{"id":52,"date":"2023-01-17T18:02:32","date_gmt":"2023-01-17T23:02:32","guid":{"rendered":"https:\/\/pressbooks.bccampus.ca\/math023\/chapter\/division-problems\/"},"modified":"2025-07-04T00:05:45","modified_gmt":"2025-07-04T04:05:45","slug":"division-problems","status":"publish","type":"chapter","link":"https:\/\/pressbooks.bccampus.ca\/math023\/chapter\/division-problems\/","title":{"raw":"Topic F: Division Problems","rendered":"Topic F: Division Problems"},"content":{"raw":"<div>\r\n\r\nReview <a href=\"https:\/\/opentextbc.ca\/alfm2\/chapter\/problem-solving\/\">Topic F: Problem Solving<\/a> in <em>Adult Literacy Fundamentals Mathematics: Book Two<\/em>.\r\n\r\nOne common type of division problem gives a total amount for <strong>several <\/strong>things and asks you to <strong>find <\/strong>what the amount would be for <strong>one<\/strong>.\r\n<table class=\"grid\" style=\"width: 100%\">\r\n<tbody>\r\n<tr>\r\n<th scope=\"col\">Problems may tell you\u2026<\/th>\r\n<th scope=\"col\">and ask you to find\u2026<\/th>\r\n<\/tr>\r\n<tr>\r\n<td>kilometres driven in 8 hours (h)<\/td>\r\n<td>km driven in 1 h<\/td>\r\n<\/tr>\r\n<tr>\r\n<td>cost for 15 kg (or litres, etc.)<\/td>\r\n<td>cost for one kg<\/td>\r\n<\/tr>\r\n<tr>\r\n<td>pay for 40 hours<\/td>\r\n<td>pay for one hour<\/td>\r\n<\/tr>\r\n<tr>\r\n<td>rent for one year (12 months)<\/td>\r\n<td>rent for one month<\/td>\r\n<\/tr>\r\n<tr>\r\n<td>work done in eight hours<\/td>\r\n<td>work done in one hour<\/td>\r\n<\/tr>\r\n<tr>\r\n<td>kilometres driven on 55 L of gas<\/td>\r\n<td>km driven on 1 L of gas<\/td>\r\n<\/tr>\r\n<\/tbody>\r\n<\/table>\r\nThe word <em>per <\/em>is a Latin word meaning \u201cfor each\u201d. For example, \u201cFind the kilometres <em>per <\/em>hour\u201d may be used to mean, \u201cFind the kilometres driven in one hour.\u201d A slash (\/ ) also means per\u00a0 e.g. km\/h.\r\n<p style=\"text-align: center\"><strong><em>\u201cFind the average\u201d <\/em><\/strong>is another way of asking you to find the amount for one.<\/p>\r\nIt may be difficult to decide which number is the dividend and which is the divisor. These suggestions should help:\r\n<ul>\r\n \t<li>\u00a0Look at the question in the problem. What do you have to find out? Look for the words \u201cper\u201d and \u201cfor one.\u201d<\/li>\r\n \t<li>How will the answer be written? That is your clue. If the answer is km\/h then the division equation will be total km \u00f7 h.\u00a0 Study these examples:\r\n<ul>\r\n \t<li>[latex]\\text{total of kilometres} \\div \\text{number of hours}\r\n= km\/h[\/latex]<\/li>\r\n \t<li>[latex]\\text{total of kilometres} \\div \\text{number of litres} = km\/L[\/latex]<\/li>\r\n \t<li>[latex]\\text{total cost} \\div \\text{unit} = \\text{cost per unit}[\/latex]<\/li>\r\n \t<li>[latex]\\text{total pay} \\div \\text{hours (or days, etc.)} = \\text{pay per hour}[\/latex]<\/li>\r\n \t<li>[latex]\\text{total rent}\\div \\text{number of months} = \\text{rent\/month}[\/latex]<\/li>\r\n \t<li>[latex]\\text{total things done} \\div \\text{total time} = \\text{number done\/unit of time}[\/latex]<\/li>\r\n<\/ul>\r\n<\/li>\r\n \t<li>Do a quick estimate.<\/li>\r\n \t<li>\u00a0Look at your estimate\u00a0 and\u00a0 re-read the problem. Does your answer make sense?<\/li>\r\n<\/ul>\r\n<\/div>\r\nTo <strong>find the average<\/strong>, divide the total amount by the number of items that make up the total. You may first have to add the different items together to find the total.