Topic A: Multiplying Larger Numbers

It is usually easier to multiply larger numbers if they are written underneath each other. The bottom number is called the multiplier.

To find the product of a one digit multiplier, use as many of these steps as you need to complete each multiplication question:

  • Step 1: Multiply the ones digit in the large number by the one-digit multiplier.
  • Step 2: Multiply the tens digit in the large number by the multiplier.
  • Step 3: Multiply the hundreds digit in the large number by the multiplier.
  • Step 4: Multiply the thousands digit in the large number by the multiplier.

Example A

62 × 4 =

Step 1: 4 × 2 ones = 8

[latex]\begin{array}{rr}&62\\\times&4\\\hline&8\end{array}[/latex]

Step 2: 4 × 6 tens = 24 tens = 2 hundreds and 4 tens

[latex]\begin{array}{rr}&62\\\times&4\\\hline&248\end{array}[/latex]

The product of 62 × 4 is 248.

Exercise 1

Find the product. Check your work using the answer key at the end of the exercise.

  1. [latex]\begin{array}{rr}&72\\\times&2\\\hline\\\end{array}[/latex]
  2. [latex]\begin{array}{rr}&81\\\times&5\\\hline\\\end{array}[/latex]
  3. [latex]\begin{array}{rr}&21\\\times&8\\\hline\\\end{array}[/latex]
  4. [latex]\begin{array}{rr}&80\\\times&6\\\hline\\\end{array}[/latex]
  5. [latex]\begin{array}{rr}&73\\\times&3\\\hline\\\end{array}[/latex]
  6. [latex]\begin{array}{rr}&71\\\times&3\\\hline\\\end{array}[/latex]
  7. [latex]\begin{array}{rr}&40\\\times&7\\\hline\\\end{array}[/latex]
  8. [latex]\begin{array}{rr}&90\\\times&9\\\hline\\\end{array}[/latex]
  9. [latex]\begin{array}{rr}&82\\\times&4\\\hline\\\end{array}[/latex]
  10. [latex]\begin{array}{rr}&40\\\times&5\\\hline\\\end{array}[/latex]
  11. [latex]\begin{array}{rr}&92\\\times&4\\\hline\\\end{array}[/latex]
  12. [latex]\begin{array}{rr}&83\\\times&3\\\hline\\\end{array}[/latex]
  13. [latex]\begin{array}{rr}&90\\\times&8\\\hline\\\end{array}[/latex]
  14. [latex]\begin{array}{rr}&71\\\times&9\\\hline\\\end{array}[/latex]
  15. [latex]\begin{array}{rr}&53\\\times&2\\\hline\\\end{array}[/latex]
  16. [latex]\begin{array}{rr}&30\\\times&6\\\hline\\\end{array}[/latex]
  17. [latex]\begin{array}{rr}&81\\\times&7\\\hline\\\end{array}[/latex]
  18. [latex]\begin{array}{rr}&61\\\times&2\\\hline\\\end{array}[/latex]
  19. [latex]\begin{array}{rr}&70\\\times&8\\\hline\\\end{array}[/latex]
  20. [latex]\begin{array}{rr}&41\\\times&6\\\hline\\\end{array}[/latex]
  21. [latex]\begin{array}{rr}&90\\\times&5\\\hline\\\end{array}[/latex]
  22. [latex]\begin{array}{rr}&60\\\times&9\\\hline\\\end{array}[/latex]
  23. [latex]\begin{array}{rr}&92\\\times&3\\\hline\\\end{array}[/latex]
  24. [latex]\begin{array}{rr}&81\\\times&4\\\hline\\\end{array}[/latex]
Answers to Exercise 1
  1. 144
  2. 405
  3. 168
  4. 480
  5. 219
  6. 213
  7. 280
  8. 810
  9. 328
  10. 200
  11. 368
  12. 249
  13. 720
  14. 639
  15. 106
  16. 180
  17. 567
  18. 122
  19. 560
  20. 246
  21. 450
  22. 540
  23. 276
  24. 324

Example B

523 × 3 =

[latex]\begin{array}{rr}&523\\\times&3\\\hline&1569\end{array}[/latex]

Step 1: 3 × 3 ones = 9 ones

Step 2: 3 × 2 tens = 6 tens

Step 3: 3 × 5 hundreds = 15 hundreds = 1 thousand and 5 hundreds

The product of 523 × 3 is 1569.

Example C

901 × 8 =

[latex]\begin{array}{rr}&901\\\times&8\\\hline&7208\end{array}[/latex]

Step 1: 8 × 1 one = 8 ones

Step 2: 8 × 0 tens = 0 tens

Step 3: 8 × 9 hundreds = 72 hundreds = 7 thousands and 2 hundreds

The product of 901 × 8 is 7208.

