{"id":25,"date":"2023-01-05T18:24:51","date_gmt":"2023-01-05T23:24:51","guid":{"rendered":"https:\/\/pressbooks.bccampus.ca\/math023\/chapter\/multiplying-larger-numbers\/"},"modified":"2025-07-03T22:33:16","modified_gmt":"2025-07-04T02:33:16","slug":"multiplying-larger-numbers","status":"publish","type":"chapter","link":"https:\/\/pressbooks.bccampus.ca\/math023\/chapter\/multiplying-larger-numbers\/","title":{"raw":"Topic A: Multiplying Larger Numbers","rendered":"Topic A: Multiplying Larger Numbers"},"content":{"raw":"It is usually easier to multiply larger numbers if they are written underneath each other. The bottom number is called the multiplier.\r\n\r\n<strong>To find the product of a one digit multiplier,<\/strong> use as many of these steps as you need to complete each multiplication question:\r\n<ul type=\"none\">\r\n \t<li><strong>Step 1:<\/strong> Multiply the ones digit in the large number by the one-digit multiplier.<\/li>\r\n \t<li><strong>Step 2:<\/strong> Multiply the tens digit in the large number by the multiplier.<\/li>\r\n \t<li><strong>Step 3:<\/strong> Multiply the hundreds digit in the large number by the multiplier.<\/li>\r\n \t<li><strong>Step 4:<\/strong> Multiply the thousands digit in the large number by the multiplier.<\/li>\r\n<\/ul>\r\n<div class=\"textbox textbox--examples\"><header class=\"textbox__header\">\r\n<p class=\"textbox__title\">Example A<\/p>\r\n\r\n<\/header>\r\n<div class=\"textbox__content\">\r\n\r\n62 \u00d7 4 =\r\n\r\n<strong>Step 1:<\/strong> 4 \u00d7 2 ones = 8\r\n<p style=\"text-align: center\">[latex]\\begin{array}{rr}&amp;62\\\\\\times&amp;4\\\\\\hline&amp;8\\end{array}[\/latex]<\/p>\r\n<strong>Step 2:<\/strong> 4 \u00d7 6 tens = 24 tens = 2 hundreds and 4 tens\r\n<p style=\"text-align: center\">[latex]\\begin{array}{rr}&amp;62\\\\\\times&amp;4\\\\\\hline&amp;248\\end{array}[\/latex]<\/p>\r\nThe product of 62 \u00d7 4 is 248.\r\n\r\n<\/div>\r\n<\/div>\r\n<div class=\"textbox textbox--exercises\"><header class=\"textbox__header\">\r\n<p class=\"textbox__title\">Exercise 1<\/p>\r\n\r\n<\/header>\r\n<div class=\"textbox__content\">\r\n\r\nFind the product. Check your work using the answer key at the\r\nend of the exercise.\r\n<ol class=\"threecolumn\" type=\"a\">\r\n \t<li>[latex]\\begin{array}{rr}&amp;72\\\\\\times&amp;2\\\\\\hline\\\\\\end{array}[\/latex]<\/li>\r\n \t<li>[latex]\\begin{array}{rr}&amp;81\\\\\\times&amp;5\\\\\\hline\\\\\\end{array}[\/latex]<\/li>\r\n \t<li>[latex]\\begin{array}{rr}&amp;21\\\\\\times&amp;8\\\\\\hline\\\\\\end{array}[\/latex]<\/li>\r\n \t<li>[latex]\\begin{array}{rr}&amp;80\\\\\\times&amp;6\\\\\\hline\\\\\\end{array}[\/latex]<\/li>\r\n \t<li>[latex]\\begin{array}{rr}&amp;73\\\\\\times&amp;3\\\\\\hline\\\\\\end{array}[\/latex]<\/li>\r\n \t<li>[latex]\\begin{array}{rr}&amp;71\\\\\\times&amp;3\\\\\\hline\\\\\\end{array}[\/latex]<\/li>\r\n \t<li>[latex]\\begin{array}{rr}&amp;40\\\\\\times&amp;7\\\\\\hline\\\\\\end{array}[\/latex]<\/li>\r\n \t<li>[latex]\\begin{array}{rr}&amp;90\\\\\\times&amp;9\\\\\\hline\\\\\\end{array}[\/latex]<\/li>\r\n \t<li>[latex]\\begin{array}{rr}&amp;82\\\\\\times&amp;4\\\\\\hline\\\\\\end{array}[\/latex]<\/li>\r\n \t<li>[latex]\\begin{array}{rr}&amp;40\\\\\\times&amp;5\\\\\\hline\\\\\\end{array}[\/latex]<\/li>\r\n \t<li>[latex]\\begin{array}{rr}&amp;92\\\\\\times&amp;4\\\\\\hline\\\\\\end{array}[\/latex]<\/li>\r\n \t<li>[latex]\\begin{array}{rr}&amp;83\\\\\\times&amp;3\\\\\\hline\\\\\\end{array}[\/latex]<\/li>\r\n \t<li>[latex]\\begin{array}{rr}&amp;90\\\\\\times&amp;8\\\\\\hline\\\\\\end{array}[\/latex]<\/li>\r\n \t<li>[latex]\\begin{array}{rr}&amp;71\\\\\\times&amp;9\\\\\\hline\\\\\\end{array}[\/latex]<\/li>\r\n \t<li>[latex]\\begin{array}{rr}&amp;53\\\\\\times&amp;2\\\\\\hline\\\\\\end{array}[\/latex]<\/li>\r\n \t<li>[latex]\\begin{array}{rr}&amp;30\\\\\\times&amp;6\\\\\\hline\\\\\\end{array}[\/latex]<\/li>\r\n \t<li>[latex]\\begin{array}{rr}&amp;81\\\\\\times&amp;7\\\\\\hline\\\\\\end{array}[\/latex]<\/li>\r\n \t<li>[latex]\\begin{array}{rr}&amp;61\\\\\\times&amp;2\\\\\\hline\\\\\\end{array}[\/latex]<\/li>\r\n \t<li>[latex]\\begin{array}{rr}&amp;70\\\\\\times&amp;8\\\\\\hline\\\\\\end{array}[\/latex]<\/li>\r\n \t<li>[latex]\\begin{array}{rr}&amp;41\\\\\\times&amp;6\\\\\\hline\\\\\\end{array}[\/latex]<\/li>\r\n \t<li>[latex]\\begin{array}{rr}&amp;90\\\\\\times&amp;5\\\\\\hline\\\\\\end{array}[\/latex]<\/li>\r\n \t<li>[latex]\\begin{array}{rr}&amp;60\\\\\\times&amp;9\\\\\\hline\\\\\\end{array}[\/latex]<\/li>\r\n \t<li>[latex]\\begin{array}{rr}&amp;92\\\\\\times&amp;3\\\\\\hline\\\\\\end{array}[\/latex]<\/li>\r\n \t<li>[latex]\\begin{array}{rr}&amp;81\\\\\\times&amp;4\\\\\\hline\\\\\\end{array}[\/latex]<\/li>\r\n<\/ol>\r\n<strong>Answers to Exercise 1<\/strong>\r\n<ol class=\"threecolumn\" type=\"a\">\r\n \t<li>144<\/li>\r\n \t<li>405<\/li>\r\n \t<li>168<\/li>\r\n \t<li>480<\/li>\r\n \t<li>219<\/li>\r\n \t<li>213<\/li>\r\n \t<li>280<\/li>\r\n \t<li>810<\/li>\r\n \t<li>328<\/li>\r\n \t<li>200<\/li>\r\n \t<li>368<\/li>\r\n \t<li>249<\/li>\r\n \t<li>720<\/li>\r\n \t<li>639<\/li>\r\n \t<li>106<\/li>\r\n \t<li>180<\/li>\r\n \t<li>567<\/li>\r\n \t<li>122<\/li>\r\n \t<li>560<\/li>\r\n \t<li>246<\/li>\r\n \t<li>450<\/li>\r\n \t<li>540<\/li>\r\n \t<li>276<\/li>\r\n \t<li>324<\/li>\r\n<\/ol>\r\n<\/div>\r\n<\/div>\r\n<div class=\"textbox textbox--examples\"><header class=\"textbox__header\">\r\n<p class=\"textbox__title\">Example B<\/p>\r\n\r\n<\/header>\r\n<div class=\"textbox__content\">\r\n\r\n523 \u00d7 3 =\r\n<p style=\"text-align: center\">[latex]\\begin{array}{rr}&amp;523\\\\\\times&amp;3\\\\\\hline&amp;1569\\end{array}[\/latex]<\/p>\r\n<strong>Step 1:<\/strong> 3 \u00d7 3 ones = 9 ones\r\n\r\n<strong>Step 2:<\/strong> 3 \u00d7 2 tens = 6 tens\r\n\r\n<strong>Step 3:<\/strong> 3 \u00d7 5 hundreds = 15 hundreds = 1 thousand and 5 hundreds\r\n\r\nThe product of 523 \u00d7 3 is 1<span style=\"margin-left: 0.25em\">569<\/span>.\r\n\r\n<\/div>\r\n<\/div>\r\n<div class=\"textbox textbox--examples\"><header class=\"textbox__header\">\r\n<p class=\"textbox__title\">Example C<\/p>\r\n\r\n<\/header>\r\n<div class=\"textbox__content\">\r\n\r\n901 \u00d7 8 =\r\n<p style=\"text-align: center\">[latex]\\begin{array}{rr}&amp;901\\\\\\times&amp;8\\\\\\hline&amp;7208\\end{array}[\/latex]<\/p>\r\n<strong>Step 1:<\/strong> 8 \u00d7 1 one = 8 ones\r\n\r\n<strong>Step 2:<\/strong> 8 \u00d7 0 tens = 0 tens\r\n\r\n<strong>Step 3:<\/strong> 8 \u00d7 9 hundreds = 72 hundreds = 7 thousands and 2 hundreds\r\n\r\nThe product of 901 \u00d7 8 is 7<span style=\"margin-left: 0.25em\">208.<\/span>\r\n\r\n<\/div>\r\n<\/div>\r\n<div class=\"textbox textbox--exercises\"><header class=\"textbox__header\">\r\n<p class=\"textbox__title\">Exercise 2<\/p>\r\n\r\n<\/header>\r\n<div class=\"textbox__content\">\r\n\r\nFind the product. Check your work using the answer key at the\r\nend of the exercise.