\r\n<p style=\"text-align: center\">Average = The sum of all values given \u00f7\u00a0 the number of values added up<\/p>\r\n\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\nYou bowled 5 games with scores of 124, 187, 164, 205, 130. What was your average score?\r\n<ol>\r\n \t<li>Find the total by adding [latex]124 + 187 + 164 + 205 + 130 = 810[\/latex]<\/li>\r\n \t<li>Divide the total by number of items [latex]810 \\div 5 \\text{ games} = 162 \\text{ per game}[\/latex]<\/li>\r\n<\/ol>\r\n<\/div>\r\n<\/div>\r\n<div class=\"textbox textbox--examples\"><header class=\"textbox__header\">\r\n<p class=\"textbox__title\">Example B<\/p>\r\n\r\n<\/header>\r\n<div class=\"textbox__content\">\r\n\r\nJoan and Rick have been keeping track of their household costs. They want to plan a monthly budget. Their grocery bills for six months were $428, $605, $397, $530, $590, and $474. What is their average monthly grocery cost?\r\n<ol>\r\n \t<li>Find the total amount.<\/li>\r\n<\/ol>\r\n<p style=\"text-align: center\">$428 + $605 + $397 + $530 + $590 + $474 = $3<span style=\"margin-left: 0.25em\">024<\/span><\/p>\r\n\r\n<ol start=\"2\">\r\n \t<li><span style=\"text-align: initial\">Divide total amount by number of items.<\/span><\/li>\r\n<\/ol>\r\n<p style=\"text-align: center\">$3<span style=\"margin-left: 0.25em\">024<\/span> \u00f7 6 = $504 average cost per month<\/p>\r\n\r\n<\/div>\r\n<\/div>\r\nSome details to remember:\r\n<ul>\r\n \t<li>1 minute = 60 seconds<\/li>\r\n \t<li>1 hour = 60 minutes<\/li>\r\n \t<li>1 year = 365 days<\/li>\r\n \t<li>1 year = 12 months<\/li>\r\n \t<li>1 year = 52 weeks<\/li>\r\n<\/ul>\r\nKey words that point to division:\r\n<ul class=\"twocolumn\">\r\n \t<li>Find the average<\/li>\r\n \t<li>Separated<\/li>\r\n \t<li>Find the ____ per ____<\/li>\r\n \t<li>Split<\/li>\r\n \t<li>Find the unit price<\/li>\r\n \t<li>Shared<\/li>\r\n<\/ul>\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\nSolve these problems.\u00a0 Use the five problem solving steps. Be sure to write down an estimate and check that the estimate makes sense <strong>before <\/strong>you find the actual solution. Check your work using the answer key at the end of the exercise.\r\n<ol type=\"a\">\r\n \t<li>A machine shop can stamp out 360 car parts in an 8 hour working How many parts is that per hour?<\/li>\r\n \t<li>Izyan paid $560 for 4 tires. How much did each tire cost?<\/li>\r\n \t<li>Bjork earned $8<span style=\"margin-left: 0.25em\">840<\/span> in 4 months.\r\n<ol type=\"i\">\r\n \t<li>How much did he earn each month?<\/li>\r\n \t<li>How much did he earn per week? (4 months is 17 weeks)<\/li>\r\n<\/ol>\r\n<\/li>\r\n \t<li>Theron used 9 L of gasoline to drive 207 km. How many kilometres did he drive per litre?<\/li>\r\n \t<li>The total cost of the car Elena bought is $14<span style=\"margin-left: 0.25em\">880<\/span> including taxes and interest. She will pay for it in 24 equal payments. How much will each payment be?<\/li>\r\n \t<li>Diego worked 8 hours a day for five days and earned $360. How much was he paid per hour? (This is a 2 step problem \u2013 you must first find the total number of)<\/li>\r\n \t<li>a) Dae-Hyun and Mi-Ok can afford no more than a total of $14<span style=\"margin-left: 0.25em\">940<\/span> per year for rent, electricity, and phone. How much can they pay per month?