{"id":191,"date":"2022-10-07T12:57:46","date_gmt":"2022-10-07T16:57:46","guid":{"rendered":"https:\/\/opentextbc.ca\/alfm5\/chapter\/topic-c-problems-using-common-fractions\/"},"modified":"2025-12-15T18:08:57","modified_gmt":"2025-12-15T23:08:57","slug":"problems-using-common-fractions","status":"publish","type":"chapter","link":"https:\/\/opentextbc.ca\/alfm5\/chapter\/problems-using-common-fractions\/","title":{"raw":"Topic C: Problems Using Common Fractions","rendered":"Topic C: Problems Using Common Fractions"},"content":{"raw":"Review the <a href=\"https:\/\/opentextbc.ca\/alfm2\/chapter\/problem-solving\/#FiveSteps\">five steps for problem solving<\/a>:\r\n<ol>\r\n \t<li><strong>Read <\/strong>the problem and <strong>find<\/strong> the <strong>question<\/strong>.<\/li>\r\n \t<li>Get the <strong>necessary information<\/strong> from the problem.<\/li>\r\n \t<li><strong>Decide<\/strong> on the <strong>arithmetic operation<\/strong>.<\/li>\r\n \t<li><strong>Estimate<\/strong> the answer, using rounded numbers. <strong>Does the answer to the problem seem sensible?<\/strong><\/li>\r\n \t<li><strong>Solve<\/strong> the problem using the <strong>actual numbers<\/strong>. Check. Is the answer close to the estimate?<\/li>\r\n<\/ol>\r\nFraction problems with mixed numbers are easily estimated by rounding the fraction to the nearest whole number.\r\n\r\nIf the problem uses <strong>proper fractions<\/strong> it is <strong>harder to estimate the answer<\/strong> using a rounded number because proper fractions will round off to either 0 or 1, which isn't too useful. However, to figure out the operation to use (Step 3), it sometimes helps to <strong>substitute whole numbers<\/strong> for the proper fraction; this may help you to make sense of the problem. Drawing a sketch might also be helpful.\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\nDecide on the arithmetic operation ( + ,\u00a0 \u2212, \u00d7 , \u00f7 ) and then solve.\r\n<ol type=\"a\">\r\n \t<li>The following recipe for macaroni and cheese is very tasty. It feeds six people. Look at the recipe and then complete the chart according to these questions.\r\n<ol type=\"i\">\r\n \t<li>You want to make enough macaroni and cheese for 9 people. That is [latex]\\tfrac{9}{6}[\/latex] ([latex]\\tfrac{3}{2}[\/latex] or [latex]1\\tfrac{1}{2}[\/latex]) of the recipe.<\/li>\r\n \t<li>Figure out the quantities for [latex]1\\tfrac{1}{2}[\/latex] of the recipe in order to feed 9 people.<\/li>\r\n \t<li>Figure out the quantities for [latex]\\tfrac{1}{2}[\/latex] of the recipe in order to feed 3 people.\r\n<table class=\"grid\" style=\"border-collapse: collapse; width: 100%; height: 257px;\" border=\"0\"><caption>Tasty Macaroni and Cheese Recipe<\/caption>\r\n<thead>\r\n<tr style=\"height: 16px;\">\r\n<th style=\"width: 33.0233%; height: 16px; text-align: left;\" scope=\"col\"><strong>Ingredients for 6 people<\/strong><\/th>\r\n<th style=\"width: 30.9303%; height: 16px; text-align: left;\" scope=\"col\"><strong>Quantities for 9 <\/strong><strong>people [latex]\\left(1\\dfrac{1}{2}\\times\\right)[\/latex]<\/strong><\/th>\r\n<th style=\"width: 35.8139%; height: 16px; text-align: left;\" scope=\"col\"><strong>Quantities for 3 people [latex]\\left(\\dfrac{1}{2}\\times\\right)[\/latex]<\/strong><\/th>\r\n<\/tr>\r\n<\/thead>\r\n<tbody>\r\n<tr style=\"height: 16px;\">\r\n<td style=\"width: 33.0233%; height: 16px;\">[latex]1\\dfrac{3}{4}[\/latex] cup elbow macaroni<\/td>\r\n<td style=\"width: 30.9303%; height: 16px;\"><\/td>\r\n<td style=\"width: 35.8139%; height: 16px;\"><\/td>\r\n<\/tr>\r\n<tr style=\"height: 16px;\">\r\n<td style=\"width: 33.0233%; height: 16px;\">[latex]\\dfrac{3}{4}[\/latex] cup chopped onion<\/td>\r\n<td style=\"width: 30.9303%; height: 16px;\"><\/td>\r\n<td style=\"width: 35.8139%; height: 16px;\"><\/td>\r\n<\/tr>\r\n<tr style=\"height: 16px;\">\r\n<td style=\"width: 33.0233%; height: 