\r\n<ol class=\"threecolumn\" type=\"a\">\r\n \t<li>[latex]\\begin{array}{rr}&amp;601\\\\\\times&amp;7\\\\\\hline\\\\\\end{array}[\/latex]<\/li>\r\n \t<li>[latex]\\begin{array}{rr}&amp;423\\\\\\times&amp;3\\\\\\hline\\\\\\end{array}[\/latex]<\/li>\r\n \t<li>[latex]\\begin{array}{rr}&amp;641\\\\\\times&amp;2\\\\\\hline\\\\\\end{array}[\/latex]<\/li>\r\n \t<li>[latex]\\begin{array}{rr}&amp;922\\\\\\times&amp;4\\\\\\hline\\\\\\end{array}[\/latex]<\/li>\r\n \t<li>[latex]\\begin{array}{rr}&amp;820\\\\\\times&amp;4\\\\\\hline\\\\\\end{array}[\/latex]<\/li>\r\n \t<li>[latex]\\begin{array}{rr}&amp;211\\\\\\times&amp;5\\\\\\hline\\\\\\end{array}[\/latex]<\/li>\r\n \t<li>[latex]\\begin{array}{rr}&amp;803\\\\\\times&amp;2\\\\\\hline\\\\\\end{array}[\/latex]<\/li>\r\n \t<li>[latex]\\begin{array}{rr}&amp;542\\\\\\times&amp;2\\\\\\hline\\\\\\end{array}[\/latex]<\/li>\r\n \t<li>[latex]\\begin{array}{rr}&amp;813\\\\\\times&amp;3\\\\\\hline\\\\\\end{array}[\/latex]<\/li>\r\n \t<li>[latex]\\begin{array}{rr}&amp;610\\\\\\times&amp;4\\\\\\hline\\\\\\end{array}[\/latex]<\/li>\r\n \t<li>[latex]\\begin{array}{rr}&amp;901\\\\\\times&amp;6\\\\\\hline\\\\\\end{array}[\/latex]<\/li>\r\n \t<li>[latex]\\begin{array}{rr}&amp;711\\\\\\times&amp;8\\\\\\hline\\\\\\end{array}[\/latex]<\/li>\r\n \t<li>[latex]\\begin{array}{rr}&amp;720\\\\\\times&amp;3\\\\\\hline\\\\\\end{array}[\/latex]<\/li>\r\n \t<li>[latex]\\begin{array}{rr}&amp;910\\\\\\times&amp;5\\\\\\hline\\\\\\end{array}[\/latex]<\/li>\r\n \t<li>[latex]\\begin{array}{rr}&amp;801\\\\\\times&amp;6\\\\\\hline\\\\\\end{array}[\/latex]<\/li>\r\n \t<li>[latex]\\begin{array}{rr}&amp;932\\\\\\times&amp;3\\\\\\hline\\\\\\end{array}[\/latex]<\/li>\r\n \t<li>[latex]\\begin{array}{rr}&amp;731\\\\\\times&amp;2\\\\\\hline\\\\\\end{array}[\/latex]<\/li>\r\n \t<li>[latex]\\begin{array}{rr}&amp;701\\\\\\times&amp;5\\\\\\hline\\\\\\end{array}[\/latex]<\/li>\r\n \t<li>[latex]\\begin{array}{rr}&amp;521\\\\\\times&amp;2\\\\\\hline\\\\\\end{array}[\/latex]<\/li>\r\n \t<li>[latex]\\begin{array}{rr}&amp;632\\\\\\times&amp;3\\\\\\hline\\\\\\end{array}[\/latex]<\/li>\r\n \t<li>[latex]\\begin{array}{rr}&amp;720\\\\\\times&amp;4\\\\\\hline\\\\\\end{array}[\/latex]<\/li>\r\n \t<li>[latex]\\begin{array}{rr}&amp;942\\\\\\times&amp;2\\\\\\hline\\\\\\end{array}[\/latex]<\/li>\r\n \t<li>[latex]\\begin{array}{rr}&amp;710\\\\\\times&amp;9\\\\\\hline\\\\\\end{array}[\/latex]<\/li>\r\n \t<li>[latex]\\begin{array}{rr}&amp;601\\\\\\times&amp;8\\\\\\hline\\\\\\end{array}[\/latex]<\/li>\r\n<\/ol>\r\n<strong>Answers to Exercise 2<\/strong>\r\n<ol class=\"threecolumn\" type=\"a\">\r\n \t<li>4<span style=\"margin-left: 0.25em\">207<\/span><\/li>\r\n \t<li>1<span style=\"margin-left: 0.25em\">269<\/span><\/li>\r\n \t<li>1<span style=\"margin-left: 0.25em\">282<\/span><\/li>\r\n \t<li>3<span style=\"margin-left: 0.25em\">688<\/span><\/li>\r\n \t<li>3<span style=\"margin-left: 0.25em\">280<\/span><\/li>\r\n \t<li>1<span style=\"margin-left: 0.25em\">055<\/span><\/li>\r\n \t<li>1<span style=\"margin-left: 0.25em\">606<\/span><\/li>\r\n \t<li>1<span style=\"margin-left: 0.25em\">084<\/span><\/li>\r\n \t<li>2<span style=\"margin-left: 0.25em\">439<\/span><\/li>\r\n \t<li>2<span style=\"margin-left: 0.25em\">440<\/span><\/li>\r\n \t<li>5<span style=\"margin-left: 0.25em\">406<\/span><\/li>\r\n \t<li>5<span style=\"margin-left: 0.25em\">688<\/span><\/li>\r\n \t<li>2<span style=\"margin-left: 0.25em\">160<\/span><\/li>\r\n \t<li>4<span style=\"margin-left: 0.25em\">550<\/span><\/li>\r\n \t<li>4<span style=\"margin-left: 0.25em\">806<\/span><\/li>\r\n \t<li>2<span style=\"margin-left: 0.25em\">796<\/span><\/li>\r\n \t<li>1<span style=\"margin-left: 0.25em\">462<\/span><\/li>\r\n \t<li>3<span style=\"margin-left: 0.25em\">505<\/span><\/li>\r\n \t<li>1<span style=\"margin-left: 0.25em\">042<\/span><\/li>\r\n \t<li>1<span style=\"margin-left: 0.25em\">896<\/span><\/li>\r\n \t<li>2<span style=\"margin-left: 0.25em\">880<\/span><\/li>\r\n \t<li>1<span style=\"margin-left: 0.25em\">884<\/span><\/li>\r\n \t<li>6<span style=\"margin-left: 0.25em\">390<\/span><\/li>\r\n \t<li>4<span style=\"margin-left: 0.25em\">808<\/span><\/li>\r\n<\/ol>\r\n<\/div>\r\n<\/div>\r\n<h1>Renaming and Carrying<\/h1>\r\nIn 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.\r\n<div class=\"textbox textbox--examples\"><header class=\"textbox__header\">\r\n<p class=\"textbox__title\">Example D<\/p>\r\n\r\n<\/header>\r\n<div class=\"textbox__content\">\r\n\r\n[latex]\\begin{array}{rr}&amp;68\\\\\\times&amp;7\\\\\\hline\\end{array}[\/latex]\r\n\r\n<strong>Step 1:<\/strong> Multiply the ones by the multiplier.\r\n\r\n7 \u00d7 8 ones = 56 ones = 5 tens + 6 ones\r\n\r\nWrite the 6 ones in the product.\r\n\r\nCarry the 5 tens to the tens column and make a note of it for yourself. You might write it above the tens column.\r\n<p style=\"text-align: center\">[latex]\\begin{array}{rrr}&amp;_5\\hspace{0.5em}\\\\&amp;68\\\\\\times&amp;7\\\\\\hline&amp;6\\end{array}[\/latex]<\/p>\r\n<strong>Step 2:<\/strong> Multiply the tens by the multiplier.\r\n\r\n7 \u00d7 6 tens = 42 tens\r\n\r\nNow add on the 5 tens that you carried.\r\n\r\n42 tens + 5 tens = 47 tens = 4 hundreds and 7 tens\r\n<p style=\"text-align: center\">[latex]\\begin{array}{rrr}&amp;_5\\hspace{0.5em}\\\\&amp;68\\\\\\times&amp;7\\\\\\hline&amp;476\\end{array}[\/latex]<\/p>\r\n\r\n<\/div>\r\n<\/div>\r\n<div class=\"textbox textbox--exercises\"><header class=\"textbox__header\">\r\n<p class=\"textbox__title\">Exercise 3<\/p>\r\n\r\n<\/header>\r\n<div class=\"textbox__content\">\r\n\r\nFind the product. Check your work using the answer key at the end of the exercise.\r\n<ol class=\"threecolumn\" type=\"a\">\r\n \t<li>[latex]\\begin{array}{rr}&amp;16\\\\\\times&amp;8\\\\\\hline\\\\\\end{array}[\/latex]<\/li>\r\n \t<li>[latex]\\begin{array}{rr}&amp;62\\\\\\times&amp;6\\\\\\hline\\\\\\end{array}[\/latex]<\/li>\r\n \t<li>[latex]\\begin{array}{rr}&amp;37\\\\\\times&amp;4\\\\\\hline\\\\\\end{array}[\/latex]<\/li>\r\n \t<li>[latex]\\begin{array}{rr}&amp;14\\\\\\times&amp;9\\\\\\hline\\\\\\end{array}[\/latex]<\/li>\r\n \t<li>[latex]\\begin{array}{rr}&amp;36\\\\\\times&amp;7\\\\\\hline\\\\\\end{array}[\/latex]<\/li>\r\n \t<li>[latex]\\begin{array}{rr}&amp;92\\\\\\times&amp;9\\\\\\hline\\\\\\end{array}[\/latex]<\/li>\r\n \t<li>[latex]\\begin{array}{rr}&amp;48\\\\\\times&amp;6\\\\\\hline\\\\\\end{array}[\/latex]<\/li>\r\n \t<li>[latex]\\begin{array}{rr}&amp;17\\\\\\times&amp;2\\\\\\hline\\\\\\end{array}[\/latex]<\/li>\r\n \t<li>[latex]\\begin{array}{rr}&amp;26\\\\\\times&amp;4\\\\\\hline\\\\\\end{array}[\/latex]<\/li>\r\n \t<li>[latex]\\begin{array}{rr}&amp;54\\\\\\times&amp;7\\\\\\hline\\\\\\end{array}[\/latex]<\/li>\r\n \t<li>[latex]\\begin{array}{rr}&amp;58\\\\\\times&amp;8\\\\\\hline\\\\\\end{array}[\/latex]<\/li>\r\n \t<li>[latex]\\begin{array}{rr}&amp;45\\\\\\times&amp;4\\\\\\hline\\\\\\end{array}[\/latex]<\/li>\r\n \t<li>[latex]\\begin{array}{rr}&amp;56\\\\\\times&amp;3\\\\\\hline\\\\\\end{array}[\/latex]<\/li>\r\n \t<li>[latex]\\begin{array}{rr}&amp;47\\\\\\times&amp;5\\\\\\hline\\\\\\end{array}[\/latex]<\/li>\r\n \t<li>[latex]\\begin{array}{rr}&amp;39\\\\\\times&amp;6\\\\\\hline\\\\\\end{array}[\/latex]<\/li>\r\n \t<li>[latex]\\begin{array}{rr}&amp;75\\\\\\times&amp;6\\\\\\hline\\\\\\end{array}[\/latex]<\/li>\r\n \t<li>[latex]\\begin{array}{rr}&amp;38\\\\\\times&amp;5\\\\\\hline\\\\\\end{array}[\/latex]<\/li>\r\n \t<li>[latex]\\begin{array}{rr}&amp;82\\\\\\times&amp;7\\\\\\hline\\\\\\end{array}[\/latex]<\/li>\r\n \t<li>[latex]\\begin{array}{rr}&amp;98\\\\\\times&amp;3\\\\\\hline\\\\\\end{array}[\/latex]<\/li>\r\n \t<li>[latex]\\begin{array}{rr}&amp;29\\\\\\times&amp;5\\\\\\hline\\\\\\end{array}[\/latex]<\/li>\r\n \t<li>[latex]\\begin{array}{rr}&amp;47\\\\\\times&amp;3\\\\\\hline\\\\\\end{array}[\/latex]<\/li>\r\n \t<li>[latex]\\begin{array}{rr}&amp;74\\\\\\times&amp;8\\\\\\hline\\\\\\end{array}[\/latex]<\/li>\r\n \t<li>[latex]\\begin{array}{rr}&amp;56\\\\\\times&amp;5\\\\\\hline\\\\\\end{array}[\/latex]<\/li>\r\n \t<li>[latex]\\begin{array}{rr}&amp;98\\\\\\times&amp;4\\\\\\hline\\\\\\end{array}[\/latex]<\/li>\r\n<\/ol>\r\n<strong>Answers to Exercise 3<\/strong>\r\n<ol class=\"threecolumn\" type=\"a\">\r\n \t<li>128<\/li>\r\n \t<li>372<\/li>\r\n \t<li>148<\/li>\r\n \t<li>126<\/li>\r\n \t<li>252<\/li>\r\n \t<li>828<\/li>\r\n \t<li>288<\/li>\r\n \t<li>34<\/li>\r\n \t<li>104<\/li>\r\n \t<li>378<\/li>\r\n \t<li>464<\/li>\r\n \t<li>180<\/li>\r\n \t<li>168<\/li>\r\n \t<li>235<\/li>\r\n \t<li>234<\/li>\r\n \t<li>450<\/li>\r\n \t<li>190<\/li>\r\n \t<li>574<\/li>\r\n \t<li>294<\/li>\r\n \t<li>145<\/li>\r\n \t<li>141<\/li>\r\n \t<li>592<\/li>\r\n \t<li>280<\/li>\r\n \t<li>392<\/li>\r\n<\/ol>\r\n<\/div>\r\n<\/div>\r\n<div class=\"textbox textbox--examples\"><header class=\"textbox__header\">\r\n<p class=\"textbox__title\">Example E<\/p>\r\n\r\n<\/header>\r\n<div class=\"textbox__content\">\r\n\r\n[latex]4\\times224=[\/latex]\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0 [latex]\\begin{array}{rr}&amp;224\\\\\\times&amp;4\\\\\\hline\\end{array}[\/latex]\r\n\r\n<strong>Step 1:<\/strong> 4 \u00d7 4 ones = 16 ones = 1 ten and 6 ones\r\n<p style=\"padding-left: 40px\">Write the 6 ones in the product and carry the one ten.<\/p>\r\n<p style=\"text-align: center\">[latex]\\begin{array}{rr}&amp;_1\\hspace{0.5em}\\\\&amp;224\\\\\\times&amp;4\\\\\\hline&amp;6\\end{array}[\/latex]<\/p>\r\n<strong>Step 2:<\/strong> 4 \u00d7 2 tens = 8 tens\r\n<p style=\"padding-left: 40px\">8 tens + 1 ten we carried = 9 tens<\/p>\r\n<p style=\"text-align: center\">[latex]\\begin{array}{rr}&amp;_1\\hspace{0.5em}\\\\&amp;224\\\\\\times&amp;4\\\\\\hline&amp;96\\end{array}[\/latex]<\/p>\r\n<strong>Step 3:<\/strong> 4 \u00d7 2 hundreds = 8 hundreds\r\n<p style=\"text-align: center\">[latex]\\begin{array}{rr}&amp;_1\\hspace{0.5em}\\\\&amp;224\\\\\\times&amp;4\\\\\\hline&amp;896\\end{array}[\/latex]<\/p>\r\n&nbsp;\r\n\r\n<\/div>\r\n<\/div>\r\n<div class=\"textbox textbox--examples\"><header class=\"textbox__header\">\r\n<p class=\"textbox__title\">Example F<\/p>\r\n\r\n<\/header>\r\n<div class=\"textbox__content\">\r\n\r\n[latex]4\\times456=[\/latex] \u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0 [latex]\\begin{array}{rr}&amp;456\\\\\\times&amp;5\\\\\\hline\\end{array}[\/latex]\r\n\r\n<strong>Step 1:<\/strong> 5 \u00d7 6 ones = 30 ones = 3 ten and 0 ones\r\n<p style=\"padding-left: 40px\">The 0 must be written to hold the ones place. Carry the 3 tens.<\/p>\r\n<p style=\"text-align: center\">[latex]\\begin{array}{rr}&amp;_3\\hspace{0.5em}\\\\&amp;456\\\\\\times&amp;5\\\\\\hline&amp;0\\end{array}[\/latex]<\/p>\r\n<strong>Step 2:<\/strong> 5 \u00d7 5 tens = 25 tens\r\n<p style=\"padding-left: 40px\">25 tens + 3 tens = 28 tens = 2 hundreds and 8 tens<\/p>\r\n<p style=\"padding-left: 40px\">Write the 8 tens in the product. Carry the 2 hundreds.<\/p>\r\n<p style=\"text-align: center\">[latex]\\begin{array}{rr}&amp;_{2\\text{ }3}\\hspace{0.5em}\\\\&amp;456\\\\\\times&amp;5\\\\\\hline&amp;80\\end{array}[\/latex]<\/p>\r\n<strong>Step 3:<\/strong> 5 \u00d7 4 hundreds = 20 hundreds + 2 hundreds = 22 hundreds = 2 thousands and 2 hundreds\r\n<p style=\"text-align: center\">[latex]\\begin{array}{rr}&amp;_{2\\text{ }3}\\hspace{0.5em}\\\\&amp;456\\\\\\times&amp;5\\\\\\hline&amp;2280\\end{array}[\/latex]<\/p>\r\n\r\n<\/div>\r\n<\/div>\r\n<div class=\"textbox textbox--exercises\"><header class=\"textbox__header\">\r\n<p class=\"textbox__title\">Exercise 4<\/p>\r\n\r\n<\/header>\r\n<div class=\"textbox__content\">\r\n\r\nFind the products. Check your work using the answer key at the end of the exercise.\r\n<ol class=\"threecolumn\" type=\"a\">\r\n \t<li>[latex]\\begin{array}{rr}&amp;648\\\\\\times&amp;9\\\\\\hline\\\\\\end{array}[\/latex]<\/li>\r\n \t<li>[latex]\\begin{array}{rr}&amp;240\\\\\\times&amp;7\\\\\\hline\\\\\\end{array}[\/latex]<\/li>\r\n \t<li>[latex]\\begin{array}{rr}&amp;457\\\\\\times&amp;8\\\\\\hline\\\\\\end{array}[\/latex]<\/li>\r\n \t<li>[latex]\\begin{array}{rr}&amp;404\\\\\\times&amp;2\\\\\\hline\\\\\\end{array}[\/latex]<\/li>\r\n \t<li>[latex]\\begin{array}{rr}&amp;106\\\\\\times&amp;9\\\\\\hline\\\\\\end{array}[\/latex]<\/li>\r\n \t<li>[latex]\\begin{array}{rr}&amp;156\\\\\\times&amp;4\\\\\\hline\\\\\\end{array}[\/latex]<\/li>\r\n \t<li>[latex]\\begin{array}{rr}&amp;407\\\\\\times&amp;8\\\\\\hline\\\\\\end{array}[\/latex]<\/li>\r\n \t<li>[latex]\\begin{array}{rr}&amp;239\\\\\\times&amp;6\\\\\\hline\\\\\\end{array}[\/latex]<\/li>\r\n \t<li>[latex]\\begin{array}{rr}&amp;118\\\\\\times&amp;9\\\\\\hline\\\\\\end{array}[\/latex]<\/li>\r\n \t<li>[latex]\\begin{array}{rr}&amp;425\\\\\\times&amp;7\\\\\\hline\\\\\\end{array}[\/latex]<\/li>\r\n \t<li>[latex]\\begin{array}{rr}&amp;139\\\\\\times&amp;8\\\\\\hline\\\\\\end{array}[\/latex]<\/li>\r\n \t<li>[latex]\\begin{array}{rr}&amp;565\\\\\\times&amp;2\\\\\\hline\\\\\\end{array}[\/latex]<\/li>\r\n \t<li>[latex]\\begin{array}{rr}&amp;248\\\\\\times&amp;3\\\\\\hline\\\\\\end{array}[\/latex]<\/li>\r\n \t<li>[latex]\\begin{array}{rr}&amp;604\\\\\\times&amp;6\\\\\\hline\\\\\\end{array}[\/latex]<\/li>\r\n \t<li>[latex]\\begin{array}{rr}&amp;239\\\\\\times&amp;4\\\\\\hline\\\\\\end{array}[\/latex]<\/li>\r\n \t<li>[latex]\\begin{array}{rr}&amp;576\\\\\\times&amp;3\\\\\\hline\\\\\\end{array}[\/latex]<\/li>\r\n \t<li>[latex]\\begin{array}{rr}&amp;857\\\\\\times&amp;6\\\\\\hline\\\\\\end{array}[\/latex]<\/li>\r\n \t<li>[latex]\\begin{array}{rr}&amp;478\\\\\\times&amp;9\\\\\\hline\\\\\\end{array}[\/latex]<\/li>\r\n \t<li>[latex]\\begin{array}{rr}&amp;674\\\\\\times&amp;7\\\\\\hline\\\\\\end{array}[\/latex]<\/li>\r\n \t<li>[latex]\\begin{array}{rr}&amp;629\\\\\\times&amp;8\\\\\\hline\\\\\\end{array}[\/latex]<\/li>\r\n \t<li>[latex]\\begin{array}{rr}&amp;893\\\\\\times&amp;5\\\\\\hline\\\\\\end{array}[\/latex]<\/li>\r\n \t<li>[latex]\\begin{array}{rr}&amp;583\\\\\\times&amp;8\\\\\\hline\\\\\\end{array}[\/latex]<\/li>\r\n \t<li>[latex]\\begin{array}{rr}&amp;952\\\\\\times&amp;9\\\\\\hline\\\\\\end{array}[\/latex]<\/li>\r\n \t<li>[latex]\\begin{array}{rr}&amp;293\\\\\\times&amp;7\\\\\\hline\\\\\\end{array}[\/latex]<\/li>\r\n<\/ol>\r\n<strong>Answers to Exercise 4<\/strong>\r\n<ol class=\"threecolumn\" type=\"a\">\r\n \t<li>5<span style=\"margin-left: 0.25em\">832<\/span><\/li>\r\n \t<li>1<span style=\"margin-left: 0.25em\">680<\/span><\/li>\r\n \t<li>3<span style=\"margin-left: 0.25em\">656<\/span><\/li>\r\n \t<li>808<\/li>\r\n \t<li>954<\/li>\r\n \t<li>624<\/li>\r\n \t<li>3<span style=\"margin-left: 0.25em\">256<\/span><\/li>\r\n \t<li>1<span style=\"margin-left: 0.25em\">434<\/span><\/li>\r\n \t<li>1<span style=\"margin-left: 0.25em\">062<\/span><\/li>\r\n \t<li>2<span style=\"margin-left: 0.25em\">975<\/span><\/li>\r\n \t<li>1<span style=\"margin-left: 0.25em\">112<\/span><\/li>\r\n \t<li>1<span style=\"margin-left: 0.25em\">130<\/span><\/li>\r\n \t<li>744<\/li>\r\n \t<li>3<span style=\"margin-left: 0.25em\">624<\/span><\/li>\r\n \t<li>956<\/li>\r\n \t<li>1<span style=\"margin-left: 0.25em\">728<\/span><\/li>\r\n \t<li>5<span style=\"margin-left: 0.25em\">142<\/span><\/li>\r\n \t<li>4<span style=\"margin-left: 0.25em\">302<\/span><\/li>\r\n \t<li>4<span style=\"margin-left: 0.25em\">718<\/span><\/li>\r\n \t<li>5<span style=\"margin-left: 0.25em\">032<\/span><\/li>\r\n \t<li>4<span style=\"margin-left: 0.25em\">465<\/span><\/li>\r\n \t<li>4<span style=\"margin-left: 0.25em\">664<\/span><\/li>\r\n \t<li>8<span style=\"margin-left: 0.25em\">568<\/span><\/li>\r\n \t<li>2<span style=\"margin-left: 0.25em\">051<\/span><\/li>\r\n<\/ol>\r\n&nbsp;\r\n\r\n<\/div>\r\n<\/div>\r\n<div class=\"textbox textbox--examples\"><header class=\"textbox__header\">\r\n<p class=\"textbox__title\">Example G<\/p>\r\n\r\n<\/header>\r\n<div class=\"textbox__content\">\r\n\r\n[latex]\\begin{array}{rr}&amp;2408\\\\\\times&amp;9\\\\\\hline\\end{array}[\/latex]\r\n<p style=\"text-align: center\">[latex]\\begin{array}{rr}&amp;_3\\hspace{0.7em}_7\\hspace{0.5em}\\\\&amp;2408\\\\\\times&amp;9\\\\\\hline&amp;21672\\end{array}[\/latex]<\/p>\r\n<strong>Step 1:<\/strong> 9 \u00d7 8 ones = 72 ones = 7 tens and 2 ones\r\n\r\n<strong>Step 2:<\/strong> 9 \u00d7 0 = 0 tens. 0 tens + 7 tens = 7 tens\r\n\r\n<strong>Step 3:<\/strong> 9 \u00d7 4 hundreds = 36 hundreds = 3 thousands and 6 hundreds\r\n\r\n<strong>Step 4:<\/strong> 9 \u00d7 2 thousands = 18 thousands. 