hline\\\\\\end{array}[\/latex]<\/li>\n<\/ol>\n

                                                                      Answers to Exercise 4<\/strong><\/p>\n

                                                                        \n
                                                                      1. 371969<\/span><\/li>\n
                                                                      2. 89640<\/span><\/li>\n
                                                                      3. 99292<\/span><\/li>\n
                                                                      4. 88560<\/span><\/li>\n
                                                                      5. 253 125<\/li>\n
                                                                      6. 84150<\/span><\/li>\n
                                                                      7. 387090<\/span><\/li>\n
                                                                      8. 1106<\/span>352<\/span><\/li>\n
                                                                      9. 174960<\/span><\/li>\n
                                                                      10. 255625<\/span><\/li>\n
                                                                      11. 53550<\/span><\/li>\n
                                                                      12. 1815<\/span>066<\/span><\/li>\n
                                                                      13. 767936<\/span><\/li>\n
                                                                      14. 3942<\/span>414<\/span><\/li>\n<\/ol>\n<\/div>\n<\/div>\n

                                                                        Multiplying by 10, 100, and 1000<\/span><\/h1>\n
                                                                        \n
                                                                        \n

                                                                        Exercise 5<\/p>\n<\/header>\n

                                                                        \n

                                                                        Do the following questions and see if you can find the pattern. Check your work using the answer key at the end of the exercise.<\/p>\n

                                                                          \n
                                                                        1. [latex]\\begin{array}{rr}&83\\\\\\times&10\\\\\\hline&830\\end{array}[\/latex]<\/li>\n
                                                                        2. [latex]\\begin{array}{rr}&46\\\\\\times&10\\\\\\hline\\\\\\end{array}[\/latex]<\/li>\n
                                                                        3. [latex]\\begin{array}{rr}&97\\\\\\times&10\\\\\\hline\\\\\\end{array}[\/latex]<\/li>\n
                                                                        4. [latex]\\begin{array}{rr}&123\\\\\\times&10\\\\\\hline\\\\\\end{array}[\/latex]<\/li>\n
                                                                        5. [latex]\\begin{array}{rr}&70\\\\\\times&10\\\\\\hline\\\\\\end{array}[\/latex]<\/li>\n
                                                                        6. [latex]\\begin{array}{rr}&129\\\\\\times&10\\\\\\hline\\\\\\end{array}[\/latex]<\/li>\n
                                                                        7. [latex]\\begin{array}{rr}&1852\\\\\\times&10\\\\\\hline\\\\\\end{array}[\/latex]<\/li>\n
                                                                        8. [latex]\\begin{array}{rr}&29871\\\\\\times&10\\\\\\hline\\\\\\end{array}[\/latex]<\/li>\n
                                                                        9. [latex]\\begin{array}{rr}&45\\\\\\times&100\\\\\\hline\\\\\\end{array}[\/latex]<\/li>\n
                                                                        10. [latex]\\begin{array}{rr}&26\\\\\\times&100\\\\\\hline\\\\\\end{array}[\/latex]<\/li>\n
                                                                        11. [latex]\\begin{array}{rr}&432\\\\\\times&100\\\\\\hline\\\\\\end{array}[\/latex]<\/li>\n
                                                                        12. [latex]\\begin{array}{rr}&679\\\\\\times&100\\\\\\hline\\\\\\end{array}[\/latex]<\/li>\n
                                                                        13. [latex]\\begin{array}{rr}&2482\\\\\\times&100\\\\\\hline\\\\\\end{array}[\/latex]<\/li>\n
                                                                        14. [latex]\\begin{array}{rr}&9037\\\\\\times&100\\\\\\hline\\\\\\end{array}[\/latex]<\/li>\n
                                                                        15. [latex]\\begin{array}{rr}&46207\\\\\\times&100\\\\\\hline\\\\\\end{array}[\/latex]<\/li>\n
                                                                        16. [latex]\\begin{array}{rr}&97512\\\\\\times&100\\\\\\hline\\\\\\end{array}[\/latex]<\/li>\n
                                                                        17. [latex]\\begin{array}{rr}&23\\\\\\times&1000\\\\\\hline\\\\\\end{array}[\/latex]<\/li>\n
                                                                        18. [latex]\\begin{array}{rr}&452\\\\\\times&1000\\\\\\hline\\\\\\end{array}[\/latex]<\/li>\n
                                                                        19. [latex]\\begin{array}{rr}&207\\\\\\times&1000\\\\\\hline\\\\\\end{array}[\/latex]<\/li>\n
                                                                        20. [latex]\\begin{array}{rr}&348\\\\\\times&1000\\\\\\hline\\\\\\end{array}[\/latex]<\/li>\n
                                                                        21. [latex]\\begin{array}{rr}&2118\\\\\\times&1000\\\\\\hline\\\\\\end{array}[\/latex]<\/li>\n
                                                                        22. [latex]\\begin{array}{rr}&2431\\\\\\times&1000\\\\\\hline\\\\\\end{array}[\/latex]<\/li>\n
                                                                        23. [latex]\\begin{array}{rr}&23681\\\\\\times&1000\\\\\\hline\\\\\\end{array}[\/latex]<\/li>\n
                                                                        24. [latex]\\begin{array}{rr}&48203\\\\\\times&1000\\\\\\hline\\\\\\end{array}[\/latex]<\/li>\n<\/ol>\n