16px;\">[latex]\\dfrac{1}{2}[\/latex] cup chopped green pepper<\/td>\r\n<td style=\"width: 30.9303%; height: 16px;\"><\/td>\r\n<td style=\"width: 35.8139%; height: 16px;\"><\/td>\r\n<\/tr>\r\n<tr style=\"height: 16px;\">\r\n<td style=\"width: 33.0233%; height: 16px;\">10 sliced mushrooms<\/td>\r\n<td style=\"width: 30.9303%; height: 16px;\"><\/td>\r\n<td style=\"width: 35.8139%; height: 16px;\"><\/td>\r\n<\/tr>\r\n<tr style=\"height: 16px;\">\r\n<td style=\"width: 33.0233%; height: 16px;\">3 Tbsp. butter or margarine<\/td>\r\n<td style=\"width: 30.9303%; height: 16px;\"><\/td>\r\n<td style=\"width: 35.8139%; height: 16px;\"><\/td>\r\n<\/tr>\r\n<tr style=\"height: 16px;\">\r\n<td style=\"width: 33.0233%; height: 16px;\">[latex]1\\dfrac{1}{2}[\/latex] Tbsp. flour<\/td>\r\n<td style=\"width: 30.9303%; height: 16px;\"><\/td>\r\n<td style=\"width: 35.8139%; height: 16px;\"><\/td>\r\n<\/tr>\r\n<tr style=\"height: 16px;\">\r\n<td style=\"width: 33.0233%; height: 16px;\">1 tsp. dry mustard<\/td>\r\n<td style=\"width: 30.9303%; height: 16px;\"><\/td>\r\n<td style=\"width: 35.8139%; height: 16px;\"><\/td>\r\n<\/tr>\r\n<tr style=\"height: 16px;\">\r\n<td style=\"width: 33.0233%; height: 16px;\">[latex]\\dfrac{3}{4}[\/latex] tsp. salt<\/td>\r\n<td style=\"width: 30.9303%; height: 16px;\"><\/td>\r\n<td style=\"width: 35.8139%; height: 16px;\"><\/td>\r\n<\/tr>\r\n<tr style=\"height: 16px;\">\r\n<td style=\"width: 33.0233%; height: 16px;\">[latex]\\dfrac{1}{4}[\/latex] tsp. oregano<\/td>\r\n<td style=\"width: 30.9303%; height: 16px;\"><\/td>\r\n<td style=\"width: 35.8139%; height: 16px;\"><\/td>\r\n<\/tr>\r\n<tr style=\"height: 16px;\">\r\n<td style=\"width: 33.0233%; height: 16px;\">[latex]2\\dfrac{1}{2}[\/latex] cups milk<\/td>\r\n<td style=\"width: 30.9303%; height: 16px;\"><\/td>\r\n<td style=\"width: 35.8139%; height: 16px;\"><\/td>\r\n<\/tr>\r\n<tr style=\"height: 33px;\">\r\n<td style=\"width: 33.0233%; height: 33px;\">[latex]2\\dfrac{1}{2}[\/latex] cups shredded cheddar cheese<\/td>\r\n<td style=\"width: 30.9303%; height: 33px;\"><\/td>\r\n<td style=\"width: 35.8139%; height: 33px;\"><\/td>\r\n<\/tr>\r\n<tr style=\"height: 48px;\">\r\n<td style=\"width: 33.0233%; height: 48px;\">[latex]\\dfrac{1}{2}[\/latex] cup fine dry breadcrumbs<\/td>\r\n<td style=\"width: 30.9303%; height: 48px;\"><\/td>\r\n<td style=\"width: 35.8139%; height: 48px;\"><\/td>\r\n<\/tr>\r\n<\/tbody>\r\n<\/table>\r\n<\/li>\r\n<\/ol>\r\n<\/li>\r\n \t<li>Jack spent his school day this way: [latex]1\\tfrac{1}{4}[\/latex] hours on English, [latex]1\\tfrac{3}{4}[\/latex] hours on math, [latex]\\tfrac{1}{2}[\/latex] hour on science and 2 hours on lunch and coffee breaks. How long was his school day?<\/li>\r\n \t<li>The canoe trip usually takes [latex]4\\tfrac{1}{4}[\/latex] hours for the 34-kilometre trip. What is the average time per kilometre?<\/li>\r\n \t<li>The \"Walkyerbunsoff\" Club members walk [latex]4\\tfrac{3}{4}[\/latex] kilometres around the shopping mall six mornings a week.\r\n<ol type=\"i\">\r\n \t<li>How far do they walk each week?<\/li>\r\n \t<li>How far do they walk in one year if they keep the same schedule? (1 year = 52 weeks)<\/li>\r\n<\/ol>\r\n<\/li>\r\n \t<li>The test has 30 multiple-choice questions to be completed in [latex]\\tfrac{3}{4}[\/latex] of an hour. How much time can be spent on each question? (It might be easier to work with minutes. 1 hour = 60 minutes, so [latex]\\tfrac{3}{4}[\/latex] of an hour = ? minutes.)<\/li>\r\n \t<li>The gas tank was filled before the family left Hazelton. When they pulled into Prince Rupert that afternoon, the gas gauge showed they had used [latex]\\tfrac{5}{8}[\/latex] of the gas.\r\n<ol type=\"i\">\r\n \t<li>What fraction of the gas was left?<\/li>\r\n \t<li>The full gas tank holds 54 litres. How many litres of gas did they use in the trip from Hazelton to Prince Rupert?