18 thousands + 3 thousands = 21 thousands\r\n\r\n<\/div>\r\n<\/div>\r\n<div class=\"textbox textbox--exercises\"><header class=\"textbox__header\">\r\n<p class=\"textbox__title\">Exercise 5<\/p>\r\n\r\n<\/header>\r\n<div class=\"textbox__content\">\r\n\r\nFind the products. Check your work using the answer key at the end of the exercise.\r\n<ol class=\"threecolumn\" type=\"a\">\r\n \t<li>[latex]\\begin{array}{rr}&amp;4103\\\\\\times&amp;8\\\\\\hline\\\\\\end{array}[\/latex]<\/li>\r\n \t<li>[latex]\\begin{array}{rr}&amp;6087\\\\\\times&amp;4\\\\\\hline\\\\\\end{array}[\/latex]<\/li>\r\n \t<li>[latex]\\begin{array}{rr}&amp;3280\\\\\\times&amp;6\\\\\\hline\\\\\\end{array}[\/latex]<\/li>\r\n \t<li>[latex]\\begin{array}{rr}&amp;7034\\\\\\times&amp;5\\\\\\hline\\\\\\end{array}[\/latex]<\/li>\r\n \t<li>[latex]\\begin{array}{rr}&amp;8456\\\\\\times&amp;2\\\\\\hline\\\\\\end{array}[\/latex]<\/li>\r\n \t<li>[latex]\\begin{array}{rr}&amp;4758\\\\\\times&amp;7\\\\\\hline\\\\\\end{array}[\/latex]<\/li>\r\n \t<li>[latex]\\begin{array}{rr}&amp;4735\\\\\\times&amp;3\\\\\\hline\\\\\\end{array}[\/latex]<\/li>\r\n \t<li>[latex]\\begin{array}{rr}&amp;5402\\\\\\times&amp;9\\\\\\hline\\\\\\end{array}[\/latex]<\/li>\r\n \t<li>[latex]\\begin{array}{rr}&amp;5394\\\\\\times&amp;4\\\\\\hline\\\\\\end{array}[\/latex]<\/li>\r\n \t<li>[latex]\\begin{array}{rr}&amp;2034\\\\\\times&amp;8\\\\\\hline\\\\\\end{array}[\/latex]<\/li>\r\n \t<li>[latex]\\begin{array}{rr}&amp;8652\\\\\\times&amp;5\\\\\\hline\\\\\\end{array}[\/latex]<\/li>\r\n \t<li>[latex]\\begin{array}{rr}&amp;6392\\\\\\times&amp;7\\\\\\hline\\\\\\end{array}[\/latex]<\/li>\r\n \t<li>[latex]\\begin{array}{rr}&amp;4187\\\\\\times&amp;6\\\\\\hline\\\\\\end{array}[\/latex]<\/li>\r\n \t<li>[latex]\\begin{array}{rr}&amp;1376\\\\\\times&amp;9\\\\\\hline\\\\\\end{array}[\/latex]<\/li>\r\n \t<li>[latex]\\begin{array}{rr}&amp;3297\\\\\\times&amp;2\\\\\\hline\\\\\\end{array}[\/latex]<\/li>\r\n \t<li>[latex]\\begin{array}{rr}&amp;9628\\\\\\times&amp;3\\\\\\hline\\\\\\end{array}[\/latex]<\/li>\r\n \t<li>[latex]\\begin{array}{rr}&amp;7689\\\\\\times&amp;8\\\\\\hline\\\\\\end{array}[\/latex]<\/li>\r\n \t<li>[latex]\\begin{array}{rr}&amp;5160\\\\\\times&amp;3\\\\\\hline\\\\\\end{array}[\/latex]<\/li>\r\n \t<li>[latex]\\begin{array}{rr}&amp;4256\\\\\\times&amp;7\\\\\\hline\\\\\\end{array}[\/latex]<\/li>\r\n \t<li>[latex]\\begin{array}{rr}&amp;5491\\\\\\times&amp;5\\\\\\hline\\\\\\end{array}[\/latex]<\/li>\r\n \t<li>[latex]\\begin{array}{rr}&amp;8032\\\\\\times&amp;9\\\\\\hline\\\\\\end{array}[\/latex]<\/li>\r\n \t<li>[latex]\\begin{array}{rr}&amp;8645\\\\\\times&amp;6\\\\\\hline\\\\\\end{array}[\/latex]<\/li>\r\n \t<li>[latex]\\begin{array}{rr}&amp;6453\\\\\\times&amp;2\\\\\\hline\\\\\\end{array}[\/latex]<\/li>\r\n \t<li>[latex]\\begin{array}{rr}&amp;8129\\\\\\times&amp;4\\\\\\hline\\\\\\end{array}[\/latex]<\/li>\r\n<\/ol>\r\n<strong>Answers to Exercise 5<\/strong>\r\n<ol class=\"threecolumn\" type=\"a\">\r\n \t<li>32<span style=\"margin-left: 0.25em\">824<\/span><\/li>\r\n \t<li>24<span style=\"margin-left: 0.25em\">348<\/span><\/li>\r\n \t<li>19<span style=\"margin-left: 0.25em\">680<\/span><\/li>\r\n \t<li>35<span style=\"margin-left: 0.25em\">170<\/span><\/li>\r\n \t<li>16<span style=\"margin-left: 0.25em\">912<\/span><\/li>\r\n \t<li>33<span style=\"margin-left: 0.25em\">306<\/span><\/li>\r\n \t<li>14<span style=\"margin-left: 0.25em\">205<\/span><\/li>\r\n \t<li>48<span style=\"margin-left: 0.25em\">618<\/span><\/li>\r\n \t<li>21<span style=\"margin-left: 0.25em\">576<\/span><\/li>\r\n \t<li>16<span style=\"margin-left: 0.25em\">272<\/span><\/li>\r\n \t<li>43<span style=\"margin-left: 0.25em\">260<\/span><\/li>\r\n \t<li>44<span style=\"margin-left: 0.25em\">744<\/span><\/li>\r\n \t<li>25<span style=\"margin-left: 0.25em\">122<\/span><\/li>\r\n \t<li>12<span style=\"margin-left: 0.25em\">384<\/span><\/li>\r\n \t<li>6<span style=\"margin-left: 0.25em\">594<\/span><\/li>\r\n \t<li>28<span style=\"margin-left: 0.25em\">884<\/span><\/li>\r\n \t<li>61<span style=\"margin-left: 0.25em\">512<\/span><\/li>\r\n \t<li>15<span style=\"margin-left: 0.25em\">480<\/span><\/li>\r\n \t<li>29<span style=\"margin-left: 0.25em\">792<\/span><\/li>\r\n \t<li>27<span style=\"margin-left: 0.25em\">455<\/span><\/li>\r\n \t<li>72<span style=\"margin-left: 0.25em\">288<\/span><\/li>\r\n \t<li>51<span style=\"margin-left: 0.25em\">870<\/span><\/li>\r\n \t<li>12<span style=\"margin-left: 0.25em\">906<\/span><\/li>\r\n \t<li>32<span style=\"margin-left: 0.25em\">516<\/span><\/li>\r\n<\/ol>\r\n<\/div>\r\n<\/div>\r\n<h1 class=\"page-break-before\">Topic A: Self-Test<\/h1>\r\n<strong>Mark\u00a0\u00a0 \/14 \u00a0\u00a0 Aim 11\/14<\/strong>\r\n<ol type=\"A\">\r\n \t<li>Find the products. (6 marks)\r\n<ol class=\"twocolumn\" type=\"a\">\r\n \t<li>[latex]\\begin{array}{rr}&amp;62\\\\\\times&amp;4\\\\\\hline\\\\\\end{array}[\/latex]<\/li>\r\n \t<li>[latex]\\begin{array}{rr}&amp;31\\\\\\times&amp;4\\\\\\hline\\\\\\end{array}[\/latex]<\/li>\r\n \t<li>[latex]\\begin{array}{rr}&amp;423\\\\\\times&amp;3\\\\\\hline\\\\\\end{array}[\/latex]<\/li>\r\n \t<li>[latex]\\begin{array}{rr}&amp;734\\\\\\times&amp;2\\\\\\hline\\\\\\end{array}[\/latex]<\/li>\r\n \t<li>[latex]\\begin{array}{rr}&amp;8342\\\\\\times&amp;2\\\\\\hline\\\\\\end{array}[\/latex]<\/li>\r\n \t<li>[latex]\\begin{array}{rr}&amp;5231\\\\\\times&amp;3\\\\\\hline\\\\\\end{array}[\/latex]<\/li>\r\n<\/ol>\r\n<\/li>\r\n \t<li>Multiply these numbers. (4 marks)\r\n<ol class=\"twocolumn\" type=\"a\">\r\n \t<li>[latex]\\begin{array}{rr}&amp;44\\\\\\times&amp;7\\\\\\hline\\\\\\end{array}[\/latex]<\/li>\r\n \t<li>[latex]\\begin{array}{rr}&amp;69\\\\\\times&amp;8\\\\\\hline\\\\\\end{array}[\/latex]<\/li>\r\n \t<li>[latex]\\begin{array}{rr}&amp;207\\\\\\times&amp;9\\\\\\hline\\\\\\end{array}[\/latex]<\/li>\r\n \t<li>[latex]\\begin{array}{rr}&amp;184\\\\\\times&amp;6\\\\\\hline\\\\\\end{array}[\/latex]<\/li>\r\n<\/ol>\r\n<\/li>\r\n \t<li>Find the products. (4 marks)\r\n<ol class=\"twocolumn\" type=\"a\">\r\n \t<li>[latex]\\begin{array}{rr}&amp;2834\\\\\\times&amp;5\\\\\\hline\\\\\\end{array}[\/latex]<\/li>\r\n \t<li>[latex]\\begin{array}{rr}&amp;4037\\\\\\times&amp;6\\\\\\hline\\\\\\end{array}[\/latex]<\/li>\r\n \t<li>[latex]\\begin{array}{rr}&amp;9241\\\\\\times&amp;8\\\\\\hline\\\\\\end{array}[\/latex]<\/li>\r\n \t<li>[latex]\\begin{array}{rr}&amp;3652\\\\\\times&amp;4\\\\\\hline\\\\\\end{array}[\/latex]<\/li>\r\n<\/ol>\r\n<\/li>\r\n<\/ol>\r\n<h2>Answers to Topic A Self-Test<\/h2>\r\n<ol type=\"A\">\r\n \t<li>Find the products.