<\/li>\r\n<\/ol>\r\n<strong>Answers to Exercise 1<\/strong>\r\n<ol class=\"twocolumn\" type=\"a\">\r\n \t<li>45 parts per hour<\/li>\r\n \t<li>$140 per tire<\/li>\r\n \t<li>\r\n<ol type=\"i\">\r\n \t<li>$2210 per month<\/li>\r\n \t<li>$520 per week<\/li>\r\n<\/ol>\r\n<\/li>\r\n \t<li>23 km\/L<\/li>\r\n \t<li>$620 per payment<\/li>\r\n \t<li>$9 per hour<\/li>\r\n \t<li>$1245 per month<\/li>\r\n<\/ol>\r\n<\/div>\r\n<\/div>\r\nA second type of division problem gives the total amount and the size of each group. You will find the number of groups. You will notice that <strong>both numbers have the same units. <\/strong>The <strong>answer <\/strong>to the problem <strong>will give another unit. <\/strong>This other unit will be asked for in the problem.\r\n<div class=\"textbox textbox--examples\"><header class=\"textbox__header\">\r\n<p class=\"textbox__title\">Example C<\/p>\r\n\r\n<\/header>\r\n<div class=\"textbox__content\">\r\n\r\nOne necklace uses <strong>125 beads<\/strong>. How many necklaces can Susan make for the craft fair if she has <strong>6<span style=\"margin-left: 0.25em\">250<\/span> beads?<\/strong>\r\n\r\n<strong>\u00a0<\/strong>Find how many groups of 125 there are in 6<span style=\"margin-left: 0.25em\">520<\/span>.\r\n<p style=\"text-align: center\">6<span style=\"margin-left: 0.25em\">250<\/span> \u00f7 125 =<\/p>\r\n<p style=\"text-align: center\">[latex]\\begin{array}{r}50\\\\125\\enclose{longdiv}{6250}\\\\625 \\\\ \\hline 0 \\end{array}[\/latex]<\/p>\r\nShe can make <strong>50 necklaces.<\/strong>\r\n\r\n<\/div>\r\n<\/div>\r\n<div class=\"textbox textbox--examples\"><header class=\"textbox__header\">\r\n<p class=\"textbox__title\">Example D<\/p>\r\n\r\n<\/header>\r\n<div class=\"textbox__content\">\r\n\r\nIf you drive an average speed of 80 km an hour, how many hours will it take you to drive 560 km?\r\n\r\nFind how many groups of 80 km there are in 560 km.\r\n<p style=\"text-align: center\">[latex]56\\cancel{0} \\div 8\\cancel{0} = 7[\/latex]<\/p>\r\nThe 560 km trip will take 7 hours.\r\n\r\n<\/div>\r\n<\/div>\r\n<div class=\"textbox textbox--exercises\"><header class=\"textbox__header\">\r\n<p class=\"textbox__title\">Exercise 2<\/p>\r\n\r\n<\/header>\r\n<div class=\"textbox__content\">\r\n\r\nPay attention to wording and situations as you solve these problems. Use the five problem solving steps. Be sure to write down an estimate and check that the estimate makes sense <strong>before <\/strong>you find the actual solution. Check your work using the answer key at the end of the exercise.\r\n<ol type=\"a\">\r\n \t<li>A train travels 90 km per hour. How many hours will it take the train to go 540 km?<\/li>\r\n \t<li>A car gets 16 km per litre of gasoline. How many litres will the car need to go 128 km?<\/li>\r\n \t<li>About 8 m is needed for one parking space. How many parking spaces can be made along a street that is 232 m long?<\/li>\r\n \t<li>If you spend an average of 8 minutes on one math problem, how many problems can you finish in one hour? Will you have any time left?\u00a0 How much?<\/li>\r\n \t<li>The Skating Club members decided to sell home-made candy to raise money. The boxes they bought will hold 45 pieces of candy. If everyone makes a double batch of fudge they will have 2<span style=\"margin-left: 0.25em\">590<\/span> pieces of How many boxes can they fill? How many pieces of fudge are left-over for them to eat?