<\/li>\r\n<\/ol>\r\n<\/li>\r\n \t<li>About [latex]\\tfrac{2}{5}[\/latex] of the population of our city has an Italian background. The population is 6500. How many people in our city have an Italian background?<\/li>\r\n \t<li>Four children carefully planted 3 rows of corn together and promised to share the work and the corn. Only [latex]2\\tfrac{1}{4}[\/latex] rows of corn came up. How much of a row does each child need to look after?<\/li>\r\n \t<li>Gail was supposed to babysit for [latex]2\\tfrac{3}{4}[\/latex] hours, but she didn't feel well, so her sister Debbie said she would come for [latex]\\tfrac{1}{2}[\/latex] of the time. How long did each sister babysit?<\/li>\r\n \t<li>The stocks closed at [latex]6\\tfrac{1}{8}[\/latex] on Monday. On Tuesday, they fell [latex]\\tfrac{1}{4}[\/latex]. What was the value of the stocks at closing on Tuesday?<\/li>\r\n \t<li>The same stocks had a good day on Wednesday. They rose [latex]\\tfrac{3}{4}[\/latex] from the Tuesday closing price (see question j). What was the value of the stocks at closing on Wednesday?<\/li>\r\n \t<li>Victor and his family heat their house with wood. Last year, they cut and hauled [latex]12\\tfrac{1}{2}[\/latex] cords of wood from the bush. At [latex]\\tfrac{1}{2}[\/latex] cord per pickup truck load, how many trips did they have to make with their one truck?<\/li>\r\n \t<li>Canadian Mortgage Housing Corporation (CMHC) suggests that, when you buy a home, the cost of the house should be no more than [latex]2 \\tfrac{1}{2}[\/latex] times your annual income. Between them, John and Pam Miller have a gross annual income of $68 000. About how much would CMHC say they should spend on a house?<\/li>\r\n \t<li>The loaded logging trucks cover [latex]38\\tfrac{1}{2}[\/latex] km from the logging site down the steep logging roads to the highway in [latex]1\\tfrac{1}{4}[\/latex] hours. What is their average speed in kilometres per hour?<\/li>\r\n<\/ol>\r\n<strong>Answers to Exercise 1<\/strong>\r\n<ol type=\"a\">\r\n \t<li style=\"list-style-type: none;\">\r\n<ol type=\"a\">\r\n \t<li>\r\n<table class=\"grid\" style=\"border-collapse: collapse; width: 100%; height: 257px;\" border=\"0\"><caption>Tasty Macaroni and Cheese Recipe<\/caption>\r\n<thead>\r\n<tr style=\"height: 16px;\">\r\n<th style=\"width: 33.0233%; height: 16px; text-align: left;\" scope=\"col\"><strong>Ingredients for 6 people<\/strong><\/th>\r\n<th style=\"width: 32.5582%; height: 16px; text-align: left;\" scope=\"col\"><strong>Quantities for 9 <\/strong><strong>people [latex]\\left(1\\dfrac{1}{2}\\times\\right)[\/latex]<\/strong><\/th>\r\n<th style=\"width: 34.186%; height: 16px; text-align: left;\" scope=\"col\"><strong>Quantities for 3 people [latex]\\left(\\dfrac{1}{2}\\times\\right)[\/latex]<\/strong><\/th>\r\n<\/tr>\r\n<\/thead>\r\n<tbody>\r\n<tr style=\"height: 16px;\">\r\n<td style=\"width: 33.0233%; height: 16px;\">[latex]1\\dfrac{3}{4}[\/latex] cup elbow macaroni<\/td>\r\n<td style=\"width: 32.5582%; height: 16px;\">[latex]2\\dfrac{5}{8}[\/latex] cups<\/td>\r\n<td style=\"width: 34.186%; height: 16px;\">[latex]\\dfrac{7}{8}[\/latex] cup<\/td>\r\n<\/tr>\r\n<tr style=\"height: 16px;\">\r\n<td style=\"width: 33.0233%; height: 16px;\">[latex]\\dfrac{3}{4}[\/latex] cup chopped onion<\/td>\r\n<td style=\"width: 32.5582%; height: 16px;\">[latex]1\\dfrac{1}{8}[\/latex] cups<\/td>\r\n<td style=\"width: 34.186%; height: 16px;\">[latex]\\dfrac{3}{8}[\/latex] cup<\/td>\r\n<\/tr>\r\n<tr style=\"height: 16px;\">\r\n<td style=\"width: 33.0233%; height: 16px;\">[latex]\\dfrac{1}{2}[\/latex] cup chopped green pepper<\/td>\r\n<td style=\"width: 32.5582%; height: 16px;\">[latex]\\dfrac{3}{4}[\/latex] cup<\/td>\r\n<td style=\"width: 34.186%; height: 16px;\">[latex]\\dfrac{1}{4}[\/latex] cup<\/td>\r\n<\/tr>\r\n<tr style=\"height: 16px;\">\r\n<td style=\"width: 33.0233%; height: 16px;\">10 sliced mushrooms<\/td>\r\n<td style=\"width: 32.5582%; height: 16px;\">15<\/td>\r\n<td style=\"width: 34.186%; height: 16px;\">5<\/td>\r\n<\/tr>\r\n<tr style=\"height: 16px;\">\r\n<td style=\"width: 33.0233%; height: 16px;\">3 Tbsp. butter or margarine<\/td>\r\n<td style=\"width: 32.5582%; height: 16px;\">[latex]4\\dfrac{1}{2}[\/latex] Tbsp.