{"id":78,"date":"2022-12-21T12:49:03","date_gmt":"2022-12-21T17:49:03","guid":{"rendered":"https:\/\/pressbooks.bccampus.ca\/math024\/chapter\/adding-decimals\/"},"modified":"2025-07-15T22:35:07","modified_gmt":"2025-07-16T02:35:07","slug":"adding-decimals","status":"publish","type":"chapter","link":"https:\/\/pressbooks.bccampus.ca\/math024\/chapter\/adding-decimals\/","title":{"raw":"Topic A: Adding Decimals","rendered":"Topic A: Adding Decimals"},"content":{"raw":"<h1>Line Up the Decimals<\/h1>\r\nReview [pb_glossary id=\"200\"]place value[\/pb_glossary] in whole numbers and in decimal fractions.\r\n\r\nHere is a place value chart for decimals:\r\n<table class=\"grid\" style=\"border-collapse: collapse;width: 100%;height: 72px\" border=\"0\">\r\n<tbody>\r\n<tr style=\"height: 36px\">\r\n<th style=\"width: 11.1111%;height: 36px\" scope=\"col\">Hundreds<\/th>\r\n<th style=\"width: 11.1111%;height: 36px\" scope=\"col\">Tens<\/th>\r\n<th style=\"width: 11.1111%;height: 36px\" scope=\"col\">Ones<\/th>\r\n<th style=\"width: 11.1111%;height: 36px\" scope=\"col\">.<\/th>\r\n<th style=\"width: 11.1111%;height: 36px\" scope=\"col\">Tenths<\/th>\r\n<th style=\"width: 11.1111%;height: 36px\" scope=\"col\">Hundred<span style=\"color: #eb0000\">ths<\/span><\/th>\r\n<th style=\"width: 11.1111%;height: 36px\" scope=\"col\">Thousand<span style=\"color: #eb0000\">ths<\/span><\/th>\r\n<th style=\"width: 11.1111%;height: 36px\" scope=\"col\">Ten thousand<span style=\"color: #eb0000\">ths<\/span><\/th>\r\n<th style=\"width: 11.1111%;height: 36px\" scope=\"col\">Hundred thousand<span style=\"color: #eb0000\">ths<\/span><\/th>\r\n<\/tr>\r\n<tr style=\"height: 18px\">\r\n<td style=\"width: 11.1111%;height: 18px\"><\/td>\r\n<td style=\"width: 11.1111%;height: 18px\"><\/td>\r\n<td style=\"width: 11.1111%;height: 18px\">3<\/td>\r\n<td style=\"width: 11.1111%;height: 18px\">.<\/td>\r\n<td style=\"width: 11.1111%;height: 18px\">4<\/td>\r\n<td style=\"width: 11.1111%;height: 18px\">5<\/td>\r\n<td style=\"width: 11.1111%;height: 18px\">3<\/td>\r\n<td style=\"width: 11.1111%;height: 18px\"><\/td>\r\n<td style=\"width: 11.1111%;height: 18px\"><\/td>\r\n<\/tr>\r\n<tr style=\"height: 18px\">\r\n<td style=\"width: 11.1111%;height: 18px\"><\/td>\r\n<td style=\"width: 11.1111%;height: 18px\"><\/td>\r\n<td style=\"width: 11.1111%;height: 18px\">0<\/td>\r\n<td style=\"width: 11.1111%;height: 18px\">.<\/td>\r\n<td style=\"width: 11.1111%;height: 18px\">9<\/td>\r\n<td style=\"width: 11.1111%;height: 18px\">6<\/td>\r\n<td style=\"width: 11.1111%;height: 18px\"><\/td>\r\n<td style=\"width: 11.1111%;height: 18px\"><\/td>\r\n<td style=\"width: 11.1111%;height: 18px\"><\/td>\r\n<\/tr>\r\n<\/tbody>\r\n<\/table>\r\n<div class=\"textbox\">\r\n\r\n<strong>Vocabulary Review <\/strong>\r\n\r\nUse the example below and the glossary to help you write the definitions.\r\n\r\n<img class=\"aligncenter wp-image-60\" src=\"https:\/\/pressbooks.bccampus.ca\/wp-content\/uploads\/sites\/2382\/2022\/12\/addend-and-sum.jpg\" alt=\"In 3+5=8, 3 and 5 are addends, and 8 is the sum.\" width=\"190\" height=\"101\" \/>\r\n\r\n<strong>Definition of Addends:<\/strong>\r\n\r\n<strong>Definition of Sum:<\/strong>\r\n\r\n<\/div>\r\nWhen adding decimals, you must be very careful to add together the [pb_glossary id=\"169\"]digits[\/pb_glossary] with the same place value.\r\n<ul>\r\n \t<li>Add thousandths to thousandths.<\/li>\r\n \t<li>Add hundredths to hundredths.<\/li>\r\n \t<li>Add tenths to tenths.<\/li>\r\n<\/ul>\r\nThe best way to do this is to <strong>line up your decimals<\/strong>.\r\n<h2>How to Add Decimals<\/h2>\r\n<ol>\r\n \t<li>Write the [pb_glossary id=\"158\"]addends[\/pb_glossary] underneath each other so the decimal points are in a straight column. Notice how lining up the decimals also lines up the place values.\r\n[latex]0.43+0.2+0.804+0.1=[\/latex]\r\nRewrite as: [latex]\\begin{array}{ll}&amp;0.43\\\\&amp;0.2\\\\&amp;0.804\\\\+&amp;0.1\\\\ \\hline\\end{array}[\/latex]<\/li>\r\n \t<li>Put zeros at the end of the decimal fractions so that all fractions have the same number of decimal places.\r\n[latex]\\begin{array}{ll}&amp;0.430\\\\&amp;0.200\\\\&amp;0.804\\\\+&amp;0.100\\\\ \\hline\\end{array}[\/latex]<\/li>\r\n \t<li>It may help you to put the decimal point in the answer line before you do the addition.\r\n[latex]\\begin{array}{ll}&amp;0.430\\\\&amp;0.200\\\\&amp;0.804\\\\+&amp;0.100\\\\ \\hline &amp;\\phantom{0}\\mathbf{.}\\end{array}[\/latex]<\/li>\r\n \t<li>When adding [pb_glossary id=\"188\"]mixed decimals[\/pb_glossary], be sure to keep the whole number places lined up as well. As you know, ones add to ones, tens to tens, hundreds to hundreds and so on. Put a decimal point after any whole numbers.\r\n[latex]62.1 + 14.58 + 6. + 7.311 + 6.23 =\\\\ \\begin{array}{lr}&amp;62.100\\\\&amp;14.580\\\\&amp;6.000\\\\&amp;7.311\\\\+&amp;6.230 \\\\ \\hline\\end{array}[\/latex]<\/li>\r\n \t<li>Add each column, starting with the decimal place farthest to the right. If the total of a column is ten or more, carry the ten number to the next column as you are used to doing with whole numbers.\r\n[latex]\\begin{array}{ll}&amp;\\small{1\\; 1}\\\\&amp;0.470\\\\&amp;0.298\\\\&amp;0.100\\\\+&amp;5.600\\\\ \\hline &amp;6.468\\end{array}[\/latex]<\/li>\r\n<\/ol>\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\nRewrite each question in columns and add.\r\n<ol class=\"twocolumn\" type=\"a\">\r\n \t<li>0.24 + 0.73 + 0.51 =\r\n[latex]\\begin{array}{ll}&amp;\\scriptsize{1}\\\\&amp;0.24\\\\&amp;0.73\\\\+&amp;0.51\\\\ \\hline &amp;1.48\\end{array}[\/latex]<\/li>\r\n \t<li>0.821 + 0.14 + 0.019 =\r\n[latex]\\begin{array}{ll}&amp;\\phantom{0.8}\\scriptsize{1}\\\\&amp;0.821\\\\&amp;0.140\\\\+&amp;0.019\\\\ \\hline &amp;0.980\\end{array}[\/latex]<\/li>\r\n<\/ol>\r\n<ol class=\"twocolumn\" start=\"3\" type=\"a\">\r\n \t<li>0.084 + 0.291 + 0.652 =<\/li>\r\n \t<li>0.195 + 0.982 + 0.605 =<\/li>\r\n \t<li>0.625 + 0.845 + 0.33 =<\/li>\r\n \t<li>0.442 + 0.782 + 0.254 =<\/li>\r\n<\/ol>\r\n<strong>Answers to Exercise 1<\/strong>\r\n<ol class=\"twocolumn\" type=\"a\">\r\n \t<li>1.48<\/li>\r\n \t<li>0.980<\/li>\r\n \t<li>1.027<\/li>\r\n \t<li>1.782<\/li>\r\n \t<li>1.8<\/li>\r\n \t<li>1.478<\/li>\r\n<\/ol>\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\nRewrite in columns and add.\r\n<ol class=\"twocolumn\" type=\"a\">\r\n \t<li>1.003 + 141.2 + 0.47 =\r\n[latex]\\begin{array}{rr}&amp;1.003\\\\&amp;141.200\\\\+&amp;0.470\\\\ \\hline &amp;142.673\\end{array}[\/latex]<\/li>\r\n \t<li>5.6 + 3.59 + 1<span style=\"margin-left: 0.25em\">829<\/span> =\r\n[latex]\\begin{array}{rr}&amp;5.60\\\\&amp;3.59\\\\+&amp;1829.00\\\\ \\hline &amp;1838.19\\end{array}[\/latex]<\/li>\r\n<\/ol>\r\n<ol class=\"twocolumn\" start=\"3\" type=\"a\">\r\n \t<li>4.6 + 2.59 + 1<span style=\"margin-left: 0.25em\">629<\/span> =<\/li>\r\n \t<li>0.391 + 80 + 4.63 =<\/li>\r\n \t<li>16.34 + 211.684 + 75.0697 =<\/li>\r\n \t<li>321.6 + 485.791 + 0.001 =<\/li>\r\n \t<li>0.22 + 46.84 + 95.6 =<\/li>\r\n \t<li>0.042 + 0.018 + 19.1 =<\/li>\r\n<\/ol>\r\n<strong>Answers to Exercise 2<\/strong>\r\n<ol class=\"twocolumn\" type=\"a\">\r\n \t<li>142.673<\/li>\r\n \t<li>1838.19<\/li>\r\n \t<li>1636.19<\/li>\r\n \t<li>85.021<\/li>\r\n \t<li>303.0937<\/li>\r\n \t<li>807.392<\/li>\r\n \t<li>142.66<\/li>\r\n \t<li>19.16<\/li>\r\n<\/ol>\r\n<\/div>\r\n<\/div>\r\n<div class=\"textbox\">Remember that [pb_glossary id=\"199\"]perimeter[\/pb_glossary] is the measurement around the outside edge of an object. To find perimeter, you add the lengths of all the sides together.<\/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 perimeter of the squares described in each question. The measure of one side has been given. Draw a picture of each square to help visualize the question.\r\n<ol type=\"a\">\r\n \t<li>S = 75.3 m\r\nP = S + S + S + S\r\nP = 75.3 + 75.3 + 75.3 + 75.3 m\r\nP = 301.2 m\r\n<img class=\"aligncenter wp-image-61\" src=\"https:\/\/pressbooks.bccampus.ca\/wp-content\/uploads\/sites\/2382\/2025\/01\/square.png\" alt=\"A square. Each side is labelled 75.3 m.