Exercise 2

Find the product. Check your work using the answer key at the end of the exercise.

  1. [latex]\begin{array}{rr}&601\\\times&7\\\hline\\\end{array}[/latex]
  2. [latex]\begin{array}{rr}&423\\\times&3\\\hline\\\end{array}[/latex]
  3. [latex]\begin{array}{rr}&641\\\times&2\\\hline\\\end{array}[/latex]
  4. [latex]\begin{array}{rr}&922\\\times&4\\\hline\\\end{array}[/latex]
  5. [latex]\begin{array}{rr}&820\\\times&4\\\hline\\\end{array}[/latex]
  6. [latex]\begin{array}{rr}&211\\\times&5\\\hline\\\end{array}[/latex]
  7. [latex]\begin{array}{rr}&803\\\times&2\\\hline\\\end{array}[/latex]
  8. [latex]\begin{array}{rr}&542\\\times&2\\\hline\\\end{array}[/latex]
  9. [latex]\begin{array}{rr}&813\\\times&3\\\hline\\\end{array}[/latex]
  10. [latex]\begin{array}{rr}&610\\\times&4\\\hline\\\end{array}[/latex]
  11. [latex]\begin{array}{rr}&901\\\times&6\\\hline\\\end{array}[/latex]
  12. [latex]\begin{array}{rr}&711\\\times&8\\\hline\\\end{array}[/latex]
  13. [latex]\begin{array}{rr}&720\\\times&3\\\hline\\\end{array}[/latex]
  14. [latex]\begin{array}{rr}&910\\\times&5\\\hline\\\end{array}[/latex]
  15. [latex]\begin{array}{rr}&801\\\times&6\\\hline\\\end{array}[/latex]
  16. [latex]\begin{array}{rr}&932\\\times&3\\\hline\\\end{array}[/latex]
  17. [latex]\begin{array}{rr}&731\\\times&2\\\hline\\\end{array}[/latex]
  18. [latex]\begin{array}{rr}&701\\\times&5\\\hline\\\end{array}[/latex]
  19. [latex]\begin{array}{rr}&521\\\times&2\\\hline\\\end{array}[/latex]
  20. [latex]\begin{array}{rr}&632\\\times&3\\\hline\\\end{array}[/latex]
  21. [latex]\begin{array}{rr}&720\\\times&4\\\hline\\\end{array}[/latex]
  22. [latex]\begin{array}{rr}&942\\\times&2\\\hline\\\end{array}[/latex]
  23. [latex]\begin{array}{rr}&710\\\times&9\\\hline\\\end{array}[/latex]
  24. [latex]\begin{array}{rr}&601\\\times&8\\\hline\\\end{array}[/latex]
Answers to Exercise 2
  1. 4207
  2. 1269
  3. 1282
  4. 3688
  5. 3280
  6. 1055
  7. 1606
  8. 1084
  9. 2439
  10. 2440
  11. 5406
  12. 5688
  13. 2160
  14. 4550
  15. 4806
  16. 2796
  17. 1462
  18. 3505
  19. 1042
  20. 1896
  21. 2880
  22. 1884
  23. 6390
  24. 4808

Renaming and Carrying

In the times tables, the products are often two digit numbers. You must rename and carry. The amount you carry is added onto the product of the next column.

Example D

[latex]\begin{array}{rr}&68\\\times&7\\\hline\end{array}[/latex]

 

Step 1: Multiply the ones by the multiplier.

7 × 8 ones = 56 ones = 5 tens + 6 ones

Write the 6 ones in the product.

Carry the 5 tens to the tens column and make a note of it for yourself. You might write it above the tens column.

[latex]\begin{array}{rrr}&_5\hspace{0.5em}\\&68\\\times&7\\\hline&6\end{array}[/latex]

Step 2: Multiply the tens by the multiplier.

7 × 6 tens = 42 tens

Now add on the 5 tens that you carried.

42 tens + 5 tens = 47 tens = 4 hundreds and 7 tens

[latex]\begin{array}{rrr}&_5\hspace{0.5em}\\&68\\\times&7\\\hline&476\end{array}[/latex]

Exercise 3

Find the product. Check your work using the answer key at the end of the exercise.