<\/td>\r\n<td style=\"width: 34.186%; height: 16px;\">[latex]1\\dfrac{1}{2}[\/latex] Tbsp.<\/td>\r\n<\/tr>\r\n<tr style=\"height: 16px;\">\r\n<td style=\"width: 33.0233%; height: 16px;\">[latex]1\\dfrac{1}{2}[\/latex] Tbsp. flour<\/td>\r\n<td style=\"width: 32.5582%; height: 16px;\">[latex]2\\dfrac{1}{4}[\/latex] Tbsp.<\/td>\r\n<td style=\"width: 34.186%; height: 16px;\">[latex]\\dfrac{3}{4}[\/latex] Tbsp.<\/td>\r\n<\/tr>\r\n<tr style=\"height: 16px;\">\r\n<td style=\"width: 33.0233%; height: 16px;\">1 tsp. dry mustard<\/td>\r\n<td style=\"width: 32.5582%; height: 16px;\">[latex]1\\dfrac{1}{2}[\/latex] tsp.<\/td>\r\n<td style=\"width: 34.186%; height: 16px;\">[latex]\\dfrac{1}{2}[\/latex] tsp.<\/td>\r\n<\/tr>\r\n<tr style=\"height: 16px;\">\r\n<td style=\"width: 33.0233%; height: 16px;\">[latex]\\dfrac{3}{4}[\/latex] tsp. salt<\/td>\r\n<td style=\"width: 32.5582%; height: 16px;\">[latex]1\\dfrac{1}{8}[\/latex] tsp.<\/td>\r\n<td style=\"width: 34.186%; height: 16px;\">[latex]\\dfrac{3}{8}[\/latex] tsp.<\/td>\r\n<\/tr>\r\n<tr style=\"height: 16px;\">\r\n<td style=\"width: 33.0233%; height: 16px;\">[latex]\\dfrac{1}{4}[\/latex] tsp. oregano<\/td>\r\n<td style=\"width: 32.5582%; height: 16px;\">[latex]\\dfrac{3}{8}[\/latex] tsp.<\/td>\r\n<td style=\"width: 34.186%; height: 16px;\">[latex]\\dfrac{1}{8}[\/latex] tsp.<\/td>\r\n<\/tr>\r\n<tr style=\"height: 16px;\">\r\n<td style=\"width: 33.0233%; height: 16px;\">[latex]2\\dfrac{1}{2}[\/latex] cups milk<\/td>\r\n<td style=\"width: 32.5582%; height: 16px;\">[latex]3\\dfrac{3}{4}[\/latex] cups<\/td>\r\n<td style=\"width: 34.186%; height: 16px;\">[latex]1\\dfrac{1}{4}[\/latex] cups<\/td>\r\n<\/tr>\r\n<tr style=\"height: 33px;\">\r\n<td style=\"width: 33.0233%; height: 33px;\">[latex]2\\dfrac{1}{2}[\/latex] cups shredded cheddar cheese<\/td>\r\n<td style=\"width: 32.5582%; height: 33px;\">[latex]3\\dfrac{3}{4}[\/latex] cups<\/td>\r\n<td style=\"width: 34.186%; height: 33px;\">[latex]1\\dfrac{1}{4}[\/latex] cups<\/td>\r\n<\/tr>\r\n<tr style=\"height: 48px;\">\r\n<td style=\"width: 33.0233%; height: 48px;\">[latex]\\dfrac{1}{2}[\/latex] cup fine dry breadcrumbs<\/td>\r\n<td style=\"width: 32.5582%; height: 48px;\">[latex]\\dfrac{3}{4}[\/latex] cup<\/td>\r\n<td style=\"width: 34.186%; height: 48px;\">[latex]\\dfrac{1}{4}[\/latex] cup<\/td>\r\n<\/tr>\r\n<\/tbody>\r\n<\/table>\r\n<\/li>\r\n<\/ol>\r\n<\/li>\r\n<\/ol>\r\n<ol class=\"twocolumn\" start=\"2\" type=\"a\">\r\n \t<li>[latex]5\\dfrac{1}{2}[\/latex] hours<\/li>\r\n \t<li>[latex]\\dfrac{1}{8}[\/latex]\u00a0 hours\/km or [latex]7\\dfrac{1}{2}[\/latex] min\/km<\/li>\r\n \t<li>\u00a0 answers\r\n<ol type=\"i\">\r\n \t<li>[latex]28\\dfrac{1}{2}[\/latex] km<\/li>\r\n \t<li>1482 km<\/li>\r\n<\/ol>\r\n<\/li>\r\n \t<li>[latex]1\\dfrac{1}{2}[\/latex] minutes\/question<\/li>\r\n \t<li style=\"break-inside: avoid;\">answers\r\n<ol type=\"i\">\r\n \t<li>[latex]\\dfrac{3}{8}[\/latex] tank<\/li>\r\n \t<li>[latex]33\\dfrac{3}{4}[\/latex] L<\/li>\r\n<\/ol>\r\n<\/li>\r\n \t<li>2600 people<\/li>\r\n \t<li>[latex]\\dfrac{3}{4}[\/latex] of a row<\/li>\r\n \t<li>[latex]1\\dfrac{3}{8}[\/latex] hours<\/li>\r\n \t<li>[latex]5\\dfrac{7}{8}[\/latex]<\/li>\r\n \t<li>[latex]6\\dfrac{5}{8}[\/latex]<\/li>\r\n \t<li>25 trips<\/li>\r\n \t<li>$170 000<\/li>\r\n \t<li>[latex]30\\dfrac{4}{5}[\/latex] km\/h<\/li>\r\n<\/ol>\r\n<\/div>\r\n<\/div>","rendered":"<p>Review the <a href=\"https:\/\/opentextbc.ca\/alfm2\/chapter\/problem-solving\/#FiveSteps\">five steps for problem solving<\/a>:<\/p>\n<ol>\n<li><strong>Read <\/strong>the problem and <strong>find<\/strong> the <strong>question<\/strong>.<\/li>\n<li>Get the <strong>necessary information<\/strong> from the problem.