                                                                          Answers to Exercise 5<\/strong><\/p>\n

                                                                            \n
                                                                          1. 830<\/li>\n
                                                                          2. 460<\/li>\n
                                                                          3. 970<\/li>\n
                                                                          4. 1230<\/span><\/li>\n
                                                                          5. 700<\/li>\n
                                                                          6. 1290<\/span><\/li>\n
                                                                          7. 18520<\/span><\/li>\n
                                                                          8. 298710<\/span><\/li>\n
                                                                          9. 4500<\/span><\/li>\n
                                                                          10. 2600<\/span><\/li>\n
                                                                          11. 43200<\/span><\/li>\n
                                                                          12. 67900<\/span><\/li>\n
                                                                          13. 248200<\/span><\/li>\n
                                                                          14. 903700<\/span><\/li>\n
                                                                          15. 4620700<\/span><\/span><\/li>\n
                                                                          16. 9751200<\/span><\/span><\/li>\n
                                                                          17. 23000<\/span><\/li>\n
                                                                          18. 452000<\/span><\/li>\n
                                                                          19. 207000<\/span><\/li>\n
                                                                          20. 348000<\/span><\/li>\n
                                                                          21. 2118000<\/span><\/span><\/li>\n
                                                                          22. 2431000<\/span><\/span><\/li>\n
                                                                          23. 23681000<\/span><\/span><\/li>\n
                                                                          24. 48203000<\/span><\/span><\/li>\n<\/ol>\n<\/div>\n<\/div>\n

                                                                            And the pattern is \u2026<\/p>\n

                                                                            When multiplying by 10, 100, 1000, 10000, etc., place as many zeros to the right of the number as there are zeros in the 10, 100, 1000, etc.<\/span><\/span><\/span><\/p>\n

                                                                              \n
                                                                            • To multiply by 10 put one zero after the number.<\/li>\n
                                                                            • To multiply by 100 put two zeros after the number.<\/li>\n
                                                                            • To multiply by 1000 put three zeros after the number.<\/span><\/li>\n<\/ul>\n
                                                                              \n
                                                                              \n

                                                                              Exercise 6<\/p>\n<\/header>\n

                                                                              \n

                                                                              Find the products using the short method.\u00a0 Do not rewrite the questions. Check your work using the answer key at the end of the exercise.<\/p>\n