\" width=\"200\" height=\"131\" \/><\/li>\r\n \t<li>S = 12.4 mm\r\nP =<\/li>\r\n \t<li>S = 100.73 km\r\nP =<\/li>\r\n \t<li>S = 50.2 cm<\/li>\r\n \t<li>S = 16.5 m<\/li>\r\n \t<li>S = 3.25 m<\/li>\r\n<\/ol>\r\n<strong>Answers to Exercise 3\r\n<\/strong>\r\n<ol class=\"twocolumn\" type=\"a\">\r\n \t<li>301.2 m<\/li>\r\n \t<li>49.6 mm<\/li>\r\n \t<li>402.92 km<\/li>\r\n \t<li>200.8 cm<\/li>\r\n \t<li>66 m<\/li>\r\n \t<li>13 m<\/li>\r\n<\/ol>\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 perimeter of the rectangles described below. Draw your own rectangle if there is no picture.\r\n<ol type=\"a\">\r\n \t<li>P = side + side + side + side\r\nP =\r\n<img class=\"aligncenter wp-image-62 size-full\" src=\"https:\/\/pressbooks.bccampus.ca\/wp-content\/uploads\/sites\/2382\/2025\/01\/4a.png\" alt=\"a rectangle whose length=7.5m, width=3.1m\" width=\"170\" height=\"93\" \/><\/li>\r\n \t<li>P = side + side + side + side\r\nP =\r\n<img class=\"aligncenter size-full wp-image-63\" src=\"https:\/\/pressbooks.bccampus.ca\/wp-content\/uploads\/sites\/2382\/2025\/01\/4b.png\" alt=\"\" width=\"242\" height=\"88\" \/><\/li>\r\n \t<li><img class=\"aligncenter wp-image-64 size-full\" src=\"https:\/\/pressbooks.bccampus.ca\/wp-content\/uploads\/sites\/2382\/2025\/01\/4c.png\" alt=\"a rectangle whose length=7.5cm, width=2.1cm\" width=\"128\" height=\"158\" \/><\/li>\r\n \t<li><img class=\"aligncenter wp-image-65 size-full\" src=\"https:\/\/pressbooks.bccampus.ca\/wp-content\/uploads\/sites\/2382\/2025\/01\/4d-e1671661742599.png\" alt=\"a rectangle whose length=7.5m, width=1.5m\" width=\"322\" height=\"99\" \/><\/li>\r\n \t<li>l = 10.3 cm\r\nw = 6.6 cm\r\n<img class=\"aligncenter wp-image-66 size-full\" src=\"https:\/\/pressbooks.bccampus.ca\/wp-content\/uploads\/sites\/2382\/2025\/01\/4e.png\" alt=\"a rectangle whose length=10.3cm, width=6.6cm\" width=\"172\" height=\"77\" \/><\/li>\r\n \t<li>l = 100.03 km\r\nw = 70.96 km<\/li>\r\n \t<li>l = 9.75 cm\r\nw = 3.5 cm<\/li>\r\n<\/ol>\r\n<strong>Answers to Exercise 4<\/strong>\r\n<ol class=\"twocolumn\" type=\"a\">\r\n \t<li>21.2 m<\/li>\r\n \t<li>31.5 cm<\/li>\r\n \t<li>19.2 cm<\/li>\r\n \t<li>18 m<\/li>\r\n \t<li>33.8 cm<\/li>\r\n \t<li>341.98 km<\/li>\r\n \t<li>26.5 cm<\/li>\r\n<\/ol>\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 perimeter of the polygons described below. Be sure the measurements are in the same unit value. Use a formula for each calculation, the formula work is started in the first two for you.\r\n<ol type=\"a\">\r\n \t<li>P = Side + Side + Side\r\nP = 6.5 km + 7.5 km + 9.5 km\r\nP =\r\n<img class=\"aligncenter wp-image-67 size-full\" src=\"https:\/\/pressbooks.bccampus.ca\/wp-content\/uploads\/sites\/2382\/2025\/01\/5a.png\" alt=\"a triangle whose sides are 6.5km, 7.5km, 9.5km\" width=\"221\" height=\"80\" \/><\/li>\r\n \t<li>P = Side + Side + Side + Side + Side + Side\r\nP =\u00a0<span style=\"text-decoration: underline\" aria-label=\"blank\">\u00a0 \u00a0 \u00a0\u00a0<\/span> + <span style=\"text-decoration: underline\" aria-label=\"blank\">\u00a0 \u00a0 \u00a0\u00a0<\/span> + <span style=\"text-decoration: underline\" aria-label=\"blank\">\u00a0 \u00a0 \u00a0\u00a0<\/span> + <span style=\"text-decoration: underline\" aria-label=\"blank\">\u00a0 \u00a0 \u00a0\u00a0<\/span> + <span style=\"text-decoration: underline\" aria-label=\"blank\">\u00a0 \u00a0 \u00a0\u00a0<\/span> + <span style=\"text-decoration: underline\" aria-label=\"blank\">\u00a0 \u00a0 \u00a0\u00a0<\/span>\r\nP =\r\nP =\r\n<img class=\"aligncenter wp-image-68 size-full\" src=\"https:\/\/pressbooks.bccampus.ca\/wp-content\/uploads\/sites\/2382\/2025\/01\/5b.png\" alt=\"a hexagon whose sides are 80.3m, 80.3m, 80.3m, 80.3m, 80.3m, 80.3m\" width=\"172\" height=\"121\" \/><\/li>\r\n \t<li>P =\r\n<img class=\"aligncenter wp-image-69 size-full\" src=\"https:\/\/pressbooks.bccampus.ca\/wp-content\/uploads\/sites\/2382\/2025\/01\/5c.png\" alt=\"a triangle whose sides are 7.2cm, 5cm, 4.85cm\" width=\"244\" height=\"76\" \/><\/li>\r\n \t<li>P =\r\n<img class=\"aligncenter wp-image-70 size-full\" src=\"https:\/\/pressbooks.bccampus.ca\/wp-content\/uploads\/sites\/2382\/2025\/01\/5d.png\" alt=\"a quadrilateral whose sides are 12 units, 7 units, 6 units, 7 units\" width=\"269\" height=\"123\" \/><\/li>\r\n \t<li>P =\r\n<img class=\"aligncenter wp-image-71 size-full\" src=\"https:\/\/pressbooks.bccampus.ca\/wp-content\/uploads\/sites\/2382\/2025\/01\/5e.png\" alt=\"a rectangle whose length=8.94km, width=1.45km\" width=\"113\" height=\"176\" \/><\/li>\r\n \t<li>P =\r\n<img class=\"aligncenter wp-image-72 size-full\" src=\"https:\/\/pressbooks.bccampus.ca\/wp-content\/uploads\/sites\/2382\/2025\/01\/5f.png\" alt=\"a square whose sides are 30.3m\" width=\"159\" height=\"146\" \/><\/li>\r\n<\/ol>\r\n<strong>Answers to Exercise 5<\/strong>\r\n<ol class=\"twocolumn\" type=\"a\">\r\n \t<li>23.5 km<\/li>\r\n \t<li>481.8 m<\/li>\r\n \t<li>17.05 cm<\/li>\r\n \t<li>32 units<\/li>\r\n \t<li>20.78 km<\/li>\r\n \t<li>121.2 m<\/li>\r\n<\/ol>\r\n<\/div>\r\n<\/div>\r\n<h1>How to Solve Word Problems<\/h1>\r\nIn math, word problems describe real-life situations that involve numbers.\r\n\r\nOften the most difficult part of a word problem is knowing what we should do. Once we know what to do, it is much easier to figure out how to do it.\r\n\r\n<img class=\"alignleft wp-image-73\" src=\"https:\/\/pressbooks.bccampus.ca\/wp-content\/uploads\/sites\/2382\/2025\/01\/image96.png\" alt=\"A drawing of a winding road with lots of signs.\" width=\"200\" height=\"186\" \/>It is sort of like driving. You may be all ready to go, but before you get into the car, turn on the engine, or put your foot on the gas pedal, you need to know <strong>where<\/strong> you are going and figure out how to get there.\r\n\r\nThe first thing to do is decide on your destination. <img class=\"alignright wp-image-74\" src=\"https:\/\/pressbooks.bccampus.ca\/wp-content\/uploads\/sites\/2382\/2025\/01\/image98.png\" alt=\"A road sign showing a car driving through a large pothole.\" width=\"200\" height=\"200\" \/>\r\n\r\nOkay, how do you \"decide on a destination\" for a math problem?\r\n\r\nUse these steps:\r\n<table class=\"grid\" style=\"border-collapse: collapse;width: 100%\" border=\"0\"><caption>Steps to Solving a word problem<\/caption>\r\n<tbody>\r\n<tr>\r\n<th style=\"width: 25%\" scope=\"row\">Step 1: Question<\/th>\r\n<td style=\"width: 75%\">\r\n<ul>\r\n \t<li>Read the problem carefully.<\/li>\r\n \t<li>What is the question being asked?<\/li>\r\n \t<li>Does the problem have two parts?<\/li>\r\n \t<li>Draw a picture to help you see the problem described.<\/li>\r\n<\/ul>\r\n<\/td>\r\n<\/tr>\r\n<tr>\r\n<th style=\"width: 25%\" scope=\"row\">Step 2: Information<\/th>\r\n<td style=\"width: 75%\">\r\n<ul>\r\n \t<li>What information is necessary to solve the problem?<\/li>\r\n \t<li>Often you are given extra numbers and information that are not needed.<\/li>\r\n \t<li>Keep the question (destination) in mind.<\/li>\r\n \t<li><span style=\"border: 1px solid;border-radius: 30px;padding: 2px 2px 2px 2px\"> Circle <\/span> the information you need.<\/li>\r\n \t<li>Write that information on the picture you drew.<\/li>\r\n<\/ul>\r\n<\/td>\r\n<\/tr>\r\n<tr>\r\n<th style=\"width: 25%\" scope=\"row\">Step 3: Operation<\/th>\r\n<td style=\"width: 75%\">\r\n<ul>\r\n \t<li>Decide what arithmetic operation to use.<\/li>\r\n \t<li>Do you need to add, subtract, multiply, or divide?<\/li>\r\n \t<li>If the problem has two parts, decide what operation you need to do for each part.\r\n<ul>\r\n \t<li>Key words often point to the operation needed.<\/li>\r\n \t<li>Drawing a diagram or sketch is always helpful.<\/li>\r\n \t<li>Write an equation (a number sentence).<\/li>\r\n<\/ul>\r\n<\/li>\r\n<\/ul>\r\n<\/td>\r\n<\/tr>\r\n<tr>\r\n<th style=\"width: 25%\" scope=\"row\">Step 4: Estimate<\/th>\r\n<td style=\"width: 75%\">\r\n<ul>\r\n \t<li>[pb_glossary id=\"177\"]Estimate[\/pb_glossary] the answer to the problem.\r\n<ul>\r\n \t<li>Round the numbers so you can work with them quickly.\r\nUse the operation you chose in Step 3 and come to a quick answer.<\/li>\r\n<\/ul>\r\n<\/li>\r\n \t<li>Does this estimated answer make sense?<\/li>\r\n \t<li>Does it answer the question of the problem?<\/li>\r\n \t<li>Think carefully before you do Step 5.<\/li>\r\n<\/ul>\r\n<\/td>\r\n<\/tr>\r\n<tr>\r\n<th style=\"width: 25%\" scope=\"row\">Step 5: Solve<\/th>\r\n<td style=\"width: 75%\">\r\n<ul>\r\n \t<li>Solve the problem using the actual numbers.\r\n<ul>\r\n \t<li>Check your arithmetic.