\r\n<ol class=\"twocolumn\" type=\"a\">\r\n \t<li>248<\/li>\r\n \t<li>124<\/li>\r\n \t<li>1<span style=\"margin-left: 0.25em\">269<\/span><\/li>\r\n \t<li>1<span style=\"margin-left: 0.25em\">468<\/span><\/li>\r\n \t<li>16<span style=\"margin-left: 0.25em\">684<\/span><\/li>\r\n \t<li>15<span style=\"margin-left: 0.25em\">693<\/span><\/li>\r\n<\/ol>\r\n<\/li>\r\n \t<li>Multiply these numbers.\r\n<ol class=\"twocolumn\" type=\"a\">\r\n \t<li>308<\/li>\r\n \t<li>552<\/li>\r\n \t<li>1<span style=\"margin-left: 0.25em\">863<\/span><\/li>\r\n \t<li>1<span style=\"margin-left: 0.25em\">104<\/span><\/li>\r\n<\/ol>\r\n<\/li>\r\n \t<li>Find the products.\r\n<ol class=\"twocolumn\" type=\"a\">\r\n \t<li>14<span style=\"margin-left: 0.25em\">170<\/span><\/li>\r\n \t<li>24<span style=\"margin-left: 0.25em\">222<\/span><\/li>\r\n \t<li>73<span style=\"margin-left: 0.25em\">928<\/span><\/li>\r\n \t<li>14<span style=\"margin-left: 0.25em\">608<\/span><\/li>\r\n<\/ol>\r\n<\/li>\r\n<\/ol>","rendered":"<p>It is usually easier to multiply larger numbers if they are written underneath each other. The bottom number is called the multiplier.<\/p>\n<p><strong>To find the product of a one digit multiplier,<\/strong> use as many of these steps as you need to complete each multiplication question:<\/p>\n<ul type=\"none\">\n<li><strong>Step 1:<\/strong> Multiply the ones digit in the large number by the one-digit multiplier.<\/li>\n<li><strong>Step 2:<\/strong> Multiply the tens digit in the large number by the multiplier.<\/li>\n<li><strong>Step 3:<\/strong> Multiply the hundreds digit in the large number by the multiplier.<\/li>\n<li><strong>Step 4:<\/strong> Multiply the thousands digit in the large number by the multiplier.<\/li>\n<\/ul>\n<div class=\"textbox textbox--examples\">\n<header class=\"textbox__header\">\n<p class=\"textbox__title\">Example A<\/p>\n<\/header>\n<div class=\"textbox__content\">\n<p>62 \u00d7 4 =<\/p>\n<p><strong>Step 1:<\/strong> 4 \u00d7 2 ones = 8<\/p>\n<p style=\"text-align: center\">[latex]\\begin{array}{rr}&62\\\\\\times&4\\\\\\hline&8\\end{array}[\/latex]<\/p>\n<p><strong>Step 2:<\/strong> 4 \u00d7 6 tens = 24 tens = 2 hundreds and 4 tens<\/p>\n<p style=\"text-align: center\">[latex]\\begin{array}{rr}&62\\\\\\times&4\\\\\\hline&248\\end{array}[\/latex]<\/p>\n<p>The product of 62 \u00d7 4 is 248.<\/p>\n<\/div>\n<\/div>\n<div class=\"textbox textbox--exercises\">\n<header class=\"textbox__header\">\n<p class=\"textbox__title\">Exercise 1<\/p>\n<\/header>\n<div class=\"textbox__content\">\n<p>Find the product. Check your work using the answer key at the<br \/>\nend of the exercise.<\/p>\n<ol class=\"threecolumn\" type=\"a\">\n<li>[latex]\\begin{array}{rr}&72\\\\\\times&2\\\\\\hline\\\\\\end{array}[\/latex]<\/li>\n<li>[latex]\\begin{array}{rr}&81\\\\\\times&5\\\\\\hline\\\\\\end{array}[\/latex]<\/li>\n<li>[latex]\\begin{array}{rr}&21\\\\\\times&8\\\\\\hline\\\\\\end{array}[\/latex]<\/li>\n<li>[latex]\\begin{array}{rr}&80\\\\\\times&6\\\\\\hline\\\\\\end{array}[\/latex]<\/li>\n<li>[latex]\\begin{array}{rr}&73\\\\\\times&3\\\\\\hline\\\\\\end{array}[\/latex]<\/li>\n<li>[latex]\\begin{array}{rr}&71\\\\\\times&3\\\\\\hline\\\\\\end{array}[\/latex]<\/li>\n<li>[latex]\\begin{array}{rr}&40\\\\\\times&7\\\\\\hline\\\\\\end{array}[\/latex]<\/li>\n<li>[latex]\\begin{array}{rr}&90\\\\\\times&9\\\\\\hline\\\\\\end{array}[\/latex]<\/li>\n<li>[latex]\\begin{array}{rr}&82\\\\\\times&4\\\\\\hline\\\\\\end{array}[\/latex]<\/li>\n<li>[latex]\\begin{array}{rr}&40\\\\\\times&5\\\\\\hline\\\\\\end{array}[\/latex]<\/li>\n<li>[latex]\\begin{array}{rr}&92\\\\\\times&4\\\\\\hline\\\\\\end{array}[\/latex]<\/li>\n<li>[latex]\\begin{array}{rr}&83\\\\\\times&3\\\\\\hline\\\\\\end{array}[\/latex]<\/li>\n<li>[latex]\\begin{array}{rr}&90\\\\\\times&8\\\\\\hline\\\\\\end{array}[\/latex]<\/li>\n<li>[latex]\\begin{array}{rr}&71\\\\\\times&9\\\\\\hline\\\\\\end{array}[\/latex]<\/li>\n<li>[latex]\\begin{array}{rr}&53\\\\\\times&2\\\\\\hline\\\\\\end{array}[\/latex]<\/li>\n<li>[latex]\\begin{array}{rr}&30\\\\\\times&6\\\\\\hline\\\\\\end{array}[\/latex]<\/li>\n<li>[latex]\\begin{array}{rr}&81\\\\\\times&7\\\\\\hline\\\\\\end{array}[\/latex]<\/li>\n<li>[latex]\\begin{array}{rr}&61\\\\\\times&2\\\\\\hline\\\\\\end{array}[\/latex]<\/li>\n<li>[latex]\\begin{array}{rr}&70\\\\\\times&8\\\\\\hline\\\\\\end{array}[\/latex]<\/li>\n<li>[latex]\\begin{array}{rr}&41\\\\\\times&6\\\\\\hline\\\\\\end{array}[\/latex]<\/li>\n<li>[latex]\\begin{array}{rr}&90\\\\\\times&5\\\\\\hline\\\\\\end{array}[\/latex]<\/li>\n<li>[latex]\\begin{array}{rr}&60\\\\\\times&9\\\\\\hline\\\\\\end{array}[\/latex]<\/li>\n<li>[latex]\\begin{array}{rr}&92\\\\\\times&3\\\\\\hline\\\\\\end{array}[\/latex]<\/li>\n<li>[latex]\\begin{array}{rr}&81\\\\\\times&4\\\\\\hline\\\\\\end{array}[\/latex]<\/li>\n<\/ol>\n<p><strong>Answers to Exercise 1<\/strong><\/p>\n<ol class=\"threecolumn\" type=\"a\">\n<li>144<\/li>\n<li>405<\/li>\n<li>168<\/li>\n<li>480<\/li>\n<li>219<\/li>\n<li>213<\/li>\n<li>280<\/li>\n<li>810<\/li>\n<li>328<\/li>\n<li>200<\/li>\n<li>368<\/li>\n<li>249<\/li>\n<li>720<\/li>\n<li>639<\/li>\n<li>106<\/li>\n<li>180<\/li>\n<li>567<\/li>\n<li>122<\/li>\n<li>560<\/li>\n<li>246<\/li>\n<li>450<\/li>\n<li>540<\/li>\n<li>276<\/li>\n<li>324<\/li>\n<\/ol>\n<\/div>\n<\/div>\n<div class=\"textbox textbox--examples\">\n<header class=\"textbox__header\">\n<p class=\"textbox__title\">Example B<\/p>\n<\/header>\n<div class=\"textbox__content\">\n<p>523 \u00d7 3 =<\/p>\n<p style=\"text-align: center\">[latex]\\begin{array}{rr}&523\\\\\\times&3\\\\\\hline&1569\\end{array}[\/latex]<\/p>\n<p><strong>Step 1:<\/strong> 3 \u00d7 3 ones = 9 ones<\/p>\n<p><strong>Step 2:<\/strong> 3 \u00d7 2 tens = 6 tens<\/p>\n<p><strong>Step 3:<\/strong> 3 \u00d7 5 hundreds = 15 hundreds = 1 thousand and 5 hundreds<\/p>\n<p>The product of 523 \u00d7 3 is 1<span style=\"margin-left: 0.25em\">569<\/span>.<\/p>\n<\/div>\n<\/div>\n<div class=\"textbox textbox--examples\">\n<header class=\"textbox__header\">\n<p class=\"textbox__title\">Example C<\/p>\n<\/header>\n<div class=\"textbox__content\">\n<p>901 \u00d7 8 =<\/p>\n<p style=\"text-align: center\">[latex]\\begin{array}{rr}&901\\\\\\times&8\\\\\\hline&7208\\end{array}[\/latex]<\/p>\n<p><strong>Step 1:<\/strong> 8 \u00d7 1 one = 8 ones<\/p>\n<p><strong>Step 2:<\/strong> 8 \u00d7 0 tens = 0 tens<\/p>\n<p><strong>Step 3:<\/strong> 8 \u00d7 9 hundreds = 72 hundreds = 7 thousands and 2 hundreds<\/p>\n<p>The product of 901 \u00d7 8 is 7<span style=\"margin-left: 0.25em\">208.<\/span><\/p>\n<\/div>\n<\/div>\n<div class=\"textbox textbox--exercises\">\n<header class=\"textbox__header\">\n<p class=\"textbox__title\">Exercise 2<\/p>\n<\/header>\n<div class=\"textbox__content\">\n<p>Find the product. Check your work using the answer key at the<br \/>\nend of the exercise.