<\/li>\r\n \t<li>A class of 334 students is going to Victoria by bus. Each bus holds 43 passengers. How many buses do they need? Will there be any empty seats? (Be careful with this one!)<\/li>\r\n<\/ol>\r\n<strong>Answers to Exercise 2<\/strong>\r\n<ol class=\"twocolumn\" type=\"a\">\r\n \t<li>6 hours<\/li>\r\n \t<li>8 L<\/li>\r\n \t<li>29 parking spaces<\/li>\r\n \t<li>7 problems, yes, 4 min<\/li>\r\n \t<li>57 boxes, 25 pieces left over<\/li>\r\n \t<li>8 buses, 10 empty seats<\/li>\r\n<\/ol>\r\n<\/div>\r\n<\/div>\r\n<h1>Unit Pricing<\/h1>\r\nA unit price is the price for one of something. To find unit price, divide the total cost by the number of things bought.\r\n<div class=\"textbox textbox--examples\"><header class=\"textbox__header\">\r\n<p class=\"textbox__title\">Example E<\/p>\r\n\r\n<\/header>\r\n<div class=\"textbox__content\">\r\n\r\n5 shirts cost $60\r\n\r\nTo find the cost per shirt, [latex]$60 \\div 5 =[\/latex]\r\n<p style=\"text-align: center\">[latex]\\begin{array}{r}12\\\\5\\enclose{longdiv}{60}\\end{array}[\/latex]<\/p>\r\n<p style=\"text-align: left\">The unit price is $12.<\/p>\r\n\r\n<\/div>\r\n<\/div>\r\n<div class=\"textbox textbox--examples\"><header class=\"textbox__header\">\r\n<p class=\"textbox__title\">Example F<\/p>\r\n\r\n<\/header>\r\n<div class=\"textbox__content\">\r\n\r\n6 L of oil for $18\r\n\r\nTo find the cost per L, [latex]$18 \\div 6 =[\/latex]\r\n<p style=\"text-align: center\">[latex]\\begin{array}{r}3\\\\6\\enclose{longdiv}{18}\\end{array}[\/latex]<\/p>\r\nThe unit price is $3.\r\n\r\n<\/div>\r\n<\/div>\r\n<div class=\"textbox textbox--exercises\"><header class=\"textbox__header\">\r\n<p class=\"textbox__title\">Exercise 3<\/p>\r\n\r\n<\/header>\r\n<div class=\"textbox__content\">\r\n\r\nSolve the cost per unit price. Check your work using the answer key at the end of the exercise.\r\n<ol class=\"twocolumn\" type=\"a\">\r\n \t<li>2 CDs for $26<\/li>\r\n \t<li>3 cans of dog food for $6<\/li>\r\n \t<li>4 air fresheners for $8<\/li>\r\n \t<li>2 cat treats for $4<\/li>\r\n \t<li>2 pizzas for $22<\/li>\r\n \t<li>2 cans of peanuts for $8<\/li>\r\n \t<li>2 ice cream for $12<\/li>\r\n \t<li>4 boxes of chocolate bars for $48<\/li>\r\n \t<li>2 WD-40 for $6<\/li>\r\n \t<li>3 paint rollers for $9<\/li>\r\n \t<li>4 tie downs for $20<\/li>\r\n \t<li>3 boxes of diapers for $51<\/li>\r\n \t<li>3 work shirts for $45<\/li>\r\n \t<li>8 pairs of socks for $64<\/li>\r\n<\/ol>\r\n<strong>Answers to Exercise 3<\/strong>\r\n<ol class=\"twocolumn\" type=\"a\">\r\n \t<li>$13<\/li>\r\n \t<li>$2<\/li>\r\n \t<li>$2<\/li>\r\n \t<li>$2<\/li>\r\n \t<li>$11<\/li>\r\n \t<li>$4<\/li>\r\n \t<li>$6<\/li>\r\n \t<li>$12<\/li>\r\n \t<li>$3<\/li>\r\n \t<li>$3<\/li>\r\n \t<li>$5<\/li>\r\n \t<li>$17<\/li>\r\n \t<li>$15<\/li>\r\n \t<li>$8<\/li>\r\n<\/ol>\r\n<\/div>\r\n<\/div>\r\n<h1>Best Buy<\/h1>\r\nThe <strong>best <\/strong>buy is the <strong>lowest unit price.<\/strong>\r\n<div class=\"textbox textbox--examples\"><header class=\"textbox__header\">\r\n<p class=\"textbox__title\">Example G<\/p>\r\n\r\n<\/header>\r\n<div class=\"textbox__content\">\r\n\r\nYou can buy 4 L of canola oil for $8 or 10 L of canola oil for $30. Which is the best buy?\r\n\r\n[latex]$8\\div4=[\/latex] can be rewritten and solved: [latex]\\begin{array}{r}2\\\\4\\enclose{longdiv}{8}\\end{array}[\/latex]\r\n\r\n[latex]$30 \\div 10 =[\/latex] can be rewritten and solved: [latex]\\begin{array}{r}3\\\\10\\enclose{longdiv}{30}\\end{array}[\/latex]\r\n\r\n4 L of canola oil for $8 is a better buy since the unit price is $2 per L, while 10 L for $30 has a unit price of $3 per L.