<\/li>\r\n \t<li>Compare your answer in Step 5 to your estimate from Step 4.<\/li>\r\n \t<li>Think again about the question. Does your solution make sense?<\/li>\r\n \t<li>When you write your answer, include the units.<\/li>\r\n \t<li>For example: 3 dozen eggs, 7.5 kilometres, 68 people<\/li>\r\n<\/ul>\r\n<\/li>\r\n<\/ul>\r\n<\/td>\r\n<\/tr>\r\n<\/tbody>\r\n<\/table>\r\n<table class=\"grid aligncenter\" style=\"border-collapse: collapse;width: 50%;height: 108px\" border=\"0\"><caption>Some common metric units and their abbreviations<\/caption>\r\n<tbody>\r\n<tr style=\"height: 18px\">\r\n<th style=\"width: 50%;height: 18px\" scope=\"col\">Unit<\/th>\r\n<th style=\"width: 50%;height: 18px\" scope=\"col\">Abbreviations<\/th>\r\n<\/tr>\r\n<tr style=\"height: 18px\">\r\n<td style=\"width: 50%;height: 18px\">kilometre<\/td>\r\n<td style=\"width: 50%;height: 18px\">km<\/td>\r\n<\/tr>\r\n<tr style=\"height: 18px\">\r\n<td style=\"width: 50%;height: 18px\">metre<\/td>\r\n<td style=\"width: 50%;height: 18px\">m<\/td>\r\n<\/tr>\r\n<tr style=\"height: 18px\">\r\n<td style=\"width: 50%;height: 18px\">centimetre<\/td>\r\n<td style=\"width: 50%;height: 18px\">cm<\/td>\r\n<\/tr>\r\n<tr style=\"height: 18px\">\r\n<td style=\"width: 50%;height: 18px\">kilogram<\/td>\r\n<td style=\"width: 50%;height: 18px\">kg<\/td>\r\n<\/tr>\r\n<tr style=\"height: 18px\">\r\n<td style=\"width: 50%;height: 18px\">gram<\/td>\r\n<td style=\"width: 50%;height: 18px\">g<\/td>\r\n<\/tr>\r\n<tr>\r\n<td style=\"width: 50%\">litre<\/td>\r\n<td style=\"width: 50%\">L<\/td>\r\n<\/tr>\r\n<\/tbody>\r\n<\/table>\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\nThe nutrition information on a box of cereal says that a regular serving contains 2.8 g of protein, 0.2 g of fat, 25 g of carbohydrate, and 1.9 g of \"other nutrients.\" Give the total number of grams in a regular serving.\r\n<table class=\"grid\" style=\"border-collapse: collapse;width: 100%\" border=\"0\">\r\n<tbody>\r\n<tr>\r\n<th style=\"width: 25%\" scope=\"row\">Step 1: Question<\/th>\r\n<td>How many grams in a regular serving?\r\n\r\nDraw a picture:\r\n\r\n<img class=\"aligncenter wp-image-75 size-full\" src=\"https:\/\/pressbooks.bccampus.ca\/wp-content\/uploads\/sites\/2382\/2025\/01\/aq.png\" alt=\"protein, fat, carbohydrate, other\" width=\"466\" height=\"74\" \/><\/td>\r\n<\/tr>\r\n<tr>\r\n<th style=\"width: 25%\" scope=\"row\">Step 2: Information<\/th>\r\n<td>What information is necessary to solve the problem?\r\n<ul>\r\n \t<li>A regular serving contains 2.8 g protein, 0.2 g fat, 25 carbohydrate, and 1.9 g \"other nutrients.\"<\/li>\r\n \t<li>Add the information to your Picture.<\/li>\r\n<\/ul>\r\n<\/td>\r\n<\/tr>\r\n<tr>\r\n<th style=\"width: 25%\" scope=\"row\">Step 3: Operation<\/th>\r\n<td>\r\n<ul>\r\n \t<li>The problem lists four different amounts and asks you to find one total. \"Total\" is a key word that points to addition.<\/li>\r\n \t<li>Add the operation you need to your picture:\r\n<img class=\"aligncenter wp-image-76 size-full\" src=\"https:\/\/pressbooks.bccampus.ca\/wp-content\/uploads\/sites\/2382\/2025\/01\/o3.png\" alt=\"2.8g of protein + 0.2g of fat +25g of carbohydrate + 1.9g of other\" width=\"512\" height=\"73\" \/><\/li>\r\n \t<li>Next, write an equation: 2.8 + 0.2 + 25 + 1.9 = total number of grams<\/li>\r\n<\/ul>\r\n<\/td>\r\n<\/tr>\r\n<tr>\r\n<th style=\"width: 25%\" scope=\"row\">Step 4: Estimate<\/th>\r\n<td>\r\n<ul>\r\n \t<li>Round off each amount and add them together to get an estimated answer.\r\n<ul>\r\n \t<li>2.8 g \u2248 3 g, 0.2 g \u2248 0 g, 25 g \u2248 25 g, 1.9 g \u2248 2g<\/li>\r\n \t<li>3 g + 0 g + 25 g + 2 g = 30 g<\/li>\r\n<\/ul>\r\n<\/li>\r\n \t<li>Does this answer make sense?\r\n<ul>\r\n \t<li>A slice of bread is about 35 grams. A serving of cereal would probably weigh a similar amount. Yes, this makes sense.<\/li>\r\n<\/ul>\r\n<\/li>\r\n<\/ul>\r\n<\/td>\r\n<\/tr>\r\n<tr>\r\n<th style=\"width: 25%\" scope=\"row\">Step 5: Solve<\/th>\r\n<td>2.8 g + 0.2 g + 25.0g + 1.9 g = 29.9 g\r\n\r\n<strong>Answer<\/strong>: A regular serving of cereal is 29.9 grams \u2190 (include the units)\r\n<ul>\r\n \t<li>Check arithmetic<\/li>\r\n \t<li>Compare answer to estimate\u00a0 (estimate = 30\u00a0 \u00a0answer =29.9)<\/li>\r\n \t<li>Does the answer make sense?<\/li>\r\n \t<li>Did I include the units in my answer?<\/li>\r\n<\/ul>\r\n<\/td>\r\n<\/tr>\r\n<\/tbody>\r\n<\/table>\r\n<\/div>\r\n<\/div>\r\nSome key words that point to addition include:\r\n<ul class=\"twocolumn\">\r\n \t<li>[pb_glossary id=\"214\"]sum[\/pb_glossary]<\/li>\r\n \t<li>plus<\/li>\r\n \t<li>[pb_glossary id=\"217\"]total[\/pb_glossary]<\/li>\r\n \t<li>total amount<\/li>\r\n \t<li>altogether<\/li>\r\n \t<li>combined<\/li>\r\n \t<li>complete<\/li>\r\n \t<li>entire<\/li>\r\n \t<li>in all<\/li>\r\n \t<li>added to<\/li>\r\n \t<li>increased by<\/li>\r\n<\/ul>\r\n<h1>Word Problems Using Addition of Decimals<\/h1>\r\n<div class=\"textbox textbox--exercises\"><header class=\"textbox__header\">\r\n<p class=\"textbox__title\">Exercise 6<\/p>\r\n\r\n<\/header>\r\n<div class=\"textbox__content\">\r\n\r\nUse your skills in adding decimal fractions to do the following problems. Underline key words in the problems that will help you to recognize addition problems. Remember to draw a picture first!\r\n<ol type=\"a\">\r\n \t<li>A road construction crew finished surfacing 5.7 km of highway one week and 4.4 km the next week. How many kilometres did they complete in that two weeks?\r\n<ul type=\"a\">\r\n \t<li>5.7 km + 4.4 km<\/li>\r\n \t<li><strong>Estimation<\/strong>: 6 km + 4 km = 10 km<\/li>\r\n \t<li><strong>Actual Solution<\/strong>: [latex]\\begin{array}[t]{rr}&amp;5.7\\text{ km}\\\\+&amp;4.4\\text{ km}\\\\ \\hline &amp;10.1\\text{ km}\\end{array}[\/latex]<\/li>\r\n \t<li><strong>Answer<\/strong>: The road crew completed 10.1 km of road surfacing in two weeks.<\/li>\r\n<\/ul>\r\n<\/li>\r\n \t<li>Lisa rode her bike 2.4 km to her auntie\u2019s house for a little visit. Then she rode 1.5 km to the grocery store to get apples and 0.7 km to Walmart to get bread and chips. From Walmart, she rode 3.6 km home. How far did she go on her bike altogether? (the picture has been drawn here but you will need to fill in the information)\r\n<img class=\"aligncenter size-full wp-image-77\" src=\"https:\/\/pressbooks.bccampus.ca\/wp-content\/uploads\/sites\/2382\/2025\/01\/6b.png\" alt=\"\" width=\"381\" height=\"140\" \/>\r\n<ul type=\"a\">\r\n \t<li>Estimation:<\/li>\r\n \t<li>Actual Solution:<\/li>\r\n \t<li>Answer:<\/li>\r\n<\/ul>\r\n<\/li>\r\n \t<li>When Crystalle bought her used car, the odometer showed 12<span style=\"margin-left: 0.25em\">686.4<\/span> km. In one year, she drove 13<span style=\"margin-left: 0.25em\">294.8<\/span> km. What did the odometer read then?\u00a0 (draw your own picture)\r\n<ul type=\"a\">\r\n \t<li>Estimation:<\/li>\r\n \t<li>Actual Solution:<\/li>\r\n \t<li>Answer:<\/li>\r\n<\/ul>\r\n<\/li>\r\n \t<li>A recipe for spaghetti sauce uses 1.25 kg of ground beef, 2.4 kg of fresh tomatoes, 1 kg of onions, 0.75 kg of celery, 0.5 kg of green pepper and lots of garlic and herbs. What is the total weight of the ingredients, not counting the garlic and herbs?\r\n<ul type=\"a\">\r\n \t<li>Estimate:<\/li>\r\n \t<li>Actual Solution:<\/li>\r\n \t<li>Answer:<\/li>\r\n<\/ul>\r\n<\/li>\r\n \t<li>This month your power bill has increased $24.67, your phone bill has an extra $13.43, and your cable bill is up $2.24. It has been an expensive month! What is the combined extra cost that you are paying this month?\r\n<ul type=\"a\">\r\n \t<li>Estimate:<\/li>\r\n \t<li>Actual Solution:<\/li>\r\n \t<li>Answer:<\/li>\r\n<\/ul>\r\n<\/li>\r\n \t<li>Wanda texted her boyfriend Curtis and asked him to pick up some groceries on the way home. He answered back \u201cOnly have $20. Is that enough?\u201d Wanda wanted him to buy milk ($4.86), mac and cheese ($1.99), a bag of apples ($3.99) and laundry detergent ($8.57). Does Curtis have enough money?\r\n<ul type=\"a\">\r\n \t<li>Estimate:<\/li>\r\n \t<li>Actual Solution:<\/li>\r\n \t<li>Answer:<\/li>\r\n<\/ul>\r\n<\/li>\r\n<\/ol>\r\n<strong>Answers to Exercise 6<\/strong>\r\n<ol start=\"2\" type=\"a\">\r\n \t<li>Estimation: 2 + 2 + 1 + 4 = 9\r\nActual Solution: 2.4 + 1.5 + 0.7 + 3.6 = 8.2\r\nAnswer: Lisa rode her bike 8.2 km altogether.