<\/li>\n<li><strong>Decide<\/strong> on the <strong>arithmetic operation<\/strong>.<\/li>\n<li><strong>Estimate<\/strong> the answer, using rounded numbers. <strong>Does the answer to the problem seem sensible?<\/strong><\/li>\n<li><strong>Solve<\/strong> the problem using the <strong>actual numbers<\/strong>. Check. Is the answer close to the estimate?<\/li>\n<\/ol>\n<p>Fraction problems with mixed numbers are easily estimated by rounding the fraction to the nearest whole number.<\/p>\n<p>If the problem uses <strong>proper fractions<\/strong> it is <strong>harder to estimate the answer<\/strong> using a rounded number because proper fractions will round off to either 0 or 1, which isn&#8217;t too useful. However, to figure out the operation to use (Step 3), it sometimes helps to <strong>substitute whole numbers<\/strong> for the proper fraction; this may help you to make sense of the problem. Drawing a sketch might also be helpful.<\/p>\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>Decide on the arithmetic operation ( + ,\u00a0 \u2212, \u00d7 , \u00f7 ) and then solve.<\/p>\n<ol type=\"a\">\n<li>The following recipe for macaroni and cheese is very tasty. It feeds six people. Look at the recipe and then complete the chart according to these questions.\n<ol type=\"i\">\n<li>You want to make enough macaroni and cheese for 9 people. That is [latex]\\tfrac{9}{6}[\/latex] ([latex]\\tfrac{3}{2}[\/latex] or [latex]1\\tfrac{1}{2}[\/latex]) of the recipe.<\/li>\n<li>Figure out the quantities for [latex]1\\tfrac{1}{2}[\/latex] of the recipe in order to feed 9 people.<\/li>\n<li>Figure out the quantities for [latex]\\tfrac{1}{2}[\/latex] of the recipe in order to feed 3 people.<br \/>\n<table class=\"grid\" style=\"border-collapse: collapse; width: 100%; height: 257px;\">\n<caption>Tasty Macaroni and Cheese Recipe<\/caption>\n<thead>\n<tr style=\"height: 16px;\">\n<th style=\"width: 33.0233%; height: 16px; text-align: left;\" scope=\"col\"><strong>Ingredients for 6 people<\/strong><\/th>\n<th style=\"width: 30.9303%; height: 16px; text-align: left;\" scope=\"col\"><strong>Quantities for 9 <\/strong><strong>people [latex]\\left(1\\dfrac{1}{2}\\times\\right)[\/latex]<\/strong><\/th>\n<th style=\"width: 35.8139%; height: 16px; text-align: left;\" scope=\"col\"><strong>Quantities for 3 people [latex]\\left(\\dfrac{1}{2}\\times\\right)[\/latex]<\/strong><\/th>\n<\/tr>\n<\/thead>\n<tbody>\n<tr style=\"height: 16px;\">\n<td style=\"width: 33.0233%; height: 16px;\">[latex]1\\dfrac{3}{4}[\/latex] cup elbow macaroni<\/td>\n<td style=\"width: 30.9303%; height: 16px;\"><\/td>\n<td style=\"width: 35.8139%; height: 16px;\"><\/td>\n<\/tr>\n<tr style=\"height: 16px;\">\n<td style=\"width: 33.0233%; height: 16px;\">[latex]\\dfrac{3}{4}[\/latex] cup chopped onion<\/td>\n<td style=\"width: 30.9303%; height: 16px;\"><\/td>\n<td style=\"width: 35.8139%; height: 16px;\"><\/td>\n<\/tr>\n<tr style=\"height: 16px;\">\n<td style=\"width: 33.0233%; height: 16px;\">[latex]\\dfrac{1}{2}[\/latex] cup chopped green pepper<\/td>\n<td style=\"width: 30.9303%; height: 16px;\"><\/td>\n<td style=\"width: 35.8139%; height: 16px;\"><\/td>\n<\/tr>\n<tr style=\"height: 16px;\">\n<td style=\"width: 33.0233%; height: 16px;\">10 sliced mushrooms<\/td>\n<td style=\"width: 30.9303%; height: 16px;\"><\/td>\n<td style=\"width: 35.8139%; height: 16px;\"><\/td>\n<\/tr>\n<tr style=\"height: 16px;\">\n<td style=\"width: 33.0233%; height: 16px;\">3 Tbsp. butter or margarine<\/td>\n<td style=\"width: 30.9303%; height: 16px;\"><\/td>\n<td style=\"width: 35.8139%; height: 16px;\"><\/td>\n<\/tr>\n<tr style=\"height: 16px;\">\n<td style=\"width: 33.0233%; height: 16px;\">[latex]1\\dfrac{1}{2}[\/latex] Tbsp. flour<\/td>\n<td style=\"width: 30.9303%; height: 16px;\"><\/td>\n<td style=\"width: 35.8139%; height: 16px;\"><\/td>\n<\/tr>\n<tr style=\"height: 16px;\">\n<td style=\"width: 33.0233%; height: 