\r\n\r\n<\/div>\r\n<\/div>\r\n<div class=\"textbox textbox--exercises\"><header class=\"textbox__header\">\r\n<p class=\"textbox__title\">Exercise 4<\/p>\r\n\r\n<\/header>\r\n<div class=\"textbox__content\">\r\n\r\nSolve the unit price and then underline the best buy. \u00a0Check your work using the answer key at the end of the exercise.\r\n<ol type=\"a\">\r\n \t<li>2 L of engine oil for $8 or 5 L of engine oil for $15<\/li>\r\n \t<li>4 tires for $240 or 2 tires for $110<\/li>\r\n \t<li>6 jars of salad dressing for $24 or 3 jars of salad dressing for $15<\/li>\r\n \t<li>7 kg of dog food for $21or 16 kg of dog food for $32<\/li>\r\n \t<li>3 DVDs for $54 or 7 DVDs for $119<\/li>\r\n \t<li>3 L of laundry soap for $6 or 17 L of laundry soap for $68<\/li>\r\n<\/ol>\r\n<strong>Answers to Exercise 4<\/strong>\r\n<ol class=\"twocolumn\" type=\"a\">\r\n \t<li>$4, $3, <span style=\"text-decoration: underline\">5 L for $15<\/span> is the best buy.<\/li>\r\n \t<li>$60, $55, <span style=\"text-decoration: underline\">2 tires for $110<\/span>\u00a0is the best buy.<\/li>\r\n \t<li>$4, $5, <span style=\"text-decoration: underline\">6 salad dressing for $24<\/span>\u00a0is the best buy.<\/li>\r\n \t<li>$3, $2, <span style=\"text-decoration: underline\">16 kg for $32<\/span> is the best buy.<\/li>\r\n \t<li>$18, $17, <span style=\"text-decoration: underline\">7 DVDs for $119<\/span> is the best buy.<\/li>\r\n \t<li>$2, $4, <span style=\"text-decoration: underline\">3 L for $6<\/span> is the best buy.<\/li>\r\n<\/ol>\r\n<\/div>\r\n<\/div>\r\n<h1 class=\"page-break-before\">Topic F: Self Test<\/h1>\r\n<strong>Mark\u00a0 \/12\u00a0 \u00a0Aim\u00a0 10\/12<\/strong>\r\n<ol type=\"A\">\r\n \t<li>Solve these problems. (12 marks) <strong>2 marks each \u2013 1 for correct method, 1 for correct solution.<\/strong>\r\n<ol type=\"a\">\r\n \t<li>Enrique drove the 1 920 km from Dease Lake to Creston in 24 hours. What was his average speed in kilometres per hour?<\/li>\r\n \t<li>The Evergreen Company employs 26 people. Its total payroll for last month was $84 162.\u00a0 What was the average monthly pay cheque per person?<\/li>\r\n \t<li>The proud gardener grew a total crop of 135 cucumbers on 15 plants. What was the average crop per plant?<\/li>\r\n \t<li>In a recent truckload sale, electric stoves were sold for $432. The gross income from the stove sale was $42<span style=\"margin-left: 0.25em\">336<\/span>.\u00a0 How many stoves were sold?<\/li>\r\n \t<li>The 39 farmers in Jones Valley had a total income last year of $2<span style=\"margin-left: 0.25em\">905<\/span><span style=\"margin-left: 0.25em\">500<\/span>. What was their average income?<\/li>\r\n \t<li>A store has an inventory (stock on hand) of chairs with a total value of $1<span style=\"margin-left: 0.25em\">738<\/span>. Each chair is to be sold at $79.\u00a0 How many of these chairs are there?<\/li>\r\n<\/ol>\r\n<\/li>\r\n<\/ol>\r\n<h2>Answers to Topic E Self-Test<\/h2>\r\n<ol type=\"A\">\r\n \t<li>Give an estimated quotient. Show your work.\r\n<ol class=\"twocolumn\" type=\"a\">\r\n \t<li>80 km\/h<\/li>\r\n \t<li>$3<span style=\"margin-left: 0.25em\">237<\/span> per month<\/li>\r\n \t<li>9 cucumbers per plant<\/li>\r\n \t<li>98 stoves<\/li>\r\n \t<li>$74<span style=\"margin-left: 0.25em\">500<\/span><\/li>\r\n \t<li>22 chairs<\/li>\r\n<\/ol>\r\n<\/li>\r\n<\/ol>","rendered":"<div>\n<p>Review <a href=\"https:\/\/opentextbc.ca\/alfm2\/chapter\/problem-solving\/\">Topic F: Problem Solving<\/a> in <em>Adult Literacy Fundamentals Mathematics: Book Two<\/em>.