<\/li>\r\n \t<li>Estimation: 13<span style=\"margin-left: 0.25em\">000<\/span> km + 13<span style=\"margin-left: 0.25em\">000<\/span> km = 26<span style=\"margin-left: 0.25em\">000<\/span> km\r\nActual Solution: 12<span style=\"margin-left: 0.25em\">686.4<\/span> km + 13<span style=\"margin-left: 0.25em\">294.8<\/span> km = 25<span style=\"margin-left: 0.25em\">981.2<\/span> km\r\nAnswer: The odometer read 25 981.2 km after one year.<\/li>\r\n \t<li>Estimation: 1 kg + 2 kg + 1 kg + 1 kg + 1 kg = 6 kg\r\nActual Solution: 1.25 kg + 2.4 kg + 1 kg + 0.75 kg + 0.5 kg = 5.9 kg\r\nAnswer: The total weight of the ingredients is 5.9 kg.<\/li>\r\n \t<li>Estimation: $25 + $13 + $2 = $40\r\nActual solution: $24.67 + $13.43 + $2.24 = $40.34\r\nAnswer: The extra cost you are paying is $40.34.<\/li>\r\n \t<li>Estimation: $5 + $2 + $4 + 9 = $20\r\nActual solution: $4.86 + $1.99 + $3.99 + $8.57 = $19.41\r\nAnswer: The groceries will cost $19.41 so yes, Curtis has enough money<\/li>\r\n<\/ol>\r\n<\/div>\r\n<\/div>\r\n<h1>Topic A: Self-Test<\/h1>\r\n<strong>Mark \/6\u00a0 \u00a0 \u00a0Aim 5\/6<\/strong>\r\n<ol type=\"A\">\r\n \t<li>Find the sum. (4 marks)\r\n<ol type=\"a\">\r\n \t<li>[latex]\\begin{array}{rr}&amp;3.67\\\\&amp;12.55\\\\&amp;8.19\\\\+&amp;5.67\\\\ \\hline\\\\ \\end{array}[\/latex]<\/li>\r\n \t<li>[latex]5.27 + 2.4 + 8 + 6.93 + 10.27 =[\/latex]<\/li>\r\n \t<li>[latex]\\begin{array}{rr}&amp;4.648\\\\&amp;1.92\\phantom{0}\\\\&amp;1.275\\\\+&amp;86.9\\phantom{00}\\\\ \\hline\\\\ \\end{array}[\/latex]<\/li>\r\n \t<li>[latex]2.72 + 0.6 + 110 + 17.223 =[\/latex]<\/li>\r\n<\/ol>\r\n<\/li>\r\n \t<li>Word Problem. (2 marks)\r\nGwen mailed Christmas presents to her family. She sent a 3.7 kg box to her daughter in Vancouver, a 2.145 kg package to her sister's family in Campbell River, a box to Prince George that was 1.06 kg, and a parcel to Kitwanga that was 4 kg. What was the combined weight of Gwen's parcels?\r\n<ol type=\"a\">\r\n \t<li>Estimate:<\/li>\r\n \t<li>Actual Solution:<\/li>\r\n \t<li>Answer:<\/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 sum.\r\n<ol class=\"twocolumn\" type=\"a\">\r\n \t<li>30.08<\/li>\r\n \t<li>32.87<\/li>\r\n \t<li>94.743<\/li>\r\n \t<li>130.543<\/li>\r\n<\/ol>\r\n<\/li>\r\n \t<li>Word problem.\r\n<ol type=\"a\">\r\n \t<li>Estimation: 4 kg + 2 kg +1 kg + 4 kg = 11 kg<\/li>\r\n \t<li>Actual Solution: 3.7 kg + 2.145 kg + 1.06 kg + 4 kg = 10.905 kg<\/li>\r\n \t<li>Answer: The combined weight of the parcels was 10.905 kg.<\/li>\r\n<\/ol>\r\n<\/li>\r\n<\/ol>\r\n&nbsp;","rendered":"<h1>Line Up the Decimals<\/h1>\n<p>Review <a class=\"glossary-term\" aria-haspopup=\"dialog\" aria-describedby=\"definition\" href=\"#term_78_200\">place value<\/a> in whole numbers and in decimal fractions.<\/p>\n<p>Here is a place value chart for decimals:<\/p>\n<table class=\"grid\" style=\"border-collapse: collapse;width: 100%;height: 72px\">\n<tbody>\n<tr style=\"height: 36px\">\n<th style=\"width: 11.1111%;height: 36px\" scope=\"col\">Hundreds<\/th>\n<th style=\"width: 11.1111%;height: 36px\" scope=\"col\">Tens<\/th>\n<th style=\"width: 11.1111%;height: 36px\" scope=\"col\">Ones<\/th>\n<th style=\"width: 11.1111%;height: 36px\" scope=\"col\">.<\/th>\n<th style=\"width: 11.1111%;height: 36px\" scope=\"col\">Tenths<\/th>\n<th style=\"width: 11.1111%;height: 36px\" scope=\"col\">Hundred<span style=\"color: #eb0000\">ths<\/span><\/th>\n<th style=\"width: 11.1111%;height: 36px\" scope=\"col\">Thousand<span style=\"color: #eb0000\">ths<\/span><\/th>\n<th style=\"width: 11.1111%;height: 36px\" scope=\"col\">Ten thousand<span style=\"color: #eb0000\">ths<\/span><\/th>\n<th style=\"width: 11.1111%;height: 36px\" scope=\"col\">Hundred thousand<span style=\"color: #eb0000\">ths<\/span><\/th>\n<\/tr>\n<tr style=\"height: 18px\">\n<td style=\"width: 11.1111%;height: 18px\"><\/td>\n<td style=\"width: 11.1111%;height: 18px\"><\/td>\n<td style=\"width: 11.1111%;height: 18px\">3<\/td>\n<td style=\"width: 11.1111%;height: 18px\">.<\/td>\n<td style=\"width: 11.1111%;height: 18px\">4<\/td>\n<td style=\"width: 11.1111%;height: 18px\">5<\/td>\n<td style=\"width: 11.1111%;height: 18px\">3<\/td>\n<td style=\"width: 11.1111%;height: 18px\"><\/td>\n<td style=\"width: 11.1111%;height: 18px\"><\/td>\n<\/tr>\n<tr style=\"height: 18px\">\n<td style=\"width: 11.1111%;height: 18px\"><\/td>\n<td style=\"width: 11.1111%;height: 18px\"><\/td>\n<td style=\"width: 11.1111%;height: 18px\">0<\/td>\n<td style=\"width: 11.1111%;height: 18px\">.<\/td>\n<td style=\"width: 11.1111%;height: 18px\">9<\/td>\n<td style=\"width: 11.1111%;height: 18px\">6<\/td>\n<td style=\"width: 11.1111%;height: 18px\"><\/td>\n<td style=\"width: 11.1111%;height: 18px\"><\/td>\n<td style=\"width: 11.1111%;height: 18px\"><\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<div class=\"textbox\">\n<p><strong>Vocabulary Review <\/strong><\/p>\n<p>Use the example below and the glossary to help you write the definitions.<\/p>\n<p><img loading=\"lazy\" decoding=\"async\" class=\"aligncenter wp-image-60\" src=\"https:\/\/pressbooks.bccampus.ca\/wp-content\/uploads\/sites\/2382\/2022\/12\/addend-and-sum.jpg\" alt=\"In 3+5=8, 3 and 5 are addends, and 8 is the sum.\" width=\"190\" height=\"101\" srcset=\"https:\/\/pressbooks.bccampus.ca\/math024\/wp-content\/uploads\/sites\/2382\/2022\/12\/addend-and-sum.jpg 217w, https:\/\/pressbooks.bccampus.ca\/math024\/wp-content\/uploads\/sites\/2382\/2022\/12\/addend-and-sum-65x34.jpg 65w\" sizes=\"auto, (max-width: 190px) 100vw, 190px\" \/><\/p>\n<p><strong>Definition of Addends:<\/strong><\/p>\n<p><strong>Definition of Sum:<\/strong><\/p>\n<\/div>\n<p>When adding decimals, you must be very careful to add together the <a class=\"glossary-term\" aria-haspopup=\"dialog\" aria-describedby=\"definition\" href=\"#term_78_169\">digits<\/a> with the same place value.<\/p>\n<ul>\n<li>Add thousandths to thousandths.<\/li>\n<li>Add hundredths to hundredths.<\/li>\n<li>Add tenths to tenths.<\/li>\n<\/ul>\n<p>The best way to do this is to <strong>line up your decimals<\/strong>.<\/p>\n<h2>How to Add Decimals<\/h2>\n<ol>\n<li>Write the <a class=\"glossary-term\" aria-haspopup=\"dialog\" aria-describedby=\"definition\" href=\"#term_78_158\">addends<\/a> underneath each other so the decimal points are in a straight column. Notice how lining up the decimals also lines up the place values.<br \/>\n[latex]0.43+0.2+0.804+0.1=[\/latex]<br \/>\nRewrite as: [latex]\\begin{array}{ll}&0.43\\\\&0.2\\\\&0.804\\\\+&0.1\\\\ \\hline\\end{array}[\/latex]<\/li>\n<li>Put zeros at the end of the decimal fractions so that all fractions have the same number of decimal places.<br \/>\n[latex]\\begin{array}{ll}&0.430\\\\&0.200\\\\&0.804\\\\+&0.100\\\\ \\hline\\end{array}[\/latex]<\/li>\n<li>It may help you to put the decimal point in the answer line before you do the addition.<br \/>\n[latex]\\begin{array}{ll}&0.430\\\\&0.200\\\\&0.804\\\\+&0.100\\\\ \\hline &\\phantom{0}\\mathbf{.}\\end{array}[\/latex]<\/li>\n<li>When adding <a class=\"glossary-term\" aria-haspopup=\"dialog\" aria-describedby=\"definition\" href=\"#term_78_188\">mixed decimals<\/a>, be sure to keep the whole number places lined up as well. As you know, ones add to ones, tens to tens, hundreds to hundreds and so on. Put a decimal point after any whole numbers.<br \/>\n[latex]62.1 + 14.58 + 6. + 7.311 + 6.23 =\\\\ \\begin{array}{lr}&62.100\\\\&14.580\\\\&6.000\\\\&7.311\\\\+&6.230 \\\\ \\hline\\end{array}[\/latex]<\/li>\n<li>Add each column, starting with the decimal place farthest to the right. If the total of a column is ten or more, carry the ten number to the next column as you are used to doing with whole numbers.<br \/>\n[latex]\\begin{array}{ll}&\\small{1\\; 1}\\\\&0.470\\\\&0.298\\\\&0.100\\\\+&5.600\\\\ \\hline &6.468\\end{array}[\/latex]<\/li>\n<\/ol>\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>Rewrite each question in columns and add.<\/p>\n<ol class=\"twocolumn\" type=\"a\">\n<li>0.24 + 0.73 + 0.51 =<br \/>\n[latex]\\begin{array}{ll}&\\scriptsize{1}\\\\&0.24\\\\&0.73\\\\+&0.51\\\\ \\hline &1.48\\end{array}[\/latex]<\/li>\n<li>0.821 + 0.14 + 0.019 =<br \/>\n[latex]\\begin{array}{ll}&\\phantom{0.8}\\scriptsize{1}\\\\&0.821\\\\&0.140\\\\+&0.019\\\\ \\hline &0.980\\end{array}[\/latex]<\/li>\n<\/ol>\n<ol class=\"twocolumn\" start=\"3\" type=\"a\">\n<li>0.084 + 0.291 + 0.652 =<\/li>\n<li>0.195 + 0.982 + 0.605 =<\/li>\n<li>0.625 + 0.845 + 0.33 =<\/li>\n<li>0.442 + 0.782 + 0.254 =<\/li>\n<\/ol>\n<p><strong>Answers to Exercise 1<\/strong><\/p>\n<ol class=\"twocolumn\" type=\"a\">\n<li>1.48<\/li>\n<li>0.980<\/li>\n<li>1.027<\/li>\n<li>1.782<\/li>\n<li>1.8<\/li>\n<li>1.478<\/li>\n<\/ol>\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>Rewrite in columns and add.