16px;\">1 tsp. dry mustard<\/td>\n<td style=\"width: 30.9303%; height: 16px;\"><\/td>\n<td style=\"width: 35.8139%; height: 16px;\"><\/td>\n<\/tr>\n<tr style=\"height: 16px;\">\n<td style=\"width: 33.0233%; height: 16px;\">[latex]\\dfrac{3}{4}[\/latex] tsp. salt<\/td>\n<td style=\"width: 30.9303%; height: 16px;\"><\/td>\n<td style=\"width: 35.8139%; height: 16px;\"><\/td>\n<\/tr>\n<tr style=\"height: 16px;\">\n<td style=\"width: 33.0233%; height: 16px;\">[latex]\\dfrac{1}{4}[\/latex] tsp. oregano<\/td>\n<td style=\"width: 30.9303%; height: 16px;\"><\/td>\n<td style=\"width: 35.8139%; height: 16px;\"><\/td>\n<\/tr>\n<tr style=\"height: 16px;\">\n<td style=\"width: 33.0233%; height: 16px;\">[latex]2\\dfrac{1}{2}[\/latex] cups milk<\/td>\n<td style=\"width: 30.9303%; height: 16px;\"><\/td>\n<td style=\"width: 35.8139%; height: 16px;\"><\/td>\n<\/tr>\n<tr style=\"height: 33px;\">\n<td style=\"width: 33.0233%; height: 33px;\">[latex]2\\dfrac{1}{2}[\/latex] cups shredded cheddar cheese<\/td>\n<td style=\"width: 30.9303%; height: 33px;\"><\/td>\n<td style=\"width: 35.8139%; height: 33px;\"><\/td>\n<\/tr>\n<tr style=\"height: 48px;\">\n<td style=\"width: 33.0233%; height: 48px;\">[latex]\\dfrac{1}{2}[\/latex] cup fine dry breadcrumbs<\/td>\n<td style=\"width: 30.9303%; height: 48px;\"><\/td>\n<td style=\"width: 35.8139%; height: 48px;\"><\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<\/li>\n<\/ol>\n<\/li>\n<li>Jack spent his school day this way: [latex]1\\tfrac{1}{4}[\/latex] hours on English, [latex]1\\tfrac{3}{4}[\/latex] hours on math, [latex]\\tfrac{1}{2}[\/latex] hour on science and 2 hours on lunch and coffee breaks. How long was his school day?<\/li>\n<li>The canoe trip usually takes [latex]4\\tfrac{1}{4}[\/latex] hours for the 34-kilometre trip. What is the average time per kilometre?<\/li>\n<li>The &#8220;Walkyerbunsoff&#8221; Club members walk [latex]4\\tfrac{3}{4}[\/latex] kilometres around the shopping mall six mornings a week.\n<ol type=\"i\">\n<li>How far do they walk each week?<\/li>\n<li>How far do they walk in one year if they keep the same schedule? (1 year = 52 weeks)<\/li>\n<\/ol>\n<\/li>\n<li>The test has 30 multiple-choice questions to be completed in [latex]\\tfrac{3}{4}[\/latex] of an hour. How much time can be spent on each question? (It might be easier to work with minutes. 1 hour = 60 minutes, so [latex]\\tfrac{3}{4}[\/latex] of an hour = ? minutes.)<\/li>\n<li>The gas tank was filled before the family left Hazelton. When they pulled into Prince Rupert that afternoon, the gas gauge showed they had used [latex]\\tfrac{5}{8}[\/latex] of the gas.\n<ol type=\"i\">\n<li>What fraction of the gas was left?<\/li>\n<li>The full gas tank holds 54 litres. How many litres of gas did they use in the trip from Hazelton to Prince Rupert?<\/li>\n<\/ol>\n<\/li>\n<li>About [latex]\\tfrac{2}{5}[\/latex] of the population of our city has an Italian background. The population is 6500. How many people in our city have an Italian background?<\/li>\n<li>Four children carefully planted 3 rows of corn together and promised to share the work and the corn. Only [latex]2\\tfrac{1}{4}[\/latex] rows of corn came up. How much of a row does each child need to look after?<\/li>\n<li>Gail was supposed to babysit for [latex]2\\tfrac{3}{4}[\/latex] hours, but she didn&#8217;t feel well, so her sister Debbie said she would come for [latex]\\tfrac{1}{2}[\/latex] of the time. How long did each sister babysit?<\/li>\n<li>The stocks closed at [latex]6\\tfrac{1}{8}[\/latex] on Monday. On Tuesday, they fell [latex]\\tfrac{1}{4}[\/latex]. What was the value of the stocks at closing on Tuesday?<\/li>\n<li>The same stocks had a good day on Wednesday. They rose [latex]\\tfrac{3}{4}[\/latex] from the Tuesday closing price (see question j). What was the value of the stocks at closing on Wednesday?