<\/p>\n<p>One common type of division problem gives a total amount for <strong>several <\/strong>things and asks you to <strong>find <\/strong>what the amount would be for <strong>one<\/strong>.<\/p>\n<table class=\"grid\" style=\"width: 100%\">\n<tbody>\n<tr>\n<th scope=\"col\">Problems may tell you\u2026<\/th>\n<th scope=\"col\">and ask you to find\u2026<\/th>\n<\/tr>\n<tr>\n<td>kilometres driven in 8 hours (h)<\/td>\n<td>km driven in 1 h<\/td>\n<\/tr>\n<tr>\n<td>cost for 15 kg (or litres, etc.)<\/td>\n<td>cost for one kg<\/td>\n<\/tr>\n<tr>\n<td>pay for 40 hours<\/td>\n<td>pay for one hour<\/td>\n<\/tr>\n<tr>\n<td>rent for one year (12 months)<\/td>\n<td>rent for one month<\/td>\n<\/tr>\n<tr>\n<td>work done in eight hours<\/td>\n<td>work done in one hour<\/td>\n<\/tr>\n<tr>\n<td>kilometres driven on 55 L of gas<\/td>\n<td>km driven on 1 L of gas<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<p>The word <em>per <\/em>is a Latin word meaning \u201cfor each\u201d. For example, \u201cFind the kilometres <em>per <\/em>hour\u201d may be used to mean, \u201cFind the kilometres driven in one hour.\u201d A slash (\/ ) also means per\u00a0 e.g. km\/h.<\/p>\n<p style=\"text-align: center\"><strong><em>\u201cFind the average\u201d <\/em><\/strong>is another way of asking you to find the amount for one.<\/p>\n<p>It may be difficult to decide which number is the dividend and which is the divisor. These suggestions should help:<\/p>\n<ul>\n<li>\u00a0Look at the question in the problem. What do you have to find out? Look for the words \u201cper\u201d and \u201cfor one.\u201d<\/li>\n<li>How will the answer be written? That is your clue. If the answer is km\/h then the division equation will be total km \u00f7 h.\u00a0 Study these examples:\n<ul>\n<li>[latex]\\text{total of kilometres} \\div \\text{number of hours}  = km\/h[\/latex]<\/li>\n<li>[latex]\\text{total of kilometres} \\div \\text{number of litres} = km\/L[\/latex]<\/li>\n<li>[latex]\\text{total cost} \\div \\text{unit} = \\text{cost per unit}[\/latex]<\/li>\n<li>[latex]\\text{total pay} \\div \\text{hours (or days, etc.)} = \\text{pay per hour}[\/latex]<\/li>\n<li>[latex]\\text{total rent}\\div \\text{number of months} = \\text{rent\/month}[\/latex]<\/li>\n<li>[latex]\\text{total things done} \\div \\text{total time} = \\text{number done\/unit of time}[\/latex]<\/li>\n<\/ul>\n<\/li>\n<li>Do a quick estimate.<\/li>\n<li>\u00a0Look at your estimate\u00a0 and\u00a0 re-read the problem. Does your answer make sense?<\/li>\n<\/ul>\n<\/div>\n<p>To <strong>find the average<\/strong>, divide the total amount by the number of items that make up the total. You may first have to add the different items together to find the total.<\/p>\n<p style=\"text-align: center\">Average = The sum of all values given \u00f7\u00a0 the number of values added up<\/p>\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>You bowled 5 games with scores of 124, 187, 164, 205, 130. What was your average score?