<\/p>\n<ol class=\"threecolumn\" type=\"a\">\n<li>[latex]\\begin{array}{rr}&601\\\\\\times&7\\\\\\hline\\\\\\end{array}[\/latex]<\/li>\n<li>[latex]\\begin{array}{rr}&423\\\\\\times&3\\\\\\hline\\\\\\end{array}[\/latex]<\/li>\n<li>[latex]\\begin{array}{rr}&641\\\\\\times&2\\\\\\hline\\\\\\end{array}[\/latex]<\/li>\n<li>[latex]\\begin{array}{rr}&922\\\\\\times&4\\\\\\hline\\\\\\end{array}[\/latex]<\/li>\n<li>[latex]\\begin{array}{rr}&820\\\\\\times&4\\\\\\hline\\\\\\end{array}[\/latex]<\/li>\n<li>[latex]\\begin{array}{rr}&211\\\\\\times&5\\\\\\hline\\\\\\end{array}[\/latex]<\/li>\n<li>[latex]\\begin{array}{rr}&803\\\\\\times&2\\\\\\hline\\\\\\end{array}[\/latex]<\/li>\n<li>[latex]\\begin{array}{rr}&542\\\\\\times&2\\\\\\hline\\\\\\end{array}[\/latex]<\/li>\n<li>[latex]\\begin{array}{rr}&813\\\\\\times&3\\\\\\hline\\\\\\end{array}[\/latex]<\/li>\n<li>[latex]\\begin{array}{rr}&610\\\\\\times&4\\\\\\hline\\\\\\end{array}[\/latex]<\/li>\n<li>[latex]\\begin{array}{rr}&901\\\\\\times&6\\\\\\hline\\\\\\end{array}[\/latex]<\/li>\n<li>[latex]\\begin{array}{rr}&711\\\\\\times&8\\\\\\hline\\\\\\end{array}[\/latex]<\/li>\n<li>[latex]\\begin{array}{rr}&720\\\\\\times&3\\\\\\hline\\\\\\end{array}[\/latex]<\/li>\n<li>[latex]\\begin{array}{rr}&910\\\\\\times&5\\\\\\hline\\\\\\end{array}[\/latex]<\/li>\n<li>[latex]\\begin{array}{rr}&801\\\\\\times&6\\\\\\hline\\\\\\end{array}[\/latex]<\/li>\n<li>[latex]\\begin{array}{rr}&932\\\\\\times&3\\\\\\hline\\\\\\end{array}[\/latex]<\/li>\n<li>[latex]\\begin{array}{rr}&731\\\\\\times&2\\\\\\hline\\\\\\end{array}[\/latex]<\/li>\n<li>[latex]\\begin{array}{rr}&701\\\\\\times&5\\\\\\hline\\\\\\end{array}[\/latex]<\/li>\n<li>[latex]\\begin{array}{rr}&521\\\\\\times&2\\\\\\hline\\\\\\end{array}[\/latex]<\/li>\n<li>[latex]\\begin{array}{rr}&632\\\\\\times&3\\\\\\hline\\\\\\end{array}[\/latex]<\/li>\n<li>[latex]\\begin{array}{rr}&720\\\\\\times&4\\\\\\hline\\\\\\end{array}[\/latex]<\/li>\n<li>[latex]\\begin{array}{rr}&942\\\\\\times&2\\\\\\hline\\\\\\end{array}[\/latex]<\/li>\n<li>[latex]\\begin{array}{rr}&710\\\\\\times&9\\\\\\hline\\\\\\end{array}[\/latex]<\/li>\n<li>[latex]\\begin{array}{rr}&601\\\\\\times&8\\\\\\hline\\\\\\end{array}[\/latex]<\/li>\n<\/ol>\n<p><strong>Answers to Exercise 2<\/strong><\/p>\n<ol class=\"threecolumn\" type=\"a\">\n<li>4<span style=\"margin-left: 0.25em\">207<\/span><\/li>\n<li>1<span style=\"margin-left: 0.25em\">269<\/span><\/li>\n<li>1<span style=\"margin-left: 0.25em\">282<\/span><\/li>\n<li>3<span style=\"margin-left: 0.25em\">688<\/span><\/li>\n<li>3<span style=\"margin-left: 0.25em\">280<\/span><\/li>\n<li>1<span style=\"margin-left: 0.25em\">055<\/span><\/li>\n<li>1<span style=\"margin-left: 0.25em\">606<\/span><\/li>\n<li>1<span style=\"margin-left: 0.25em\">084<\/span><\/li>\n<li>2<span style=\"margin-left: 0.25em\">439<\/span><\/li>\n<li>2<span style=\"margin-left: 0.25em\">440<\/span><\/li>\n<li>5<span style=\"margin-left: 0.25em\">406<\/span><\/li>\n<li>5<span style=\"margin-left: 0.25em\">688<\/span><\/li>\n<li>2<span style=\"margin-left: 0.25em\">160<\/span><\/li>\n<li>4<span style=\"margin-left: 0.25em\">550<\/span><\/li>\n<li>4<span style=\"margin-left: 0.25em\">806<\/span><\/li>\n<li>2<span style=\"margin-left: 0.25em\">796<\/span><\/li>\n<li>1<span style=\"margin-left: 0.25em\">462<\/span><\/li>\n<li>3<span style=\"margin-left: 0.25em\">505<\/span><\/li>\n<li>1<span style=\"margin-left: 0.25em\">042<\/span><\/li>\n<li>1<span style=\"margin-left: 0.25em\">896<\/span><\/li>\n<li>2<span style=\"margin-left: 0.25em\">880<\/span><\/li>\n<li>1<span style=\"margin-left: 0.25em\">884<\/span><\/li>\n<li>6<span style=\"margin-left: 0.25em\">390<\/span><\/li>\n<li>4<span style=\"margin-left: 0.25em\">808<\/span><\/li>\n<\/ol>\n<\/div>\n<\/div>\n<h1>Renaming and Carrying<\/h1>\n<p>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.<\/p>\n<div class=\"textbox textbox--examples\">\n<header class=\"textbox__header\">\n<p class=\"textbox__title\">Example D<\/p>\n<\/header>\n<div class=\"textbox__content\">\n<p>[latex]\\begin{array}{rr}&68\\\\\\times&7\\\\\\hline\\end{array}[\/latex]<\/p>\n<p><strong>Step 1:<\/strong> Multiply the ones by the multiplier.<\/p>\n<p>7 \u00d7 8 ones = 56 ones = 5 tens + 6 ones<\/p>\n<p>Write the 6 ones in the product.<\/p>\n<p>Carry the 5 tens to the tens column and make a note of it for yourself. You might write it above the tens column.<\/p>\n<p style=\"text-align: center\">[latex]\\begin{array}{rrr}&_5\\hspace{0.5em}\\\\&68\\\\\\times&7\\\\\\hline&6\\end{array}[\/latex]<\/p>\n<p><strong>Step 2:<\/strong> Multiply the tens by the multiplier.<\/p>\n<p>7 \u00d7 6 tens = 42 tens<\/p>\n<p>Now add on the 5 tens that you carried.<\/p>\n<p>42 tens + 5 tens = 47 tens = 4 hundreds and 7 tens<\/p>\n<p style=\"text-align: center\">[latex]\\begin{array}{rrr}&_5\\hspace{0.5em}\\\\&68\\\\\\times&7\\\\\\hline&476\\end{array}[\/latex]<\/p>\n<\/div>\n<\/div>\n<div class=\"textbox textbox--exercises\">\n<header class=\"textbox__header\">\n<p class=\"textbox__title\">Exercise 3<\/p>\n<\/header>\n<div class=\"textbox__content\">\n<p>Find the product. Check your work using the answer key at the end of the exercise.<\/p>\n<ol class=\"threecolumn\" type=\"a\">\n<li>[latex]\\begin{array}{rr}&16\\\\\\times&8\\\\\\hline\\\\\\end{array}[\/latex]<\/li>\n<li>[latex]\\begin{array}{rr}&62\\\\\\times&6\\\\\\hline\\\\\\end{array}[\/latex]<\/li>\n<li>[latex]\\begin{array}{rr}&37\\\\\\times&4\\\\\\hline\\\\\\end{array}[\/latex]<\/li>\n<li>[latex]\\begin{array}{rr}&14\\\\\\times&9\\\\\\hline\\\\\\end{array}[\/latex]<\/li>\n<li>[latex]\\begin{array}{rr}&36\\\\\\times&7\\\\\\hline\\\\\\end{array}[\/latex]<\/li>\n<li>[latex]\\begin{array}{rr}&92\\\\\\times&9\\\\\\hline\\\\\\end{array}[\/latex]<\/li>\n<li>[latex]\\begin{array}{rr}&48\\\\\\times&6\\\\\\hline\\\\\\end{array}[\/latex]<\/li>\n<li>[latex]\\begin{array}{rr}&17\\\\\\times&2\\\\\\hline\\\\\\end{array}[\/latex]<\/li>\n<li>[latex]\\begin{array}{rr}&26\\\\\\times&4\\\\\\hline\\\\\\end{array}[\/latex]<\/li>\n<li>[latex]\\begin{array}{rr}&54\\\\\\times&7\\\\\\hline\\\\\\end{array}[\/latex]<\/li>\n<li>[latex]\\begin{array}{rr}&58\\\\\\times&8\\\\\\hline\\\\\\end{array}[\/latex]<\/li>\n<li>[latex]\\begin{array}{rr}&45\\\\\\times&4\\\\\\hline\\\\\\end{array}[\/latex]<\/li>\n<li>[latex]\\begin{array}{rr}&56\\\\\\times&3\\\\\\hline\\\\\\end{array}[\/latex]<\/li>\n<li>[latex]\\begin{array}{rr}&47\\\\\\times&5\\\\\\hline\\\\\\end{array}[\/latex]<\/li>\n<li>[latex]\\begin{array}{rr}&39\\\\\\times&6\\\\\\hline\\\\\\end{array}[\/latex]<\/li>\n<li>[latex]\\begin{array}{rr}&75\\\\\\times&6\\\\\\hline\\\\\\end{array}[\/latex]<\/li>\n<li>[latex]\\begin{array}{rr}&38\\\\\\times&5\\\\\\hline\\\\\\end{array}[\/latex]<\/li>\n<li>[latex]\\begin{array}{rr}&82\\\\\\times&7\\\\\\hline\\\\\\end{array}[\/latex]<\/li>\n<li>[latex]\\begin{array}{rr}&98\\\\\\times&3\\\\\\hline\\\\\\end{array}[\/latex]<\/li>\n<li>[latex]\\begin{array}{rr}&29\\\\\\times&5\\\\\\hline\\\\\\end{array}[\/latex]<\/li>\n<li>[latex]\\begin{array}{rr}&47\\\\\\times&3\\\\\\hline\\\\\\end{array}[\/latex]<\/li>\n<li>[latex]\\begin{array}{rr}&74\\\\\\times&8\\\\\\hline\\\\\\end{array}[\/latex]<\/li>\n<li>[latex]\\begin{array}{rr}&56\\\\\\times&5\\\\\\hline\\\\\\end{array}[\/latex]<\/li>\n<li>[latex]\\begin{array}{rr}&98\\\\\\times&4\\\\\\hline\\\\\\end{array}[\/latex]<\/li>\n<\/ol>\n<p><strong>Answers to Exercise 3<\/strong><\/p>\n<ol class=\"threecolumn\" type=\"a\">\n<li>128<\/li>\n<li>372<\/li>\n<li>148<\/li>\n<li>126<\/li>\n<li>252<\/li>\n<li>828<\/li>\n<li>288<\/li>\n<li>34<\/li>\n<li>104<\/li>\n<li>378<\/li>\n<li>464<\/li>\n<li>180<\/li>\n<li>168<\/li>\n<li>235<\/li>\n<li>234<\/li>\n<li>450<\/li>\n<li>190<\/li>\n<li>574<\/li>\n<li>294<\/li>\n<li>145<\/li>\n<li>141<\/li>\n<li>592<\/li>\n<li>280<\/li>\n<li>392<\/li>\n<\/ol>\n<\/div>\n<\/div>\n<div class=\"textbox textbox--examples\">\n<header class=\"textbox__header\">\n<p class=\"textbox__title\">Example E<\/p>\n<\/header>\n<div class=\"textbox__content\">\n<p>[latex]4\\times224=[\/latex]\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0 [latex]\\begin{array}{rr}&224\\\\\\times&4\\\\\\hline\\end{array}[\/latex]<\/p>\n<p><strong>Step 1:<\/strong> 4 \u00d7 4 ones = 16 ones = 1 ten and 6 ones<\/p>\n<p style=\"padding-left: 40px\">Write the 6 ones in the product and carry the one ten.