<\/li>\n<li>Victor and his family heat their house with wood. Last year, they cut and hauled [latex]12\\tfrac{1}{2}[\/latex] cords of wood from the bush. At [latex]\\tfrac{1}{2}[\/latex] cord per pickup truck load, how many trips did they have to make with their one truck?<\/li>\n<li>Canadian Mortgage Housing Corporation (CMHC) suggests that, when you buy a home, the cost of the house should be no more than [latex]2 \\tfrac{1}{2}[\/latex] times your annual income. Between them, John and Pam Miller have a gross annual income of $68 000. About how much would CMHC say they should spend on a house?<\/li>\n<li>The loaded logging trucks cover [latex]38\\tfrac{1}{2}[\/latex] km from the logging site down the steep logging roads to the highway in [latex]1\\tfrac{1}{4}[\/latex] hours. What is their average speed in kilometres per hour?<\/li>\n<\/ol>\n<p><strong>Answers to Exercise 1<\/strong><\/p>\n<ol type=\"a\">\n<li style=\"list-style-type: none;\">\n<ol type=\"a\">\n<li>\n<table class=\"grid\" style=\"border-collapse: collapse; width: 100%; height: 257px;\">\n<caption>Tasty Macaroni and Cheese Recipe<\/caption>\n<thead>\n<tr style=\"height: 16px;\">\n<th style=\"width: 33.0233%; height: 16px; text-align: left;\" scope=\"col\"><strong>Ingredients for 6 people<\/strong><\/th>\n<th style=\"width: 32.5582%; height: 16px; text-align: left;\" scope=\"col\"><strong>Quantities for 9 <\/strong><strong>people [latex]\\left(1\\dfrac{1}{2}\\times\\right)[\/latex]<\/strong><\/th>\n<th style=\"width: 34.186%; height: 16px; text-align: left;\" scope=\"col\"><strong>Quantities for 3 people [latex]\\left(\\dfrac{1}{2}\\times\\right)[\/latex]<\/strong><\/th>\n<\/tr>\n<\/thead>\n<tbody>\n<tr style=\"height: 16px;\">\n<td style=\"width: 33.0233%; height: 16px;\">[latex]1\\dfrac{3}{4}[\/latex] cup elbow macaroni<\/td>\n<td style=\"width: 32.5582%; height: 16px;\">[latex]2\\dfrac{5}{8}[\/latex] cups<\/td>\n<td style=\"width: 34.186%; height: 16px;\">[latex]\\dfrac{7}{8}[\/latex] cup<\/td>\n<\/tr>\n<tr style=\"height: 16px;\">\n<td style=\"width: 33.0233%; height: 16px;\">[latex]\\dfrac{3}{4}[\/latex] cup chopped onion<\/td>\n<td style=\"width: 32.5582%; height: 16px;\">[latex]1\\dfrac{1}{8}[\/latex] cups<\/td>\n<td style=\"width: 34.186%; height: 16px;\">[latex]\\dfrac{3}{8}[\/latex] cup<\/td>\n<\/tr>\n<tr style=\"height: 16px;\">\n<td style=\"width: 33.0233%; height: 16px;\">[latex]\\dfrac{1}{2}[\/latex] cup chopped green pepper<\/td>\n<td style=\"width: 32.5582%; height: 16px;\">[latex]\\dfrac{3}{4}[\/latex] cup<\/td>\n<td style=\"width: 34.186%; height: 16px;\">[latex]\\dfrac{1}{4}[\/latex] cup<\/td>\n<\/tr>\n<tr style=\"height: 16px;\">\n<td style=\"width: 33.0233%; height: 16px;\">10 sliced mushrooms<\/td>\n<td style=\"width: 32.5582%; height: 16px;\">15<\/td>\n<td style=\"width: 34.186%; height: 16px;\">5<\/td>\n<\/tr>\n<tr style=\"height: 16px;\">\n<td style=\"width: 33.0233%; height: 16px;\">3 Tbsp. butter or margarine<\/td>\n<td style=\"width: 32.5582%; height: 16px;\">[latex]4\\dfrac{1}{2}[\/latex] Tbsp.<\/td>\n<td style=\"width: 34.186%; height: 16px;\">[latex]1\\dfrac{1}{2}[\/latex] Tbsp.<\/td>\n<\/tr>\n<tr style=\"height: 16px;\">\n<td style=\"width: 33.0233%; height: 16px;\">[latex]1\\dfrac{1}{2}[\/latex] Tbsp. flour<\/td>\n<td style=\"width: 32.5582%; height: 16px;\">[latex]2\\dfrac{1}{4}[\/latex] Tbsp.<\/td>\n<td style=\"width: 34.186%; height: 16px;\">[latex]\\dfrac{3}{4}[\/latex] Tbsp.<\/td>\n<\/tr>\n<tr style=\"height: 16px;\">\n<td style=\"width: 33.0233%; height: 16px;\">1 tsp. dry mustard<\/td>\n<td style=\"width: 32.5582%; height: 16px;\">[latex]1\\dfrac{1}{2}[\/latex] tsp.<\/td>\n<td style=\"width: 34.186%; height: 16px;\">[latex]\\dfrac{1}{2}[\/latex] tsp.<\/td>\n<\/tr>\n<tr style=\"height: 16px;\">\n<td style=\"width: 33.0233%; height: 16px;\">[latex]\\dfrac{3}{4}[\/latex] tsp. salt<\/td>\n<td style=\"width: 32.5582%; height: 16px;\">[latex]1\\dfrac{1}{8}[\/latex] tsp.<\/td>\n<td style=\"width: 34.186%; height: 16px;\">[latex]\\dfrac{3}{8}[\/latex] tsp.