                                                                                \n
                                                                              1. 12 \u00d7 10 = 120<\/li>\n
                                                                              2. 10 \u00d7 3175<\/span> =<\/li>\n
                                                                              3. 162 \u00d7 10 =<\/li>\n
                                                                              4. 10 \u00d7 53821<\/span> =<\/li>\n
                                                                              5. 10 \u00d7 123 =<\/li>\n
                                                                              6. 27342<\/span> \u00d7 10 =<\/li>\n
                                                                              7. 10 \u00d7 98 =<\/li>\n
                                                                              8. 1134<\/span> \u00d7 10 =<\/li>\n
                                                                              9. 15 \u00d7 100 =<\/li>\n
                                                                              10. 100 \u00d7 278 =<\/li>\n
                                                                              11. 9134<\/span> \u00d7 100 =<\/li>\n
                                                                              12. 651 \u00d7 100 =<\/li>\n
                                                                              13. 100 \u00d7 5169<\/span> =<\/li>\n
                                                                              14. 100 \u00d7 24815<\/span> =<\/li>\n
                                                                              15. 10 \u00d7 905 =<\/li>\n
                                                                              16. 45683<\/span> \u00d7 10 =<\/li>\n
                                                                              17. 1000<\/span> \u00d7 87 =<\/li>\n
                                                                              18. 521 \u00d7 1000<\/span> =<\/li>\n
                                                                              19. 1000<\/span> \u00d7 68935<\/span> =<\/li>\n
                                                                              20. 1000<\/span> \u00d7 8902<\/span> =<\/li>\n
                                                                              21. 1576<\/span> \u00d7 1000<\/span> =<\/li>\n
                                                                              22. 31584<\/span> \u00d7 1000<\/span> =<\/li>\n
                                                                              23. 1000<\/span> \u00d7 426 =<\/li>\n
                                                                              24. 72 \u00d7 1000<\/span> =<\/li>\n<\/ol>\n

                                                                                Answers for Exercise 6<\/strong><\/p>\n

                                                                                  \n
                                                                                1. 120<\/li>\n
                                                                                2. 31750<\/span><\/li>\n
                                                                                3. 1620<\/span><\/li>\n
                                                                                4. 538210<\/span><\/li>\n
                                                                                5. 1230<\/span><\/li>\n
                                                                                6. 273420<\/span><\/li>\n
                                                                                7. 980<\/li>\n
                                                                                8. 11340<\/span><\/li>\n
                                                                                9. 1500<\/span><\/li>\n
                                                                                10. 27800<\/span><\/li>\n
                                                                                11. 913400<\/span><\/li>\n
                                                                                12. 65100<\/span><\/li>\n
                                                                                13. 516900<\/span><\/li>\n
                                                                                14. 2481500<\/span><\/span><\/li>\n
                                                                                15. 9050<\/span><\/li>\n
                                                                                16. 456830<\/span><\/li>\n
                                                                                17. 87000<\/span><\/li>\n
                                                                                18. 521000<\/span><\/li>\n
                                                                                19. 68935000<\/span><\/span><\/li>\n
                                                                                20. 8902000<\/span><\/span><\/li>\n
                                                                                21. 1576000<\/span><\/span><\/li>\n
                                                                                22. 31584000<\/span><\/span><\/li>\n
                                                                                23. 426000<\/span><\/li>\n
                                                                                24. 72000<\/span><\/li>\n<\/ol>\n<\/div>\n<\/div>\n

                                                                                  Topic B: Self-Test<\/h1>\n

                                                                                  Mark\u00a0 \/12 \u00a0\u00a0 Aim\u00a0 10\/12<\/strong><\/p>\n

                                                                                    \n
                                                                                  1. Multiply these numbers.\n
                                                                                      \n
                                                                                    1. [latex]\\begin{array}{rr}&47\\\\\\times&39\\\\\\hline\\\\\\end{array}[\/latex]<\/li>\n
                                                                                    2. [latex]\\begin{array}{rr}&58\\\\\\times&93\\\\\\hline\\\\\\end{array}[\/latex]<\/li>\n
                                                                                    3. [latex]\\begin{array}{rr}&48\\\\\\times&100\\\\\\hline\\\\\\end{array}[\/latex]<\/li>\n
                                                                                    4. [latex]\\begin{array}{rr}&982\\\\\\times&1000\\\\\\hline\\\\\\end{array}[\/latex]<\/li>\n
                                                                                    5. [latex]\\begin{array}{rr}&678\\\\\\times&39\\\\\\hline\\\\\\end{array}[\/latex]<\/li>\n
                                                                                    6. [latex]\\begin{array}{rr}&4579\\\\\\times&86\\\\\\hline\\\\\\end{array}[\/latex]<\/li>\n
                                                                                    7. [latex]\\begin{array}{rr}&8703\\\\\\times&93\\\\\\hline\\\\\\end{array}[\/latex]<\/li>\n
                                                                                    8. [latex]\\begin{array}{rr}&7390\\\\\\times&85\\\\\\hline\\\\\\end{array}[\/latex]<\/li>\n
                                                                                    9. [latex]\\begin{array}{rr}&8047\\\\\\times&236\\\\\\hline\\\\\\end{array}[\/latex]<\/li>\n
                                                                                    10. [latex]\\begin{array}{rr}&4238\\\\\\times&197\\\\\\hline\\\\\\end{array}[\/latex]<\/li>\n
                                                                                    11. [latex]\\begin{array}{rr}&8200\\\\\\times&444\\\\\\hline\\\\\\end{array}[\/latex]<\/li>\n
                                                                                    12. [latex]\\begin{array}{rr}&7265\\\\\\times&409\\\\\\hline\\\\\\end{array}[\/latex]<\/li>\n<\/ol>\n<\/li>\n<\/ol>\n