<\/p>\n<ol class=\"twocolumn\" type=\"a\">\n<li>1.003 + 141.2 + 0.47 =<br \/>\n[latex]\\begin{array}{rr}&1.003\\\\&141.200\\\\+&0.470\\\\ \\hline &142.673\\end{array}[\/latex]<\/li>\n<li>5.6 + 3.59 + 1<span style=\"margin-left: 0.25em\">829<\/span> =<br \/>\n[latex]\\begin{array}{rr}&5.60\\\\&3.59\\\\+&1829.00\\\\ \\hline &1838.19\\end{array}[\/latex]<\/li>\n<\/ol>\n<ol class=\"twocolumn\" start=\"3\" type=\"a\">\n<li>4.6 + 2.59 + 1<span style=\"margin-left: 0.25em\">629<\/span> =<\/li>\n<li>0.391 + 80 + 4.63 =<\/li>\n<li>16.34 + 211.684 + 75.0697 =<\/li>\n<li>321.6 + 485.791 + 0.001 =<\/li>\n<li>0.22 + 46.84 + 95.6 =<\/li>\n<li>0.042 + 0.018 + 19.1 =<\/li>\n<\/ol>\n<p><strong>Answers to Exercise 2<\/strong><\/p>\n<ol class=\"twocolumn\" type=\"a\">\n<li>142.673<\/li>\n<li>1838.19<\/li>\n<li>1636.19<\/li>\n<li>85.021<\/li>\n<li>303.0937<\/li>\n<li>807.392<\/li>\n<li>142.66<\/li>\n<li>19.16<\/li>\n<\/ol>\n<\/div>\n<\/div>\n<div class=\"textbox\">Remember that <a class=\"glossary-term\" aria-haspopup=\"dialog\" aria-describedby=\"definition\" href=\"#term_78_199\">perimeter<\/a> is the measurement around the outside edge of an object. To find perimeter, you add the lengths of all the sides together.<\/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 perimeter of the squares described in each question. The measure of one side has been given. Draw a picture of each square to help visualize the question.<\/p>\n<ol type=\"a\">\n<li>S = 75.3 m<br \/>\nP = S + S + S + S<br \/>\nP = 75.3 + 75.3 + 75.3 + 75.3 m<br \/>\nP = 301.2 m<br \/>\n<img loading=\"lazy\" decoding=\"async\" class=\"aligncenter wp-image-61\" src=\"https:\/\/pressbooks.bccampus.ca\/wp-content\/uploads\/sites\/2382\/2025\/01\/square.png\" alt=\"A square. Each side is labelled 75.3 m.\" width=\"200\" height=\"131\" srcset=\"https:\/\/pressbooks.bccampus.ca\/math024\/wp-content\/uploads\/sites\/2382\/2025\/01\/square.png 236w, https:\/\/pressbooks.bccampus.ca\/math024\/wp-content\/uploads\/sites\/2382\/2025\/01\/square-65x43.png 65w, https:\/\/pressbooks.bccampus.ca\/math024\/wp-content\/uploads\/sites\/2382\/2025\/01\/square-225x148.png 225w\" sizes=\"auto, (max-width: 200px) 100vw, 200px\" \/><\/li>\n<li>S = 12.4 mm<br \/>\nP =<\/li>\n<li>S = 100.73 km<br \/>\nP =<\/li>\n<li>S = 50.2 cm<\/li>\n<li>S = 16.5 m<\/li>\n<li>S = 3.25 m<\/li>\n<\/ol>\n<p><strong>Answers to Exercise 3<br \/>\n<\/strong><\/p>\n<ol class=\"twocolumn\" type=\"a\">\n<li>301.2 m<\/li>\n<li>49.6 mm<\/li>\n<li>402.92 km<\/li>\n<li>200.8 cm<\/li>\n<li>66 m<\/li>\n<li>13 m<\/li>\n<\/ol>\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 perimeter of the rectangles described below. Draw your own rectangle if there is no picture.<\/p>\n<ol type=\"a\">\n<li>P = side + side + side + side<br \/>\nP =<br \/>\n<img loading=\"lazy\" decoding=\"async\" class=\"aligncenter wp-image-62 size-full\" src=\"https:\/\/pressbooks.bccampus.ca\/wp-content\/uploads\/sites\/2382\/2025\/01\/4a.png\" alt=\"a rectangle whose length=7.5m, width=3.1m\" width=\"170\" height=\"93\" srcset=\"https:\/\/pressbooks.bccampus.ca\/math024\/wp-content\/uploads\/sites\/2382\/2025\/01\/4a.png 170w, https:\/\/pressbooks.bccampus.ca\/math024\/wp-content\/uploads\/sites\/2382\/2025\/01\/4a-65x36.png 65w\" sizes=\"auto, (max-width: 170px) 100vw, 170px\" \/><\/li>\n<li>P = side + side + side + side<br \/>\nP =<br \/>\n<img loading=\"lazy\" decoding=\"async\" class=\"aligncenter size-full wp-image-63\" src=\"https:\/\/pressbooks.bccampus.ca\/wp-content\/uploads\/sites\/2382\/2025\/01\/4b.png\" alt=\"\" width=\"242\" height=\"88\" srcset=\"https:\/\/pressbooks.bccampus.ca\/math024\/wp-content\/uploads\/sites\/2382\/2025\/01\/4b.png 242w, https:\/\/pressbooks.bccampus.ca\/math024\/wp-content\/uploads\/sites\/2382\/2025\/01\/4b-65x24.png 65w, https:\/\/pressbooks.bccampus.ca\/math024\/wp-content\/uploads\/sites\/2382\/2025\/01\/4b-225x82.png 225w\" sizes=\"auto, (max-width: 242px) 100vw, 242px\" \/><\/li>\n<li><img loading=\"lazy\" decoding=\"async\" class=\"aligncenter wp-image-64 size-full\" src=\"https:\/\/pressbooks.bccampus.ca\/wp-content\/uploads\/sites\/2382\/2025\/01\/4c.png\" alt=\"a rectangle whose length=7.5cm, width=2.1cm\" width=\"128\" height=\"158\" srcset=\"https:\/\/pressbooks.bccampus.ca\/math024\/wp-content\/uploads\/sites\/2382\/2025\/01\/4c.png 128w, https:\/\/pressbooks.bccampus.ca\/math024\/wp-content\/uploads\/sites\/2382\/2025\/01\/4c-65x80.png 65w\" sizes=\"auto, (max-width: 128px) 100vw, 128px\" \/><\/li>\n<li><img loading=\"lazy\" decoding=\"async\" class=\"aligncenter wp-image-65 size-full\" src=\"https:\/\/pressbooks.bccampus.ca\/wp-content\/uploads\/sites\/2382\/2025\/01\/4d-e1671661742599.png\" alt=\"a rectangle whose length=7.5m, width=1.5m\" width=\"322\" height=\"99\" srcset=\"https:\/\/pressbooks.bccampus.ca\/math024\/wp-content\/uploads\/sites\/2382\/2025\/01\/4d-e1671661742599.png 322w, https:\/\/pressbooks.bccampus.ca\/math024\/wp-content\/uploads\/sites\/2382\/2025\/01\/4d-e1671661742599-300x92.png 300w, https:\/\/pressbooks.bccampus.ca\/math024\/wp-content\/uploads\/sites\/2382\/2025\/01\/4d-e1671661742599-65x20.png 65w, https:\/\/pressbooks.bccampus.ca\/math024\/wp-content\/uploads\/sites\/2382\/2025\/01\/4d-e1671661742599-225x69.png 225w\" sizes=\"auto, (max-width: 322px) 100vw, 322px\" \/><\/li>\n<li>l = 10.3 cm<br \/>\nw = 6.6 cm<br \/>\n<img loading=\"lazy\" decoding=\"async\" class=\"aligncenter wp-image-66 size-full\" src=\"https:\/\/pressbooks.bccampus.ca\/wp-content\/uploads\/sites\/2382\/2025\/01\/4e.png\" alt=\"a rectangle whose length=10.3cm, width=6.6cm\" width=\"172\" height=\"77\" srcset=\"https:\/\/pressbooks.bccampus.ca\/math024\/wp-content\/uploads\/sites\/2382\/2025\/01\/4e.png 172w, https:\/\/pressbooks.bccampus.ca\/math024\/wp-content\/uploads\/sites\/2382\/2025\/01\/4e-65x29.png 65w\" sizes=\"auto, (max-width: 172px) 100vw, 172px\" \/><\/li>\n<li>l = 100.03 km<br \/>\nw = 70.96 km<\/li>\n<li>l = 9.75 cm<br \/>\nw = 3.5 cm<\/li>\n<\/ol>\n<p><strong>Answers to Exercise 4<\/strong><\/p>\n<ol class=\"twocolumn\" type=\"a\">\n<li>21.2 m<\/li>\n<li>31.5 cm<\/li>\n<li>19.2 cm<\/li>\n<li>18 m<\/li>\n<li>33.8 cm<\/li>\n<li>341.98 km<\/li>\n<li>26.5 cm<\/li>\n<\/ol>\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 perimeter of the polygons described below. Be sure the measurements are in the same unit value. Use a formula for each calculation, the formula work is started in the first two for you.<\/p>\n<ol type=\"a\">\n<li>P = Side + Side + Side<br \/>\nP = 6.5 km + 7.5 km + 9.5 km<br \/>\nP =<br \/>\n<img loading=\"lazy\" decoding=\"async\" class=\"aligncenter wp-image-67 size-full\" src=\"https:\/\/pressbooks.bccampus.ca\/wp-content\/uploads\/sites\/2382\/2025\/01\/5a.png\" alt=\"a triangle whose sides are 6.5km, 7.5km, 9.5km\" width=\"221\" height=\"80\" srcset=\"https:\/\/pressbooks.bccampus.ca\/math024\/wp-content\/uploads\/sites\/2382\/2025\/01\/5a.png 221w, https:\/\/pressbooks.bccampus.ca\/math024\/wp-content\/uploads\/sites\/2382\/2025\/01\/5a-65x24.png 65w\" sizes=\"auto, (max-width: 221px) 100vw, 221px\" \/><\/li>\n<li>P = Side + Side + Side + Side + Side + Side<br \/>\nP =\u00a0<span style=\"text-decoration: underline\" aria-label=\"blank\">\u00a0 \u00a0 \u00a0\u00a0<\/span> + <span style=\"text-decoration: underline\" aria-label=\"blank\">\u00a0 \u00a0 \u00a0\u00a0<\/span> + <span style=\"text-decoration: underline\" aria-label=\"blank\">\u00a0 \u00a0 \u00a0\u00a0<\/span> + <span style=\"text-decoration: underline\" aria-label=\"blank\">\u00a0 \u00a0 \u00a0\u00a0<\/span> + <span style=\"text-decoration: underline\" aria-label=\"blank\">\u00a0 \u00a0 \u00a0\u00a0<\/span> + <span style=\"text-decoration: underline\" aria-label=\"blank\">\u00a0 \u00a0 \u00a0\u00a0<\/span><br \/>\nP =<br \/>\nP =<br \/>\n<img loading=\"lazy\" decoding=\"async\" class=\"aligncenter wp-image-68 