<\/td>\n<\/tr>\n<tr style=\"height: 16px;\">\n<td style=\"width: 33.0233%; height: 16px;\">[latex]\\dfrac{1}{4}[\/latex] tsp. oregano<\/td>\n<td style=\"width: 32.5582%; height: 16px;\">[latex]\\dfrac{3}{8}[\/latex] tsp.<\/td>\n<td style=\"width: 34.186%; height: 16px;\">[latex]\\dfrac{1}{8}[\/latex] tsp.<\/td>\n<\/tr>\n<tr style=\"height: 16px;\">\n<td style=\"width: 33.0233%; height: 16px;\">[latex]2\\dfrac{1}{2}[\/latex] cups milk<\/td>\n<td style=\"width: 32.5582%; height: 16px;\">[latex]3\\dfrac{3}{4}[\/latex] cups<\/td>\n<td style=\"width: 34.186%; height: 16px;\">[latex]1\\dfrac{1}{4}[\/latex] cups<\/td>\n<\/tr>\n<tr style=\"height: 33px;\">\n<td style=\"width: 33.0233%; height: 33px;\">[latex]2\\dfrac{1}{2}[\/latex] cups shredded cheddar cheese<\/td>\n<td style=\"width: 32.5582%; height: 33px;\">[latex]3\\dfrac{3}{4}[\/latex] cups<\/td>\n<td style=\"width: 34.186%; height: 33px;\">[latex]1\\dfrac{1}{4}[\/latex] cups<\/td>\n<\/tr>\n<tr style=\"height: 48px;\">\n<td style=\"width: 33.0233%; height: 48px;\">[latex]\\dfrac{1}{2}[\/latex] cup fine dry breadcrumbs<\/td>\n<td style=\"width: 32.5582%; height: 48px;\">[latex]\\dfrac{3}{4}[\/latex] cup<\/td>\n<td style=\"width: 34.186%; height: 48px;\">[latex]\\dfrac{1}{4}[\/latex] cup<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<\/li>\n<\/ol>\n<\/li>\n<\/ol>\n<ol class=\"twocolumn\" start=\"2\" type=\"a\">\n<li>[latex]5\\dfrac{1}{2}[\/latex] hours<\/li>\n<li>[latex]\\dfrac{1}{8}[\/latex]\u00a0 hours\/km or [latex]7\\dfrac{1}{2}[\/latex] min\/km<\/li>\n<li>\u00a0 answers\n<ol type=\"i\">\n<li>[latex]28\\dfrac{1}{2}[\/latex] km<\/li>\n<li>1482 km<\/li>\n<\/ol>\n<\/li>\n<li>[latex]1\\dfrac{1}{2}[\/latex] minutes\/question<\/li>\n<li style=\"break-inside: avoid;\">answers\n<ol type=\"i\">\n<li>[latex]\\dfrac{3}{8}[\/latex] tank<\/li>\n<li>[latex]33\\dfrac{3}{4}[\/latex] L<\/li>\n<\/ol>\n<\/li>\n<li>2600 people<\/li>\n<li>[latex]\\dfrac{3}{4}[\/latex] of a row<\/li>\n<li>[latex]1\\dfrac{3}{8}[\/latex] hours<\/li>\n<li>[latex]5\\dfrac{7}{8}[\/latex]<\/li>\n<li>[latex]6\\dfrac{5}{8}[\/latex]<\/li>\n<li>25 trips<\/li>\n<li>$170 000<\/li>\n<li>[latex]30\\dfrac{4}{5}[\/latex] km\/h<\/li>\n<\/ol>\n<\/div>\n<\/div>\n","protected":false},"author":123,"menu_order":3,"template":"","meta":{"pb_show_title":"on","pb_short_title":"","pb_subtitle":"","pb_authors":[],"pb_section_license":""},"chapter-type":[],"contributor":[],"license":[],"class_list":["post-191","chapter","type-chapter","status-publish","hentry"],"part":154,"_links":{"self":[{"href":"https:\/\/opentextbc.ca\/alfm5\/wp-json\/pressbooks\/v2\/chapters\/191","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/opentextbc.ca\/alfm5\/wp-json\/pressbooks\/v2\/chapters"}],"about":[{"href":"https:\/\/opentextbc.ca\/alfm5\/wp-json\/wp\/v2\/types\/chapter"}],"author":[{"embeddable":true,"href":"https:\/\/opentextbc.ca\/alfm5\/wp-json\/wp\/v2\/users\/123"}],"version-history":[{"count":6,"href":"https:\/\/opentextbc.ca\/alfm5\/wp-json\/pressbooks\/v2\/chapters\/191\/revisions"}],"predecessor-version":[{"id":542,"href":"https:\/\/opentextbc.ca\/alfm5\/wp-json\/pressbooks\/v2\/chapters\/191\/revisions\/542"}],"part":[{"href":"https:\/\/opentextbc.ca\/alfm5\/wp-json\/pressbooks\/v2\/parts\/154"}],"metadata":[{"href":"https:\/\/opentextbc.ca\/alfm5\/wp-json\/pressbooks\/v2\/chapters\/191\/metadata\/"}],"wp:attachment":[{"href":"https:\/\/opentextbc.ca\/alfm5\/wp-json\/wp\/v2\/media?parent=191"}],"wp:term":[{"taxonomy":"chapter-type","embeddable":true,"href":"https:\/\/opentextbc.ca\/alfm5\/wp-json\/pressbooks\/v2\/chapter-type?post=191"},{"taxonomy":"contributor","embeddable":true,"href":"https:\/\/opentextbc.ca\/alfm5\/wp-json\/wp\/v2\/contributor?post=191"},{"taxonomy":"license","embeddable":true,"href":"https:\/\/opentextbc.ca\/alfm5\/wp-json\/wp\/v2\/license?post=191"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}