                                                                                      Answers to Topic B Self-Test<\/h2>\n
                                                                                        \n
                                                                                      1. Multiply these numbers.\n
                                                                                          \n
                                                                                        1. 1833<\/span><\/li>\n
                                                                                        2. 5394<\/span><\/li>\n
                                                                                        3. 4800<\/span><\/li>\n
                                                                                        4. 982000<\/span><\/li>\n
                                                                                        5. 26442<\/span><\/li>\n
                                                                                        6. 393794<\/span><\/li>\n
                                                                                        7. 809379<\/span><\/li>\n
                                                                                        8. 628150<\/span><\/li>\n
                                                                                        9. 1899092<\/span><\/span><\/li>\n
                                                                                        10. 834886<\/span><\/li>\n
                                                                                        11. 3640800<\/span><\/span><\/li>\n
                                                                                        12. 2 971 385<\/li>\n<\/ol>\n<\/li>\n<\/ol>\n","protected":false},"author":999,"menu_order":7,"template":"","meta":{"pb_show_title":"on","pb_short_title":"","pb_subtitle":"","pb_authors":[],"pb_section_license":""},"chapter-type":[],"contributor":[],"license":[],"class_list":["post-27","chapter","type-chapter","status-publish","hentry"],"part":24,"_links":{"self":[{"href":"https:\/\/pressbooks.bccampus.ca\/math023\/wp-json\/pressbooks\/v2\/chapters\/27","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/pressbooks.bccampus.ca\/math023\/wp-json\/pressbooks\/v2\/chapters"}],"about":[{"href":"https:\/\/pressbooks.bccampus.ca\/math023\/wp-json\/wp\/v2\/types\/chapter"}],"author":[{"embeddable":true,"href":"https:\/\/pressbooks.bccampus.ca\/math023\/wp-json\/wp\/v2\/users\/999"}],"version-history":[{"count":3,"href":"https:\/\/pressbooks.bccampus.ca\/math023\/wp-json\/pressbooks\/v2\/chapters\/27\/revisions"}],"predecessor-version":[{"id":197,"href":"https:\/\/pressbooks.bccampus.ca\/math023\/wp-json\/pressbooks\/v2\/chapters\/27\/revisions\/197"}],"part":[{"href":"https:\/\/pressbooks.bccampus.ca\/math023\/wp-json\/pressbooks\/v2\/parts\/24"}],"metadata":[{"href":"https:\/\/pressbooks.bccampus.ca\/math023\/wp-json\/pressbooks\/v2\/chapters\/27\/metadata\/"}],"wp:attachment":[{"href":"https:\/\/pressbooks.bccampus.ca\/math023\/wp-json\/wp\/v2\/media?parent=27"}],"wp:term":[{"taxonomy":"chapter-type","embeddable":true,"href":"https:\/\/pressbooks.bccampus.ca\/math023\/wp-json\/pressbooks\/v2\/chapter-type?post=27"},{"taxonomy":"contributor","embeddable":true,"href":"https:\/\/pressbooks.bccampus.ca\/math023\/wp-json\/wp\/v2\/contributor?post=27"},{"taxonomy":"license","embeddable":true,"href":"https:\/\/pressbooks.bccampus.ca\/math023\/wp-json\/wp\/v2\/license?post=27"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}