  1. [latex]\begin{array}{rr}&16\\\times&8\\\hline\\\end{array}[/latex]
  2. [latex]\begin{array}{rr}&62\\\times&6\\\hline\\\end{array}[/latex]
  3. [latex]\begin{array}{rr}&37\\\times&4\\\hline\\\end{array}[/latex]
  4. [latex]\begin{array}{rr}&14\\\times&9\\\hline\\\end{array}[/latex]
  5. [latex]\begin{array}{rr}&36\\\times&7\\\hline\\\end{array}[/latex]
  6. [latex]\begin{array}{rr}&92\\\times&9\\\hline\\\end{array}[/latex]
  7. [latex]\begin{array}{rr}&48\\\times&6\\\hline\\\end{array}[/latex]
  8. [latex]\begin{array}{rr}&17\\\times&2\\\hline\\\end{array}[/latex]
  9. [latex]\begin{array}{rr}&26\\\times&4\\\hline\\\end{array}[/latex]
  10. [latex]\begin{array}{rr}&54\\\times&7\\\hline\\\end{array}[/latex]
  11. [latex]\begin{array}{rr}&58\\\times&8\\\hline\\\end{array}[/latex]
  12. [latex]\begin{array}{rr}&45\\\times&4\\\hline\\\end{array}[/latex]
  13. [latex]\begin{array}{rr}&56\\\times&3\\\hline\\\end{array}[/latex]
  14. [latex]\begin{array}{rr}&47\\\times&5\\\hline\\\end{array}[/latex]
  15. [latex]\begin{array}{rr}&39\\\times&6\\\hline\\\end{array}[/latex]
  16. [latex]\begin{array}{rr}&75\\\times&6\\\hline\\\end{array}[/latex]
  17. [latex]\begin{array}{rr}&38\\\times&5\\\hline\\\end{array}[/latex]
  18. [latex]\begin{array}{rr}&82\\\times&7\\\hline\\\end{array}[/latex]
  19. [latex]\begin{array}{rr}&98\\\times&3\\\hline\\\end{array}[/latex]
  20. [latex]\begin{array}{rr}&29\\\times&5\\\hline\\\end{array}[/latex]
  21. [latex]\begin{array}{rr}&47\\\times&3\\\hline\\\end{array}[/latex]
  22. [latex]\begin{array}{rr}&74\\\times&8\\\hline\\\end{array}[/latex]
  23. [latex]\begin{array}{rr}&56\\\times&5\\\hline\\\end{array}[/latex]
  24. [latex]\begin{array}{rr}&98\\\times&4\\\hline\\\end{array}[/latex]
Answers to Exercise 3
  1. 128
  2. 372
  3. 148
  4. 126
  5. 252
  6. 828
  7. 288
  8. 34
  9. 104
  10. 378
  11. 464
  12. 180
  13. 168
  14. 235
  15. 234
  16. 450
  17. 190
  18. 574
  19. 294
  20. 145
  21. 141
  22. 592
  23. 280
  24. 392

Example E

[latex]4\times224=[/latex]

 

[latex]\begin{array}{rr}&224\\\times&4\\\hline\end{array}[/latex]

 

Step 1: 4 × 4 ones = 16 ones = 1 ten and 6 ones

Write the 6 ones in the product and carry the one ten.

[latex]\begin{array}{rr}&_1\hspace{0.5em}\\&224\\\times&4\\\hline&6\end{array}[/latex]

Step 2: 4 × 2 tens = 8 tens

8 tens + 1 ten we carried = 9 tens

[latex]\begin{array}{rr}&_1\hspace{0.5em}\\&224\\\times&4\\\hline&96\end{array}[/latex]

Step 3: 4 × 2 hundreds = 8 hundreds

[latex]\begin{array}{rr}&_1\hspace{0.5em}\\&224\\\times&4\\\hline&896\end{array}[/latex]

 

Example F

[latex]4\times456=[/latex]

 

[latex]\begin{array}{rr}&456\\\times&5\\\hline\end{array}[/latex]

 

Step 1: 5 × 6 ones = 30 ones = 3 ten and 0 ones

The 0 must be written to hold the ones place. Carry the 3 tens.

[latex]\begin{array}{rr}&_3\hspace{0.5em}\\&456\\\times&5\\\hline&0\end{array}[/latex]

Step 2: 5 × 5 tens = 25 tens

25 tens + 3 tens = 28 tens = 2 hundreds and 8 tens

Write the 8 tens in the product. Carry the 2 hundreds.

[latex]\begin{array}{rr}&_{2\text{ }3}\hspace{0.5em}\\&456\\\times&5\\\hline&80\end{array}[/latex]

Step 3: 5 × 4 hundreds = 20 hundreds + 2 hundreds = 22 hundreds = 2 thousands and 2 hundreds

[latex]\begin{array}{rr}&_{2\text{ }3}\hspace{0.5em}\\&456\\\times&5\\\hline&2280\end{array}[/latex]

Exercise 4

Find the products. Check your work using the answer key at the end of the exercise.