<\/p>\n<p style=\"text-align: center\">[latex]\\begin{array}{rr}&_1\\hspace{0.5em}\\\\&224\\\\\\times&4\\\\\\hline&6\\end{array}[\/latex]<\/p>\n<p><strong>Step 2:<\/strong> 4 \u00d7 2 tens = 8 tens<\/p>\n<p style=\"padding-left: 40px\">8 tens + 1 ten we carried = 9 tens<\/p>\n<p style=\"text-align: center\">[latex]\\begin{array}{rr}&_1\\hspace{0.5em}\\\\&224\\\\\\times&4\\\\\\hline&96\\end{array}[\/latex]<\/p>\n<p><strong>Step 3:<\/strong> 4 \u00d7 2 hundreds = 8 hundreds<\/p>\n<p style=\"text-align: center\">[latex]\\begin{array}{rr}&_1\\hspace{0.5em}\\\\&224\\\\\\times&4\\\\\\hline&896\\end{array}[\/latex]<\/p>\n<p>&nbsp;<\/p>\n<\/div>\n<\/div>\n<div class=\"textbox textbox--examples\">\n<header class=\"textbox__header\">\n<p class=\"textbox__title\">Example F<\/p>\n<\/header>\n<div class=\"textbox__content\">\n<p>[latex]4\\times456=[\/latex] \u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0 [latex]\\begin{array}{rr}&456\\\\\\times&5\\\\\\hline\\end{array}[\/latex]<\/p>\n<p><strong>Step 1:<\/strong> 5 \u00d7 6 ones = 30 ones = 3 ten and 0 ones<\/p>\n<p style=\"padding-left: 40px\">The 0 must be written to hold the ones place. Carry the 3 tens.<\/p>\n<p style=\"text-align: center\">[latex]\\begin{array}{rr}&_3\\hspace{0.5em}\\\\&456\\\\\\times&5\\\\\\hline&0\\end{array}[\/latex]<\/p>\n<p><strong>Step 2:<\/strong> 5 \u00d7 5 tens = 25 tens<\/p>\n<p style=\"padding-left: 40px\">25 tens + 3 tens = 28 tens = 2 hundreds and 8 tens<\/p>\n<p style=\"padding-left: 40px\">Write the 8 tens in the product. Carry the 2 hundreds.<\/p>\n<p style=\"text-align: center\">[latex]\\begin{array}{rr}&_{2\\text{ }3}\\hspace{0.5em}\\\\&456\\\\\\times&5\\\\\\hline&80\\end{array}[\/latex]<\/p>\n<p><strong>Step 3:<\/strong> 5 \u00d7 4 hundreds = 20 hundreds + 2 hundreds = 22 hundreds = 2 thousands and 2 hundreds<\/p>\n<p style=\"text-align: center\">[latex]\\begin{array}{rr}&_{2\\text{ }3}\\hspace{0.5em}\\\\&456\\\\\\times&5\\\\\\hline&2280\\end{array}[\/latex]<\/p>\n<\/div>\n<\/div>\n<div class=\"textbox textbox--exercises\">\n<header class=\"textbox__header\">\n<p class=\"textbox__title\">Exercise 4<\/p>\n<\/header>\n<div class=\"textbox__content\">\n<p>Find the products. Check your work using the answer key at the end of the exercise.<\/p>\n<ol class=\"threecolumn\" type=\"a\">\n<li>[latex]\\begin{array}{rr}&648\\\\\\times&9\\\\\\hline\\\\\\end{array}[\/latex]<\/li>\n<li>[latex]\\begin{array}{rr}&240\\\\\\times&7\\\\\\hline\\\\\\end{array}[\/latex]<\/li>\n<li>[latex]\\begin{array}{rr}&457\\\\\\times&8\\\\\\hline\\\\\\end{array}[\/latex]<\/li>\n<li>[latex]\\begin{array}{rr}&404\\\\\\times&2\\\\\\hline\\\\\\end{array}[\/latex]<\/li>\n<li>[latex]\\begin{array}{rr}&106\\\\\\times&9\\\\\\hline\\\\\\end{array}[\/latex]<\/li>\n<li>[latex]\\begin{array}{rr}&156\\\\\\times&4\\\\\\hline\\\\\\end{array}[\/latex]<\/li>\n<li>[latex]\\begin{array}{rr}&407\\\\\\times&8\\\\\\hline\\\\\\end{array}[\/latex]<\/li>\n<li>[latex]\\begin{array}{rr}&239\\\\\\times&6\\\\\\hline\\\\\\end{array}[\/latex]<\/li>\n<li>[latex]\\begin{array}{rr}&118\\\\\\times&9\\\\\\hline\\\\\\end{array}[\/latex]<\/li>\n<li>[latex]\\begin{array}{rr}&425\\\\\\times&7\\\\\\hline\\\\\\end{array}[\/latex]<\/li>\n<li>[latex]\\begin{array}{rr}&139\\\\\\times&8\\\\\\hline\\\\\\end{array}[\/latex]<\/li>\n<li>[latex]\\begin{array}{rr}&565\\\\\\times&2\\\\\\hline\\\\\\end{array}[\/latex]<\/li>\n<li>[latex]\\begin{array}{rr}&248\\\\\\times&3\\\\\\hline\\\\\\end{array}[\/latex]<\/li>\n<li>[latex]\\begin{array}{rr}&604\\\\\\times&6\\\\\\hline\\\\\\end{array}[\/latex]<\/li>\n<li>[latex]\\begin{array}{rr}&239\\\\\\times&4\\\\\\hline\\\\\\end{array}[\/latex]<\/li>\n<li>[latex]\\begin{array}{rr}&576\\\\\\times&3\\\\\\hline\\\\\\end{array}[\/latex]<\/li>\n<li>[latex]\\begin{array}{rr}&857\\\\\\times&6\\\\\\hline\\\\\\end{array}[\/latex]<\/li>\n<li>[latex]\\begin{array}{rr}&478\\\\\\times&9\\\\\\hline\\\\\\end{array}[\/latex]<\/li>\n<li>[latex]\\begin{array}{rr}&674\\\\\\times&7\\\\\\hline\\\\\\end{array}[\/latex]<\/li>\n<li>[latex]\\begin{array}{rr}&629\\\\\\times&8\\\\\\hline\\\\\\end{array}[\/latex]<\/li>\n<li>[latex]\\begin{array}{rr}&893\\\\\\times&5\\\\\\hline\\\\\\end{array}[\/latex]<\/li>\n<li>[latex]\\begin{array}{rr}&583\\\\\\times&8\\\\\\hline\\\\\\end{array}[\/latex]<\/li>\n<li>[latex]\\begin{array}{rr}&952\\\\\\times&9\\\\\\hline\\\\\\end{array}[\/latex]<\/li>\n<li>[latex]\\begin{array}{rr}&293\\\\\\times&7\\\\\\hline\\\\\\end{array}[\/latex]<\/li>\n<\/ol>\n<p><strong>Answers to Exercise 4<\/strong><\/p>\n<ol class=\"threecolumn\" type=\"a\">\n<li>5<span style=\"margin-left: 0.25em\">832<\/span><\/li>\n<li>1<span style=\"margin-left: 0.25em\">680<\/span><\/li>\n<li>3<span style=\"margin-left: 0.25em\">656<\/span><\/li>\n<li>808<\/li>\n<li>954<\/li>\n<li>624<\/li>\n<li>3<span style=\"margin-left: 0.25em\">256<\/span><\/li>\n<li>1<span style=\"margin-left: 0.25em\">434<\/span><\/li>\n<li>1<span style=\"margin-left: 0.25em\">062<\/span><\/li>\n<li>2<span style=\"margin-left: 0.25em\">975<\/span><\/li>\n<li>1<span style=\"margin-left: 0.25em\">112<\/span><\/li>\n<li>1<span style=\"margin-left: 0.25em\">130<\/span><\/li>\n<li>744<\/li>\n<li>3<span style=\"margin-left: 0.25em\">624<\/span><\/li>\n<li>956<\/li>\n<li>1<span style=\"margin-left: 0.25em\">728<\/span><\/li>\n<li>5<span style=\"margin-left: 0.25em\">142<\/span><\/li>\n<li>4<span style=\"margin-left: 0.25em\">302<\/span><\/li>\n<li>4<span style=\"margin-left: 0.25em\">718<\/span><\/li>\n<li>5<span style=\"margin-left: 0.25em\">032<\/span><\/li>\n<li>4<span style=\"margin-left: 0.25em\">465<\/span><\/li>\n<li>4<span style=\"margin-left: 0.25em\">664<\/span><\/li>\n<li>8<span style=\"margin-left: 0.25em\">568<\/span><\/li>\n<li>2<span style=\"margin-left: 0.25em\">051<\/span><\/li>\n<\/ol>\n<p>&nbsp;<\/p>\n<\/div>\n<\/div>\n<div class=\"textbox textbox--examples\">\n<header class=\"textbox__header\">\n<p class=\"textbox__title\">Example G<\/p>\n<\/header>\n<div class=\"textbox__content\">\n<p>[latex]\\begin{array}{rr}&2408\\\\\\times&9\\\\\\hline\\end{array}[\/latex]<\/p>\n<p style=\"text-align: center\">[latex]\\begin{array}{rr}&_3\\hspace{0.7em}_7\\hspace{0.5em}\\\\&2408\\\\\\times&9\\\\\\hline&21672\\end{array}[\/latex]<\/p>\n<p><strong>Step 1:<\/strong> 9 \u00d7 8 ones = 72 ones = 7 tens and 2 ones<\/p>\n<p><strong>Step 2:<\/strong> 9 \u00d7 0 = 0 tens. 0 tens + 7 tens = 7 tens<\/p>\n<p><strong>Step 3:<\/strong> 9 \u00d7 4 hundreds = 36 hundreds = 3 thousands and 6 hundreds<\/p>\n<p><strong>Step 4:<\/strong> 9 \u00d7 2 thousands = 18 thousands. 18 thousands + 3 thousands = 21 thousands<\/p>\n<\/div>\n<\/div>\n<div class=\"textbox textbox--exercises\">\n<header class=\"textbox__header\">\n<p class=\"textbox__title\">Exercise 5<\/p>\n<\/header>\n<div class=\"textbox__content\">\n<p>Find the products. Check your work using the answer key at the end of the exercise.