<\/p>\n<ol>\n<li>Find the total by adding [latex]124 + 187 + 164 + 205 + 130 = 810[\/latex]<\/li>\n<li>Divide the total by number of items [latex]810 \\div 5 \\text{ games} = 162 \\text{ per game}[\/latex]<\/li>\n<\/ol>\n<\/div>\n<\/div>\n<div class=\"textbox textbox--examples\">\n<header class=\"textbox__header\">\n<p class=\"textbox__title\">Example B<\/p>\n<\/header>\n<div class=\"textbox__content\">\n<p>Joan and Rick have been keeping track of their household costs. They want to plan a monthly budget. Their grocery bills for six months were $428, $605, $397, $530, $590, and $474. What is their average monthly grocery cost?<\/p>\n<ol>\n<li>Find the total amount.<\/li>\n<\/ol>\n<p style=\"text-align: center\">$428 + $605 + $397 + $530 + $590 + $474 = $3<span style=\"margin-left: 0.25em\">024<\/span><\/p>\n<ol start=\"2\">\n<li><span style=\"text-align: initial\">Divide total amount by number of items.<\/span><\/li>\n<\/ol>\n<p style=\"text-align: center\">$3<span style=\"margin-left: 0.25em\">024<\/span> \u00f7 6 = $504 average cost per month<\/p>\n<\/div>\n<\/div>\n<p>Some details to remember:<\/p>\n<ul>\n<li>1 minute = 60 seconds<\/li>\n<li>1 hour = 60 minutes<\/li>\n<li>1 year = 365 days<\/li>\n<li>1 year = 12 months<\/li>\n<li>1 year = 52 weeks<\/li>\n<\/ul>\n<p>Key words that point to division:<\/p>\n<ul class=\"twocolumn\">\n<li>Find the average<\/li>\n<li>Separated<\/li>\n<li>Find the ____ per ____<\/li>\n<li>Split<\/li>\n<li>Find the unit price<\/li>\n<li>Shared<\/li>\n<\/ul>\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>Solve these problems.\u00a0 Use the five problem solving steps. Be sure to write down an estimate and check that the estimate makes sense <strong>before <\/strong>you find the actual solution. Check your work using the answer key at the end of the exercise.<\/p>\n<ol type=\"a\">\n<li>A machine shop can stamp out 360 car parts in an 8 hour working How many parts is that per hour?<\/li>\n<li>Izyan paid $560 for 4 tires. How much did each tire cost?<\/li>\n<li>Bjork earned $8<span style=\"margin-left: 0.25em\">840<\/span> in 4 months.\n<ol type=\"i\">\n<li>How much did he earn each month?<\/li>\n<li>How much did he earn per week? (4 months is 17 weeks)<\/li>\n<\/ol>\n<\/li>\n<li>Theron used 9 L of gasoline to drive 207 km. How many kilometres did he drive per litre?<\/li>\n<li>The total cost of the car Elena bought is $14<span style=\"margin-left: 0.25em\">880<\/span> including taxes and interest. She will pay for it in 24 equal payments. How much will each payment be?<\/li>\n<li>Diego worked 8 hours a day for five days and earned $360. How much was he paid per hour? (This is a 2 step problem \u2013 you must first find the total number of)<\/li>\n<li>a) Dae-Hyun and Mi-Ok can afford no more than a total of $14<span style=\"margin-left: 0.25em\">940<\/span> per year for rent, electricity, and phone. How much can they pay per month?<\/li>\n<\/ol>\n<p><strong>Answers to Exercise 1<\/strong><\/p>\n<ol class=\"twocolumn\" type=\"a\">\n<li>45 parts per hour<\/li>\n<li>$140 per tire<\/li>\n<li>\n<ol type=\"i\">\n<li>$2210 per month<\/li>\n<li>$520 per week<\/li>\n<\/ol>\n<\/li>\n<li>23 km\/L<\/li>\n<li>$620 per payment<\/li>\n<li>$9 per hour<\/li>\n<li>$1245 per month<\/li>\n<\/ol>\n<\/div>\n<\/div>\n<p>A second type of division problem gives the total amount and the size of each group. You will find the number of groups. You will notice that <strong>both numbers have the same units. <\/strong>The <strong>answer <\/strong>to the problem <strong>will give another unit. <\/strong>This other unit will be asked for in the problem.