  1. [latex]\begin{array}{rr}&648\\\times&9\\\hline\\\end{array}[/latex]
  2. [latex]\begin{array}{rr}&240\\\times&7\\\hline\\\end{array}[/latex]
  3. [latex]\begin{array}{rr}&457\\\times&8\\\hline\\\end{array}[/latex]
  4. [latex]\begin{array}{rr}&404\\\times&2\\\hline\\\end{array}[/latex]
  5. [latex]\begin{array}{rr}&106\\\times&9\\\hline\\\end{array}[/latex]
  6. [latex]\begin{array}{rr}&156\\\times&4\\\hline\\\end{array}[/latex]
  7. [latex]\begin{array}{rr}&407\\\times&8\\\hline\\\end{array}[/latex]
  8. [latex]\begin{array}{rr}&239\\\times&6\\\hline\\\end{array}[/latex]
  9. [latex]\begin{array}{rr}&118\\\times&9\\\hline\\\end{array}[/latex]
  10. [latex]\begin{array}{rr}&425\\\times&7\\\hline\\\end{array}[/latex]
  11. [latex]\begin{array}{rr}&139\\\times&8\\\hline\\\end{array}[/latex]
  12. [latex]\begin{array}{rr}&565\\\times&2\\\hline\\\end{array}[/latex]
  13. [latex]\begin{array}{rr}&248\\\times&3\\\hline\\\end{array}[/latex]
  14. [latex]\begin{array}{rr}&604\\\times&6\\\hline\\\end{array}[/latex]
  15. [latex]\begin{array}{rr}&239\\\times&4\\\hline\\\end{array}[/latex]
  16. [latex]\begin{array}{rr}&576\\\times&3\\\hline\\\end{array}[/latex]
  17. [latex]\begin{array}{rr}&857\\\times&6\\\hline\\\end{array}[/latex]
  18. [latex]\begin{array}{rr}&478\\\times&9\\\hline\\\end{array}[/latex]
  19. [latex]\begin{array}{rr}&674\\\times&7\\\hline\\\end{array}[/latex]
  20. [latex]\begin{array}{rr}&629\\\times&8\\\hline\\\end{array}[/latex]
  21. [latex]\begin{array}{rr}&893\\\times&5\\\hline\\\end{array}[/latex]
  22. [latex]\begin{array}{rr}&583\\\times&8\\\hline\\\end{array}[/latex]
  23. [latex]\begin{array}{rr}&952\\\times&9\\\hline\\\end{array}[/latex]
  24. [latex]\begin{array}{rr}&293\\\times&7\\\hline\\\end{array}[/latex]
Answers to Exercise 4
  1. 5832
  2. 1680
  3. 3656
  4. 808
  5. 954
  6. 624
  7. 3256
  8. 1434
  9. 1062
  10. 2975
  11. 1112
  12. 1130
  13. 744
  14. 3624
  15. 956
  16. 1728
  17. 5142
  18. 4302
  19. 4718
  20. 5032
  21. 4465
  22. 4664
  23. 8568
  24. 2051

 

Example G

[latex]\begin{array}{rr}&2408\\\times&9\\\hline\end{array}[/latex]

 

[latex]\begin{array}{rr}&_3\hspace{0.7em}_7\hspace{0.5em}\\&2408\\\times&9\\\hline&21672\end{array}[/latex]

Step 1: 9 × 8 ones = 72 ones = 7 tens and 2 ones

Step 2: 9 × 0 = 0 tens. 0 tens + 7 tens = 7 tens

Step 3: 9 × 4 hundreds = 36 hundreds = 3 thousands and 6 hundreds

Step 4: 9 × 2 thousands = 18 thousands. 18 thousands + 3 thousands = 21 thousands

Exercise 5

Find the products. Check your work using the answer key at the end of the exercise.