size-full\" src=\"https:\/\/pressbooks.bccampus.ca\/wp-content\/uploads\/sites\/2382\/2025\/01\/5b.png\" alt=\"a hexagon whose sides are 80.3m, 80.3m, 80.3m, 80.3m, 80.3m, 80.3m\" width=\"172\" height=\"121\" srcset=\"https:\/\/pressbooks.bccampus.ca\/math024\/wp-content\/uploads\/sites\/2382\/2025\/01\/5b.png 172w, https:\/\/pressbooks.bccampus.ca\/math024\/wp-content\/uploads\/sites\/2382\/2025\/01\/5b-65x46.png 65w\" sizes=\"auto, (max-width: 172px) 100vw, 172px\" \/><\/li>\n<li>P =<br \/>\n<img loading=\"lazy\" decoding=\"async\" class=\"aligncenter wp-image-69 size-full\" src=\"https:\/\/pressbooks.bccampus.ca\/wp-content\/uploads\/sites\/2382\/2025\/01\/5c.png\" alt=\"a triangle whose sides are 7.2cm, 5cm, 4.85cm\" width=\"244\" height=\"76\" srcset=\"https:\/\/pressbooks.bccampus.ca\/math024\/wp-content\/uploads\/sites\/2382\/2025\/01\/5c.png 244w, https:\/\/pressbooks.bccampus.ca\/math024\/wp-content\/uploads\/sites\/2382\/2025\/01\/5c-65x20.png 65w, https:\/\/pressbooks.bccampus.ca\/math024\/wp-content\/uploads\/sites\/2382\/2025\/01\/5c-225x70.png 225w\" sizes=\"auto, (max-width: 244px) 100vw, 244px\" \/><\/li>\n<li>P =<br \/>\n<img loading=\"lazy\" decoding=\"async\" class=\"aligncenter wp-image-70 size-full\" src=\"https:\/\/pressbooks.bccampus.ca\/wp-content\/uploads\/sites\/2382\/2025\/01\/5d.png\" alt=\"a quadrilateral whose sides are 12 units, 7 units, 6 units, 7 units\" width=\"269\" height=\"123\" srcset=\"https:\/\/pressbooks.bccampus.ca\/math024\/wp-content\/uploads\/sites\/2382\/2025\/01\/5d.png 269w, https:\/\/pressbooks.bccampus.ca\/math024\/wp-content\/uploads\/sites\/2382\/2025\/01\/5d-65x30.png 65w, https:\/\/pressbooks.bccampus.ca\/math024\/wp-content\/uploads\/sites\/2382\/2025\/01\/5d-225x103.png 225w\" sizes=\"auto, (max-width: 269px) 100vw, 269px\" \/><\/li>\n<li>P =<br \/>\n<img loading=\"lazy\" decoding=\"async\" class=\"aligncenter wp-image-71 size-full\" src=\"https:\/\/pressbooks.bccampus.ca\/wp-content\/uploads\/sites\/2382\/2025\/01\/5e.png\" alt=\"a rectangle whose length=8.94km, width=1.45km\" width=\"113\" height=\"176\" srcset=\"https:\/\/pressbooks.bccampus.ca\/math024\/wp-content\/uploads\/sites\/2382\/2025\/01\/5e.png 113w, https:\/\/pressbooks.bccampus.ca\/math024\/wp-content\/uploads\/sites\/2382\/2025\/01\/5e-65x101.png 65w\" sizes=\"auto, (max-width: 113px) 100vw, 113px\" \/><\/li>\n<li>P =<br \/>\n<img loading=\"lazy\" decoding=\"async\" class=\"aligncenter wp-image-72 size-full\" src=\"https:\/\/pressbooks.bccampus.ca\/wp-content\/uploads\/sites\/2382\/2025\/01\/5f.png\" alt=\"a square whose sides are 30.3m\" width=\"159\" height=\"146\" srcset=\"https:\/\/pressbooks.bccampus.ca\/math024\/wp-content\/uploads\/sites\/2382\/2025\/01\/5f.png 159w, https:\/\/pressbooks.bccampus.ca\/math024\/wp-content\/uploads\/sites\/2382\/2025\/01\/5f-65x60.png 65w\" sizes=\"auto, (max-width: 159px) 100vw, 159px\" \/><\/li>\n<\/ol>\n<p><strong>Answers to Exercise 5<\/strong><\/p>\n<ol class=\"twocolumn\" type=\"a\">\n<li>23.5 km<\/li>\n<li>481.8 m<\/li>\n<li>17.05 cm<\/li>\n<li>32 units<\/li>\n<li>20.78 km<\/li>\n<li>121.2 m<\/li>\n<\/ol>\n<\/div>\n<\/div>\n<h1>How to Solve Word Problems<\/h1>\n<p>In math, word problems describe real-life situations that involve numbers.<\/p>\n<p>Often the most difficult part of a word problem is knowing what we should do. Once we know what to do, it is much easier to figure out how to do it.<\/p>\n<p><img loading=\"lazy\" decoding=\"async\" class=\"alignleft wp-image-73\" src=\"https:\/\/pressbooks.bccampus.ca\/wp-content\/uploads\/sites\/2382\/2025\/01\/image96.png\" alt=\"A drawing of a winding road with lots of signs.\" width=\"200\" height=\"186\" srcset=\"https:\/\/pressbooks.bccampus.ca\/math024\/wp-content\/uploads\/sites\/2382\/2025\/01\/image96.png 365w, https:\/\/pressbooks.bccampus.ca\/math024\/wp-content\/uploads\/sites\/2382\/2025\/01\/image96-300x279.png 300w, https:\/\/pressbooks.bccampus.ca\/math024\/wp-content\/uploads\/sites\/2382\/2025\/01\/image96-65x61.png 65w, https:\/\/pressbooks.bccampus.ca\/math024\/wp-content\/uploads\/sites\/2382\/2025\/01\/image96-225x210.png 225w, https:\/\/pressbooks.bccampus.ca\/math024\/wp-content\/uploads\/sites\/2382\/2025\/01\/image96-350x326.png 350w\" sizes=\"auto, (max-width: 200px) 100vw, 200px\" \/>It is sort of like driving. You may be all ready to go, but before you get into the car, turn on the engine, or put your foot on the gas pedal, you need to know <strong>where<\/strong> you are going and figure out how to get there.<\/p>\n<p>The first thing to do is decide on your destination. <img loading=\"lazy\" decoding=\"async\" class=\"alignright wp-image-74\" src=\"https:\/\/pressbooks.bccampus.ca\/wp-content\/uploads\/sites\/2382\/2025\/01\/image98.png\" alt=\"A road sign showing a car driving through a large pothole.\" width=\"200\" height=\"200\" srcset=\"https:\/\/pressbooks.bccampus.ca\/math024\/wp-content\/uploads\/sites\/2382\/2025\/01\/image98.png 225w, https:\/\/pressbooks.bccampus.ca\/math024\/wp-content\/uploads\/sites\/2382\/2025\/01\/image98-150x150.png 150w, https:\/\/pressbooks.bccampus.ca\/math024\/wp-content\/uploads\/sites\/2382\/2025\/01\/image98-65x65.png 65w\" sizes=\"auto, (max-width: 200px) 100vw, 200px\" \/><\/p>\n<p>Okay, how do you &#8220;decide on a destination&#8221; for a math problem?<\/p>\n<p>Use these steps:<\/p>\n<table class=\"grid\" style=\"border-collapse: collapse;width: 100%\">\n<caption>Steps to Solving a word problem<\/caption>\n<tbody>\n<tr>\n<th style=\"width: 25%\" scope=\"row\">Step 1: Question<\/th>\n<td style=\"width: 75%\">\n<ul>\n<li>Read the problem carefully.<\/li>\n<li>What is the question being asked?<\/li>\n<li>Does the problem have two parts?<\/li>\n<li>Draw a picture to help you see the problem described.<\/li>\n<\/ul>\n<\/td>\n<\/tr>\n<tr>\n<th style=\"width: 25%\" scope=\"row\">Step 2: Information<\/th>\n<td style=\"width: 75%\">\n<ul>\n<li>What information is necessary to solve the problem?<\/li>\n<li>Often you are given extra numbers and information that are not needed.<\/li>\n<li>Keep the question (destination) in mind.<\/li>\n<li><span style=\"border: 1px solid;border-radius: 30px;padding: 2px 2px 2px 2px\"> Circle <\/span> the information you need.<\/li>\n<li>Write that information on the picture you drew.<\/li>\n<\/ul>\n<\/td>\n<\/tr>\n<tr>\n<th style=\"width: 25%\" scope=\"row\">Step 3: Operation<\/th>\n<td style=\"width: 75%\">\n<ul>\n<li>Decide what arithmetic operation to use.<\/li>\n<li>Do you need to add, subtract, multiply, or divide?<\/li>\n<li>If the problem has two parts, decide what operation you need to do for each part.\n<ul>\n<li>Key words often point to the operation needed.<\/li>\n<li>Drawing a diagram or sketch is always helpful.<\/li>\n<li>Write an equation (a number sentence).<\/li>\n<\/ul>\n<\/li>\n<\/ul>\n<\/td>\n<\/tr>\n<tr>\n<th style=\"width: 25%\" scope=\"row\">Step 4: Estimate<\/th>\n<td style=\"width: 75%\">\n<ul>\n<li><a class=\"glossary-term\" aria-haspopup=\"dialog\" aria-describedby=\"definition\" href=\"#term_78_177\">Estimate<\/a> the answer to the problem.\n<ul>\n<li>Round the numbers so you can work with them quickly.<br \/>\nUse the operation you chose in Step 3 and come to a quick answer.<\/li>\n<\/ul>\n<\/li>\n<li>Does this estimated answer make sense?<\/li>\n<li>Does it answer the question of the problem?<\/li>\n<li>Think carefully before you do Step 5.<\/li>\n<\/ul>\n<\/td>\n<\/tr>\n<tr>\n<th style=\"width: 25%\" scope=\"row\">Step 5: Solve<\/th>\n<td style=\"width: 75%\">\n<ul>\n<li>Solve the problem using the actual numbers.\n<ul>\n<li>Check your arithmetic.<\/li>\n<li>Compare your answer in Step 5 to your estimate from Step 4.<\/li>\n<li>Think again about the question. Does your solution make sense?<\/li>\n<li>When you write your answer, include the units.