<\/p>\n<ol class=\"threecolumn\" type=\"a\">\n<li>[latex]\\begin{array}{rr}&4103\\\\\\times&8\\\\\\hline\\\\\\end{array}[\/latex]<\/li>\n<li>[latex]\\begin{array}{rr}&6087\\\\\\times&4\\\\\\hline\\\\\\end{array}[\/latex]<\/li>\n<li>[latex]\\begin{array}{rr}&3280\\\\\\times&6\\\\\\hline\\\\\\end{array}[\/latex]<\/li>\n<li>[latex]\\begin{array}{rr}&7034\\\\\\times&5\\\\\\hline\\\\\\end{array}[\/latex]<\/li>\n<li>[latex]\\begin{array}{rr}&8456\\\\\\times&2\\\\\\hline\\\\\\end{array}[\/latex]<\/li>\n<li>[latex]\\begin{array}{rr}&4758\\\\\\times&7\\\\\\hline\\\\\\end{array}[\/latex]<\/li>\n<li>[latex]\\begin{array}{rr}&4735\\\\\\times&3\\\\\\hline\\\\\\end{array}[\/latex]<\/li>\n<li>[latex]\\begin{array}{rr}&5402\\\\\\times&9\\\\\\hline\\\\\\end{array}[\/latex]<\/li>\n<li>[latex]\\begin{array}{rr}&5394\\\\\\times&4\\\\\\hline\\\\\\end{array}[\/latex]<\/li>\n<li>[latex]\\begin{array}{rr}&2034\\\\\\times&8\\\\\\hline\\\\\\end{array}[\/latex]<\/li>\n<li>[latex]\\begin{array}{rr}&8652\\\\\\times&5\\\\\\hline\\\\\\end{array}[\/latex]<\/li>\n<li>[latex]\\begin{array}{rr}&6392\\\\\\times&7\\\\\\hline\\\\\\end{array}[\/latex]<\/li>\n<li>[latex]\\begin{array}{rr}&4187\\\\\\times&6\\\\\\hline\\\\\\end{array}[\/latex]<\/li>\n<li>[latex]\\begin{array}{rr}&1376\\\\\\times&9\\\\\\hline\\\\\\end{array}[\/latex]<\/li>\n<li>[latex]\\begin{array}{rr}&3297\\\\\\times&2\\\\\\hline\\\\\\end{array}[\/latex]<\/li>\n<li>[latex]\\begin{array}{rr}&9628\\\\\\times&3\\\\\\hline\\\\\\end{array}[\/latex]<\/li>\n<li>[latex]\\begin{array}{rr}&7689\\\\\\times&8\\\\\\hline\\\\\\end{array}[\/latex]<\/li>\n<li>[latex]\\begin{array}{rr}&5160\\\\\\times&3\\\\\\hline\\\\\\end{array}[\/latex]<\/li>\n<li>[latex]\\begin{array}{rr}&4256\\\\\\times&7\\\\\\hline\\\\\\end{array}[\/latex]<\/li>\n<li>[latex]\\begin{array}{rr}&5491\\\\\\times&5\\\\\\hline\\\\\\end{array}[\/latex]<\/li>\n<li>[latex]\\begin{array}{rr}&8032\\\\\\times&9\\\\\\hline\\\\\\end{array}[\/latex]<\/li>\n<li>[latex]\\begin{array}{rr}&8645\\\\\\times&6\\\\\\hline\\\\\\end{array}[\/latex]<\/li>\n<li>[latex]\\begin{array}{rr}&6453\\\\\\times&2\\\\\\hline\\\\\\end{array}[\/latex]<\/li>\n<li>[latex]\\begin{array}{rr}&8129\\\\\\times&4\\\\\\hline\\\\\\end{array}[\/latex]<\/li>\n<\/ol>\n<p><strong>Answers to Exercise 5<\/strong><\/p>\n<ol class=\"threecolumn\" type=\"a\">\n<li>32<span style=\"margin-left: 0.25em\">824<\/span><\/li>\n<li>24<span style=\"margin-left: 0.25em\">348<\/span><\/li>\n<li>19<span style=\"margin-left: 0.25em\">680<\/span><\/li>\n<li>35<span style=\"margin-left: 0.25em\">170<\/span><\/li>\n<li>16<span style=\"margin-left: 0.25em\">912<\/span><\/li>\n<li>33<span style=\"margin-left: 0.25em\">306<\/span><\/li>\n<li>14<span style=\"margin-left: 0.25em\">205<\/span><\/li>\n<li>48<span style=\"margin-left: 0.25em\">618<\/span><\/li>\n<li>21<span style=\"margin-left: 0.25em\">576<\/span><\/li>\n<li>16<span style=\"margin-left: 0.25em\">272<\/span><\/li>\n<li>43<span style=\"margin-left: 0.25em\">260<\/span><\/li>\n<li>44<span style=\"margin-left: 0.25em\">744<\/span><\/li>\n<li>25<span style=\"margin-left: 0.25em\">122<\/span><\/li>\n<li>12<span style=\"margin-left: 0.25em\">384<\/span><\/li>\n<li>6<span style=\"margin-left: 0.25em\">594<\/span><\/li>\n<li>28<span style=\"margin-left: 0.25em\">884<\/span><\/li>\n<li>61<span style=\"margin-left: 0.25em\">512<\/span><\/li>\n<li>15<span style=\"margin-left: 0.25em\">480<\/span><\/li>\n<li>29<span style=\"margin-left: 0.25em\">792<\/span><\/li>\n<li>27<span style=\"margin-left: 0.25em\">455<\/span><\/li>\n<li>72<span style=\"margin-left: 0.25em\">288<\/span><\/li>\n<li>51<span style=\"margin-left: 0.25em\">870<\/span><\/li>\n<li>12<span style=\"margin-left: 0.25em\">906<\/span><\/li>\n<li>32<span style=\"margin-left: 0.25em\">516<\/span><\/li>\n<\/ol>\n<\/div>\n<\/div>\n<h1 class=\"page-break-before\">Topic A: Self-Test<\/h1>\n<p><strong>Mark\u00a0\u00a0 \/14 \u00a0\u00a0 Aim 11\/14<\/strong><\/p>\n<ol type=\"A\">\n<li>Find the products. (6 marks)\n<ol class=\"twocolumn\" type=\"a\">\n<li>[latex]\\begin{array}{rr}&62\\\\\\times&4\\\\\\hline\\\\\\end{array}[\/latex]<\/li>\n<li>[latex]\\begin{array}{rr}&31\\\\\\times&4\\\\\\hline\\\\\\end{array}[\/latex]<\/li>\n<li>[latex]\\begin{array}{rr}&423\\\\\\times&3\\\\\\hline\\\\\\end{array}[\/latex]<\/li>\n<li>[latex]\\begin{array}{rr}&734\\\\\\times&2\\\\\\hline\\\\\\end{array}[\/latex]<\/li>\n<li>[latex]\\begin{array}{rr}&8342\\\\\\times&2\\\\\\hline\\\\\\end{array}[\/latex]<\/li>\n<li>[latex]\\begin{array}{rr}&5231\\\\\\times&3\\\\\\hline\\\\\\end{array}[\/latex]<\/li>\n<\/ol>\n<\/li>\n<li>Multiply these numbers. (4 marks)\n<ol class=\"twocolumn\" type=\"a\">\n<li>[latex]\\begin{array}{rr}&44\\\\\\times&7\\\\\\hline\\\\\\end{array}[\/latex]<\/li>\n<li>[latex]\\begin{array}{rr}&69\\\\\\times&8\\\\\\hline\\\\\\end{array}[\/latex]<\/li>\n<li>[latex]\\begin{array}{rr}&207\\\\\\times&9\\\\\\hline\\\\\\end{array}[\/latex]<\/li>\n<li>[latex]\\begin{array}{rr}&184\\\\\\times&6\\\\\\hline\\\\\\end{array}[\/latex]<\/li>\n<\/ol>\n<\/li>\n<li>Find the products. (4 marks)\n<ol class=\"twocolumn\" type=\"a\">\n<li>[latex]\\begin{array}{rr}&2834\\\\\\times&5\\\\\\hline\\\\\\end{array}[\/latex]<\/li>\n<li>[latex]\\begin{array}{rr}&4037\\\\\\times&6\\\\\\hline\\\\\\end{array}[\/latex]<\/li>\n<li>[latex]\\begin{array}{rr}&9241\\\\\\times&8\\\\\\hline\\\\\\end{array}[\/latex]<\/li>\n<li>[latex]\\begin{array}{rr}&3652\\\\\\times&4\\\\\\hline\\\\\\end{array}[\/latex]<\/li>\n<\/ol>\n<\/li>\n<\/ol>\n<h2>Answers to Topic A Self-Test<\/h2>\n<ol type=\"A\">\n<li>Find the products.\n<ol class=\"twocolumn\" type=\"a\">\n<li>248<\/li>\n<li>124<\/li>\n<li>1<span style=\"margin-left: 0.25em\">269<\/span><\/li>\n<li>1<span style=\"margin-left: 0.25em\">468<\/span><\/li>\n<li>16<span style=\"margin-left: 0.25em\">684<\/span><\/li>\n<li>15<span style=\"margin-left: 0.25em\">693<\/span><\/li>\n<\/ol>\n<\/li>\n<li>Multiply these numbers.\n<ol class=\"twocolumn\" type=\"a\">\n<li>308<\/li>\n<li>552<\/li>\n<li>1<span style=\"margin-left: 0.25em\">863<\/span><\/li>\n<li>1<span style=\"margin-left: 0.25em\">104<\/span><\/li>\n<\/ol>\n<\/li>\n<li>Find the products.\n<ol class=\"twocolumn\" type=\"a\">\n<li>14<span style=\"margin-left: 0.25em\">170<\/span><\/li>\n<li>24<span style=\"margin-left: 0.25em\">222<\/span><\/li>\n<li>73<span style=\"margin-left: 0.25em\">928<\/span><\/li>\n<li>14<span style=\"margin-left: 0.25em\">608<\/span><\/li>\n<\/ol>\n<\/li>\n<\/ol>\n","protected":false},"author":999,"menu_order":6,"template":"","meta":{"pb_show_title":"on","pb_short_title":"","pb_subtitle":"","pb_authors":[],"pb_section_license":""},"chapter-type":[],"contributor":[],"license":[],"class_list":["post-25","chapter","type-chapter","status-publish","hentry"],"part":24,"_links":{"self":[{"href":"https:\/\/pressbooks.bccampus.ca\/math023\/wp-json\/pressbooks\/v2\/chapters\/25","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\/25\/revisions"}],"predecessor-version":[{"id":195,"href":"https:\/\/pressbooks.bccampus.ca\/math023\/wp-json\/pressbooks\/v2\/chapters\/25\/revisions\/195"}],"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\/25\/metadata\/"}],"wp:attachment":[{"href":"https:\/\/pressbooks.bccampus.ca\/math023\/wp-json\/wp\/v2\/media?parent=25"}],"wp:term":[{"taxonomy":"chapter-type","embeddable":true,"href":"https:\/\/pressbooks.bccampus.ca\/math023\/wp-json\/pressbooks\/v2\/chapter-type?post=25"},{"taxonomy":"contributor","embeddable":true,"href":"https:\/\/pressbooks.bccampus.ca\/math023\/wp-json\/wp\/v2\/contributor?post=25"},{"taxonomy":"license","embeddable":true,"href":"https:\/\/pressbooks.bccampus.ca\/math023\/wp-json\/wp\/v2\/license?post=25"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}