  1. [latex]\begin{array}{rr}&4103\\\times&8\\\hline\\\end{array}[/latex]
  2. [latex]\begin{array}{rr}&6087\\\times&4\\\hline\\\end{array}[/latex]
  3. [latex]\begin{array}{rr}&3280\\\times&6\\\hline\\\end{array}[/latex]
  4. [latex]\begin{array}{rr}&7034\\\times&5\\\hline\\\end{array}[/latex]
  5. [latex]\begin{array}{rr}&8456\\\times&2\\\hline\\\end{array}[/latex]
  6. [latex]\begin{array}{rr}&4758\\\times&7\\\hline\\\end{array}[/latex]
  7. [latex]\begin{array}{rr}&4735\\\times&3\\\hline\\\end{array}[/latex]
  8. [latex]\begin{array}{rr}&5402\\\times&9\\\hline\\\end{array}[/latex]
  9. [latex]\begin{array}{rr}&5394\\\times&4\\\hline\\\end{array}[/latex]
  10. [latex]\begin{array}{rr}&2034\\\times&8\\\hline\\\end{array}[/latex]
  11. [latex]\begin{array}{rr}&8652\\\times&5\\\hline\\\end{array}[/latex]
  12. [latex]\begin{array}{rr}&6392\\\times&7\\\hline\\\end{array}[/latex]
  13. [latex]\begin{array}{rr}&4187\\\times&6\\\hline\\\end{array}[/latex]
  14. [latex]\begin{array}{rr}&1376\\\times&9\\\hline\\\end{array}[/latex]
  15. [latex]\begin{array}{rr}&3297\\\times&2\\\hline\\\end{array}[/latex]
  16. [latex]\begin{array}{rr}&9628\\\times&3\\\hline\\\end{array}[/latex]
  17. [latex]\begin{array}{rr}&7689\\\times&8\\\hline\\\end{array}[/latex]
  18. [latex]\begin{array}{rr}&5160\\\times&3\\\hline\\\end{array}[/latex]
  19. [latex]\begin{array}{rr}&4256\\\times&7\\\hline\\\end{array}[/latex]
  20. [latex]\begin{array}{rr}&5491\\\times&5\\\hline\\\end{array}[/latex]
  21. [latex]\begin{array}{rr}&8032\\\times&9\\\hline\\\end{array}[/latex]
  22. [latex]\begin{array}{rr}&8645\\\times&6\\\hline\\\end{array}[/latex]
  23. [latex]\begin{array}{rr}&6453\\\times&2\\\hline\\\end{array}[/latex]
  24. [latex]\begin{array}{rr}&8129\\\times&4\\\hline\\\end{array}[/latex]

Answers to Exercise 5

  1. 32824
  2. 24348
  3. 19680
  4. 35170
  5. 16912
  6. 33306
  7. 14205
  8. 48618
  9. 21576
  10. 16272
  11. 43260
  12. 44744
  13. 25122
  14. 12384
  15. 6594
  16. 28884
  17. 61512
  18. 15480
  19. 29792
  20. 27455
  21. 72288
  22. 51870
  23. 12906
  24. 32516

Topic A: Self-Test

Mark   /14    Aim 11/14

A. Find the products. (6 marks)

  1. [latex]\begin{array}{rr}&62\\\times&4\\\hline\\\end{array}[/latex]
  2. [latex]\begin{array}{rr}&31\\\times&4\\\hline\\\end{array}[/latex]
  3. [latex]\begin{array}{rr}&423\\\times&3\\\hline\\\end{array}[/latex]
  4. [latex]\begin{array}{rr}&734\\\times&2\\\hline\\\end{array}[/latex]
  5. [latex]\begin{array}{rr}&8342\\\times&2\\\hline\\\end{array}[/latex]
  6. [latex]\begin{array}{rr}&5231\\\times&3\\\hline\\\end{array}[/latex]

B. Multiply these numbers. (4 marks)

  1. [latex]\begin{array}{rr}&44\\\times&7\\\hline\\\end{array}[/latex]
  2. [latex]\begin{array}{rr}&69\\\times&8\\\hline\\\end{array}[/latex]
  3. [latex]\begin{array}{rr}&207\\\times&9\\\hline\\\end{array}[/latex]
  4. [latex]\begin{array}{rr}&184\\\times&6\\\hline\\\end{array}[/latex]

C. Find the products. (4 marks)

  1. [latex]\begin{array}{rr}&2834\\\times&5\\\hline\\\end{array}[/latex]
  2. [latex]\begin{array}{rr}&4037\\\times&6\\\hline\\\end{array}[/latex]
  3. [latex]\begin{array}{rr}&9241\\\times&8\\\hline\\\end{array}[/latex]
  4. [latex]\begin{array}{rr}&3652\\\times&4\\\hline\\\end{array}[/latex]
Answers to Topic A Self-Test
  1. Find the products.
    1. 248
    2. 124
    3. 1269
    4. 1468
    5. 16684
    6. 15693
  2. Multiply these numbers.
    1. 308
    2. 552
    3. 1863
    4. 1104
  3. Find the products.
    1. 14170
    2. 24222
    3. 73928
    4. 14608

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Fundamentals of Mathematics 3 Copyright © 2023 by Wendy Tagami and Liz Girard is licensed under a Creative Commons Attribution 4.0 International License, except where otherwise noted.