<\/li>\n<li>For example: 3 dozen eggs, 7.5 kilometres, 68 people<\/li>\n<\/ul>\n<\/li>\n<\/ul>\n<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<table class=\"grid aligncenter\" style=\"border-collapse: collapse;width: 50%;height: 108px\">\n<caption>Some common metric units and their abbreviations<\/caption>\n<tbody>\n<tr style=\"height: 18px\">\n<th style=\"width: 50%;height: 18px\" scope=\"col\">Unit<\/th>\n<th style=\"width: 50%;height: 18px\" scope=\"col\">Abbreviations<\/th>\n<\/tr>\n<tr style=\"height: 18px\">\n<td style=\"width: 50%;height: 18px\">kilometre<\/td>\n<td style=\"width: 50%;height: 18px\">km<\/td>\n<\/tr>\n<tr style=\"height: 18px\">\n<td style=\"width: 50%;height: 18px\">metre<\/td>\n<td style=\"width: 50%;height: 18px\">m<\/td>\n<\/tr>\n<tr style=\"height: 18px\">\n<td style=\"width: 50%;height: 18px\">centimetre<\/td>\n<td style=\"width: 50%;height: 18px\">cm<\/td>\n<\/tr>\n<tr style=\"height: 18px\">\n<td style=\"width: 50%;height: 18px\">kilogram<\/td>\n<td style=\"width: 50%;height: 18px\">kg<\/td>\n<\/tr>\n<tr style=\"height: 18px\">\n<td style=\"width: 50%;height: 18px\">gram<\/td>\n<td style=\"width: 50%;height: 18px\">g<\/td>\n<\/tr>\n<tr>\n<td style=\"width: 50%\">litre<\/td>\n<td style=\"width: 50%\">L<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\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>The nutrition information on a box of cereal says that a regular serving contains 2.8 g of protein, 0.2 g of fat, 25 g of carbohydrate, and 1.9 g of &#8220;other nutrients.&#8221; Give the total number of grams in a regular serving.<\/p>\n<table class=\"grid\" style=\"border-collapse: collapse;width: 100%\">\n<tbody>\n<tr>\n<th style=\"width: 25%\" scope=\"row\">Step 1: Question<\/th>\n<td>How many grams in a regular serving?<\/p>\n<p>Draw a picture:<\/p>\n<p><img loading=\"lazy\" decoding=\"async\" class=\"aligncenter wp-image-75 size-full\" src=\"https:\/\/pressbooks.bccampus.ca\/wp-content\/uploads\/sites\/2382\/2025\/01\/aq.png\" alt=\"protein, fat, carbohydrate, other\" width=\"466\" height=\"74\" srcset=\"https:\/\/pressbooks.bccampus.ca\/math024\/wp-content\/uploads\/sites\/2382\/2025\/01\/aq.png 466w, https:\/\/pressbooks.bccampus.ca\/math024\/wp-content\/uploads\/sites\/2382\/2025\/01\/aq-300x48.png 300w, https:\/\/pressbooks.bccampus.ca\/math024\/wp-content\/uploads\/sites\/2382\/2025\/01\/aq-65x10.png 65w, https:\/\/pressbooks.bccampus.ca\/math024\/wp-content\/uploads\/sites\/2382\/2025\/01\/aq-225x36.png 225w, https:\/\/pressbooks.bccampus.ca\/math024\/wp-content\/uploads\/sites\/2382\/2025\/01\/aq-350x56.png 350w\" sizes=\"auto, (max-width: 466px) 100vw, 466px\" \/><\/td>\n<\/tr>\n<tr>\n<th style=\"width: 25%\" scope=\"row\">Step 2: Information<\/th>\n<td>What information is necessary to solve the problem?<\/p>\n<ul>\n<li>A regular serving contains 2.8 g protein, 0.2 g fat, 25 carbohydrate, and 1.9 g &#8220;other nutrients.&#8221;<\/li>\n<li>Add the information to your Picture.<\/li>\n<\/ul>\n<\/td>\n<\/tr>\n<tr>\n<th style=\"width: 25%\" scope=\"row\">Step 3: Operation<\/th>\n<td>\n<ul>\n<li>The problem lists four different amounts and asks you to find one total. &#8220;Total&#8221; is a key word that points to addition.<\/li>\n<li>Add the operation you need to your picture:<br \/>\n<img loading=\"lazy\" decoding=\"async\" class=\"aligncenter wp-image-76 size-full\" src=\"https:\/\/pressbooks.bccampus.ca\/wp-content\/uploads\/sites\/2382\/2025\/01\/o3.png\" alt=\"2.8g of protein + 0.2g of fat +25g of carbohydrate + 1.9g of other\" width=\"512\" height=\"73\" srcset=\"https:\/\/pressbooks.bccampus.ca\/math024\/wp-content\/uploads\/sites\/2382\/2025\/01\/o3.png 512w, https:\/\/pressbooks.bccampus.ca\/math024\/wp-content\/uploads\/sites\/2382\/2025\/01\/o3-300x43.png 300w, https:\/\/pressbooks.bccampus.ca\/math024\/wp-content\/uploads\/sites\/2382\/2025\/01\/o3-65x9.png 65w, https:\/\/pressbooks.bccampus.ca\/math024\/wp-content\/uploads\/sites\/2382\/2025\/01\/o3-225x32.png 225w, https:\/\/pressbooks.bccampus.ca\/math024\/wp-content\/uploads\/sites\/2382\/2025\/01\/o3-350x50.png 350w\" sizes=\"auto, (max-width: 512px) 100vw, 512px\" \/><\/li>\n<li>Next, write an equation: 2.8 + 0.2 + 25 + 1.9 = total number of grams<\/li>\n<\/ul>\n<\/td>\n<\/tr>\n<tr>\n<th style=\"width: 25%\" scope=\"row\">Step 4: Estimate<\/th>\n<td>\n<ul>\n<li>Round off each amount and add them together to get an estimated answer.\n<ul>\n<li>2.8 g \u2248 3 g, 0.2 g \u2248 0 g, 25 g \u2248 25 g, 1.9 g \u2248 2g<\/li>\n<li>3 g + 0 g + 25 g + 2 g = 30 g<\/li>\n<\/ul>\n<\/li>\n<li>Does this answer make sense?\n<ul>\n<li>A slice of bread is about 35 grams. A serving of cereal would probably weigh a similar amount. Yes, this makes sense.<\/li>\n<\/ul>\n<\/li>\n<\/ul>\n<\/td>\n<\/tr>\n<tr>\n<th style=\"width: 25%\" scope=\"row\">Step 5: Solve<\/th>\n<td>2.8 g + 0.2 g + 25.0g + 1.9 g = 29.9 g<\/p>\n<p><strong>Answer<\/strong>: A regular serving of cereal is 29.9 grams \u2190 (include the units)<\/p>\n<ul>\n<li>Check arithmetic<\/li>\n<li>Compare answer to estimate\u00a0 (estimate = 30\u00a0 \u00a0answer =29.9)<\/li>\n<li>Does the answer make sense?<\/li>\n<li>Did I include the units in my answer?<\/li>\n<\/ul>\n<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<\/div>\n<\/div>\n<p>Some key words that point to addition include:<\/p>\n<ul class=\"twocolumn\">\n<li><a class=\"glossary-term\" aria-haspopup=\"dialog\" aria-describedby=\"definition\" href=\"#term_78_214\">sum<\/a><\/li>\n<li>plus<\/li>\n<li><a class=\"glossary-term\" aria-haspopup=\"dialog\" aria-describedby=\"definition\" href=\"#term_78_217\">total<\/a><\/li>\n<li>total amount<\/li>\n<li>altogether<\/li>\n<li>combined<\/li>\n<li>complete<\/li>\n<li>entire<\/li>\n<li>in all<\/li>\n<li>added to<\/li>\n<li>increased by<\/li>\n<\/ul>\n<h1>Word Problems Using Addition of Decimals<\/h1>\n<div class=\"textbox textbox--exercises\">\n<header class=\"textbox__header\">\n<p class=\"textbox__title\">Exercise 6<\/p>\n<\/header>\n<div class=\"textbox__content\">\n<p>Use your skills in adding decimal fractions to do the following problems. Underline key words in the problems that will help you to recognize addition problems. Remember to draw a picture first!<\/p>\n<ol type=\"a\">\n<li>A road construction crew finished surfacing 5.7 km of highway one week and 4.4 km the next week. How many kilometres did they complete in that two weeks?\n<ul type=\"a\">\n<li>5.7 km + 4.4 km<\/li>\n<li><strong>Estimation<\/strong>: 6 km + 4 km = 10 km<\/li>\n<li><strong>Actual Solution<\/strong>: [latex]\\begin{array}[t]{rr}&5.7\\text{ km}\\\\+&4.4\\text{ km}\\\\ \\hline &10.1\\text{ km}\\end{array}[\/latex]<\/li>\n<li><strong>Answer<\/strong>: The road crew completed 10.1 km of road surfacing in two weeks.<\/li>\n<\/ul>\n<\/li>\n<li>Lisa rode her bike 2.4 km to her auntie\u2019s house for a little visit. Then she rode 1.5 km to the grocery store to get apples and 0.7 km to Walmart to get bread and chips. From Walmart, she rode 3.6 km home. How far did she go on her bike altogether? (the picture has been drawn here but you will need to fill in the information)<br \/>\n<img loading=\"lazy\" decoding=\"async\" class=\"aligncenter size-full wp-image-77\" src=\"https:\/\/pressbooks.bccampus.ca\/wp-content\/uploads\/sites\/2382\/2025\/01\/6b.png\" alt=\"\" width=\"381\" height=\"140\" srcset=\"https:\/\/pressbooks.bccampus.ca\/math024\/wp-content\/uploads\/sites\/2382\/2025\/01\/6b.png 381w, https:\/\/pressbooks.bccampus.ca\/math024\/wp-content\/uploads\/sites\/2382\/2025\/01\/6b-300x110.png 300w, https:\/\/pressbooks.bccampus.ca\/math024\/wp-content\/uploads\/sites\/2382\/2025\/01\/6b-65x24.png 65w, https:\/\/pressbooks.bccampus.ca\/math024\/wp-content\/uploads\/sites\/2382\/2025\/01\/6b-225x83.png 225w, https:\/\/pressbooks.bccampus.ca\/math024\/wp-content\/uploads\/sites\/2382\/2025\/01\/6b-350x129.png 350w\" sizes=\"auto, (max-width: 381px) 100vw, 381px\" \/><\/p>\n<ul type=\"a\">\n<li>Estimation:<\/li>\n<li>Actual Solution:<\/li>\n<li>Answer:<\/li>\n<\/ul>\n<\/li>\n<li>When Crystalle bought her used car, the odometer showed 12<span style=\"margin-left: 0.25em\">686.4<\/span> km. In one year, she drove 13<span style=\"margin-left: 0.25em\">294.8<\/span> km. What did the odometer read then?\u00a0 (draw your own picture)\n<ul type=\"a\">\n<li>Estimation:<\/li>\n<li>Actual Solution:<\/li>\n<li>Answer:<\/li>\n<\/ul>\n<\/li>\n<li>A recipe for spaghetti sauce uses 1.25 kg of ground beef, 2.4 kg of fresh tomatoes, 1 kg of onions, 0.75 kg of celery, 0.5 kg of green pepper and lots of garlic and herbs. What is the total weight of the ingredients, not counting the garlic and herbs?\n<ul type=\"a\">\n<li>Estimate:<\/li>\n<li>Actual Solution:<\/li>\n<li>Answer:<\/li>\n<\/ul>\n<\/li>\n<li>This month your power bill has increased $24.67, your phone bill has an extra $13.43, and your cable bill is up $2.24. It has been an expensive month! What is the combined extra cost that you are paying this month?\n<ul type=\"a\">\n<li>Estimate:<\/li>\n<li>Actual Solution:<\/li>\n<li>Answer:<\/li>\n<\/ul>\n<\/li>\n<li>Wanda texted her boyfriend Curtis and asked him to pick up some groceries on the way home. He answered back \u201cOnly have $20. Is that enough?\u201d Wanda wanted him to buy milk ($4.86), mac and cheese ($1.99), a bag of apples ($3.99) and laundry detergent ($8.57). Does Curtis have enough money?\n<ul type=\"a\">\n<li>Estimate:<\/li>\n<li>Actual Solution:<\/li>\n<li>Answer:<\/li>\n<\/ul>\n<\/li>\n<\/ol>\n<p><strong>Answers to Exercise 6<\/strong><\/p>\n<ol start=\"2\" type=\"a\">\n<li>Estimation: 2 + 2 + 1 + 4 = 9<br \/>\nActual Solution: 2.4 + 1.5 + 0.7 + 3.6 = 8.2<br \/>\nAnswer: Lisa rode her bike 8.2 km altogether.<\/li>\n<li>Estimation: 13<span style=\"margin-left: 0.25em\">000<\/span> km + 13<span style=\"margin-left: 0.25em\">000<\/span> km = 26<span style=\"margin-left: 0.25em\">000<\/span> km<br \/>\nActual Solution: 12<span style=\"margin-left: 0.25em\">686.4<\/span> km + 13<span style=\"margin-left: 0.25em\">294.8<\/span> km = 25<span style=\"margin-left: 0.25em\">981.2<\/span> km<br \/>\nAnswer: The odometer read 25 981.2 km after one year.<\/li>\n<li>Estimation: 1 kg + 2 kg + 1 kg + 1 kg + 1 kg = 6 kg<br \/>\nActual Solution: 1.25 kg + 2.4 kg + 1 kg + 0.75 kg + 0.5 kg = 5.9 kg<br \/>\nAnswer: The total weight of the ingredients is 5.9 kg.<\/li>\n<li>Estimation: $25 + $13 + $2 = $40<br \/>\nActual solution: $24.67 + $13.43 + $2.24 = $40.34<br \/>\nAnswer: The extra cost you are paying is $40.34.<\/li>\n<li>Estimation: $5 + $2 + $4 + 9 = $20<br \/>\nActual solution: $4.86 + $1.99 + $3.99 + $8.57 = $19.41<br \/>\nAnswer: The groceries will cost $19.41 so yes, Curtis has enough money<\/li>\n<\/ol>\n<\/div>\n<\/div>\n<h1>Topic A: Self-Test<\/h1>\n<p><strong>Mark \/6\u00a0 \u00a0 \u00a0Aim 5\/6<\/strong><\/p>\n<ol type=\"A\">\n<li>Find the sum. (4 marks)\n<ol type=\"a\">\n<li>[latex]\\begin{array}{rr}&3.67\\\\&12.55\\\\&8.19\\\\+&5.67\\\\ \\hline\\\\ \\end{array}[\/latex]<\/li>\n<li>[latex]5.27 + 2.4 + 8 + 6.93 + 10.27 =[\/latex]<\/li>\n<li>[latex]\\begin{array}{rr}&4.648\\\\&1.92\\phantom{0}\\\\&1.275\\\\+&86.9\\phantom{00}\\\\ \\hline\\\\ \\end{array}[\/latex]<\/li>\n<li>[latex]2.72 + 0.6 + 110 + 17.223 =[\/latex]<\/li>\n<\/ol>\n<\/li>\n<li>Word Problem. (2 marks)<br \/>\nGwen mailed Christmas presents to her family. She sent a 3.7 kg box to her daughter in Vancouver, a 2.145 kg package to her sister&#8217;s family in Campbell River, a box to Prince George that was 1.06 kg, and a parcel to Kitwanga that was 4 kg. What was the combined weight of Gwen&#8217;s parcels?<\/p>\n<ol type=\"a\">\n<li>Estimate:<\/li>\n<li>Actual Solution:<\/li>\n<li>Answer:<\/li>\n<\/ol>\n<\/li>\n<\/ol>\n<h2>Answers to Topic A Self-Test<\/h2>\n<ol type=\"A\">\n<li>Find the sum.\n<ol class=\"twocolumn\" type=\"a\">\n<li>30.08<\/li>\n<li>32.87<\/li>\n<li>94.743<\/li>\n<li>130.543<\/li>\n<\/ol>\n<\/li>\n<li>Word problem.\n<ol type=\"a\">\n<li>Estimation: 4 kg + 2 kg +1 kg + 4 kg = 11 kg<\/li>\n<li>Actual Solution: 3.7 kg + 2.145 kg + 1.06 kg + 4 kg = 10.905 kg<\/li>\n<li>Answer: The combined weight of the parcels was 10.905 kg.<\/li>\n<\/ol>\n<\/li>\n<\/ol>\n<p>&nbsp;<\/p>\n<div class=\"glossary\"><span class=\"screen-reader-text\" id=\"definition\">definition<\/span><template id=\"term_78_200\"><div class=\"glossary__definition\" role=\"dialog\" data-id=\"term_78_200\"><div tabindex=\"-1\"><p>We understand numbers by the way the digits (numerals) are arranged in relationship to each other and to the decimal point. Each position has a certain value. Our number system is a <strong>decimal system<\/strong>. The place value is based on <strong>ten<\/strong>.<\/p>\n<\/div><button><span aria-hidden=\"true\">&times;<\/span><span class=\"screen-reader-text\">Close definition<\/span><\/button><\/div><\/template><template id=\"term_78_169\"><div class=\"glossary__definition\" role=\"dialog\" data-id=\"term_78_169\"><div tabindex=\"-1\"><p>Any of the ten numerals (0 to 9) are digits. This term comes from our ten fingers which are called digits. The numerals came to be called \"digits\" from the practice of counting on the fingers!<\/p>\n<\/div><button><span aria-hidden=\"true\">&times;<\/span><span class=\"screen-reader-text\">Close definition<\/span><\/button><\/div><\/template><template id=\"term_78_158\"><div class=\"glossary__definition\" role=\"dialog\" data-id=\"term_78_158\"><div tabindex=\"-1\"><p>The numbers to be added together in an addition question. In 3 + 5 = 8, the addends are 3 and 5.<\/p>\n<\/div><button><span aria-hidden=\"true\">&times;<\/span><span class=\"screen-reader-text\">Close definition<\/span><\/button><\/div><\/template><template id=\"term_78_188\"><div class=\"glossary__definition\" role=\"dialog\" data-id=\"term_78_188\"><div tabindex=\"-1\"><p>A whole number and a decimal fraction. 1.75<\/p>\n<\/div><button><span aria-hidden=\"true\">&times;<\/span><span class=\"screen-reader-text\">Close definition<\/span><\/button><\/div><\/template><template id=\"term_78_199\"><div class=\"glossary__definition\" role=\"dialog\" data-id=\"term_78_199\"><div tabindex=\"-1\"><p>The distance around the outside of a shape.<\/p>\n<\/div><button><span aria-hidden=\"true\">&times;<\/span><span class=\"screen-reader-text\">Close definition<\/span><\/button><\/div><\/template><template id=\"term_78_177\"><div class=\"glossary__definition\" role=\"dialog\" data-id=\"term_78_177\"><div tabindex=\"-1\"><p>Make an approximate answer. Use the sign \u2248 to mean approximately equal.<\/p>\n<\/div><button><span aria-hidden=\"true\">&times;<\/span><span class=\"screen-reader-text\">Close definition<\/span><\/button><\/div><\/template><template id=\"term_78_214\"><div class=\"glossary__definition\" role=\"dialog\" data-id=\"term_78_214\"><div tabindex=\"-1\"><p>The result of an addition question, the answer to an addition question.<\/p>\n<\/div><button><span aria-hidden=\"true\">&times;<\/span><span class=\"screen-reader-text\">Close definition<\/span><\/button><\/div><\/template><template id=\"term_78_217\"><div class=\"glossary__definition\" role=\"dialog\" data-id=\"term_78_217\"><div tabindex=\"-1\"><p>The amount altogether.<\/p>\n<\/div><button><span aria-hidden=\"true\">&times;<\/span><span class=\"screen-reader-text\">Close definition<\/span><\/button><\/div><\/template><\/div>","protected":false},"author":999,"menu_order":1,"template":"","meta":{"pb_show_title":"on","pb_short_title":"","pb_subtitle":"","pb_authors":[],"pb_section_license":""},"chapter-type":[],"contributor":[],"license":[],"class_list":["post-78","chapter","type-chapter","status-publish","hentry"],"part":59,"_links":{"self":[{"href":"https:\/\/pressbooks.bccampus.ca\/math024\/wp-json\/pressbooks\/v2\/chapters\/78","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/pressbooks.bccampus.ca\/math024\/wp-json\/pressbooks\/v2\/chapters"}],"about":[{"href":"https:\/\/pressbooks.bccampus.ca\/math024\/wp-json\/wp\/v2\/types\/chapter"}],"author":[{"embeddable":true,"href":"https:\/\/pressbooks.bccampus.ca\/math024\/wp-json\/wp\/v2\/users\/999"}],"version-history":[{"count":6,"href":"https:\/\/pressbooks.bccampus.ca\/math024\/wp-json\/pressbooks\/v2\/chapters\/78\/revisions"}],"predecessor-version":[{"id":263,"href":"https:\/\/pressbooks.bccampus.ca\/math024\/wp-json\/pressbooks\/v2\/chapters\/78\/revisions\/263"}],"part":[{"href":"https:\/\/pressbooks.bccampus.ca\/math024\/wp-json\/pressbooks\/v2\/parts\/59"}],"metadata":[{"href":"https:\/\/pressbooks.bccampus.ca\/math024\/wp-json\/pressbooks\/v2\/chapters\/78\/metadata\/"}],"wp:attachment":[{"href":"https:\/\/pressbooks.bccampus.ca\/math024\/wp-json\/wp\/v2\/media?parent=78"}],"wp:term":[{"taxonomy":"chapter-type","embeddable":true,"href":"https:\/\/pressbooks.bccampus.ca\/math024\/wp-json\/pressbooks\/v2\/chapter-type?post=78"},{"taxonomy":"contributor","embeddable":true,"href":"https:\/\/pressbooks.bccampus.ca\/math024\/wp-json\/wp\/v2\/contributor?post=78"},{"taxonomy":"license","embeddable":true,"href":"https:\/\/pressbooks.bccampus.ca\/math024\/wp-json\/wp\/v2\/license?post=78"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}