<\/p>\n<div class=\"textbox textbox--examples\">\n<header class=\"textbox__header\">\n<p class=\"textbox__title\">Example C<\/p>\n<\/header>\n<div class=\"textbox__content\">\n<p>One necklace uses <strong>125 beads<\/strong>. How many necklaces can Susan make for the craft fair if she has <strong>6<span style=\"margin-left: 0.25em\">250<\/span> beads?<\/strong><\/p>\n<p><strong>\u00a0<\/strong>Find how many groups of 125 there are in 6<span style=\"margin-left: 0.25em\">520<\/span>.<\/p>\n<p style=\"text-align: center\">6<span style=\"margin-left: 0.25em\">250<\/span> \u00f7 125 =<\/p>\n<p style=\"text-align: center\">[latex]\\begin{array}{r}50\\\\125\\enclose{longdiv}{6250}\\\\625 \\\\ \\hline 0 \\end{array}[\/latex]<\/p>\n<p>She can make <strong>50 necklaces.<\/strong><\/p>\n<\/div>\n<\/div>\n<div class=\"textbox textbox--examples\">\n<header class=\"textbox__header\">\n<p class=\"textbox__title\">Example D<\/p>\n<\/header>\n<div class=\"textbox__content\">\n<p>If you drive an average speed of 80 km an hour, how many hours will it take you to drive 560 km?<\/p>\n<p>Find how many groups of 80 km there are in 560 km.<\/p>\n<p style=\"text-align: center\">[latex]56\\cancel{0} \\div 8\\cancel{0} = 7[\/latex]<\/p>\n<p>The 560 km trip will take 7 hours.<\/p>\n<\/div>\n<\/div>\n<div class=\"textbox textbox--exercises\">\n<header class=\"textbox__header\">\n<p class=\"textbox__title\">Exercise 2<\/p>\n<\/header>\n<div class=\"textbox__content\">\n<p>Pay attention to wording and situations as you solve these problems. Use the five problem solving steps. Be sure to write down an estimate and check that the estimate makes sense <strong>before <\/strong>you find the actual solution. Check your work using the answer key at the end of the exercise.<\/p>\n<ol type=\"a\">\n<li>A train travels 90 km per hour. How many hours will it take the train to go 540 km?<\/li>\n<li>A car gets 16 km per litre of gasoline. How many litres will the car need to go 128 km?<\/li>\n<li>About 8 m is needed for one parking space. How many parking spaces can be made along a street that is 232 m long?<\/li>\n<li>If you spend an average of 8 minutes on one math problem, how many problems can you finish in one hour? Will you have any time left?\u00a0 How much?<\/li>\n<li>The Skating Club members decided to sell home-made candy to raise money. The boxes they bought will hold 45 pieces of candy. If everyone makes a double batch of fudge they will have 2<span style=\"margin-left: 0.25em\">590<\/span> pieces of How many boxes can they fill? How many pieces of fudge are left-over for them to eat?<\/li>\n<li>A class of 334 students is going to Victoria by bus. Each bus holds 43 passengers. How many buses do they need? Will there be any empty seats? (Be careful with this one!)<\/li>\n<\/ol>\n<p><strong>Answers to Exercise 2<\/strong><\/p>\n<ol class=\"twocolumn\" type=\"a\">\n<li>6 hours<\/li>\n<li>8 L<\/li>\n<li>29 parking spaces<\/li>\n<li>7 problems, yes, 4 min<\/li>\n<li>57 boxes, 25 pieces left over<\/li>\n<li>8 buses, 10 empty seats<\/li>\n<\/ol>\n<\/div>\n<\/div>\n<h1>Unit Pricing<\/h1>\n<p>A unit price is the price for one of something. To find unit price, divide the total cost by the number of things bought.<\/p>\n<div class=\"textbox textbox--examples\">\n<header class=\"textbox__header\">\n<p class=\"textbox__title\">Example E<\/p>\n<\/header>\n<div class=\"textbox__content\">\n<p>5 shirts cost $60<\/p>\n<p>To find the cost per shirt, [latex]$60 \\div 5 =[\/latex]<\/p>\n<p style=\"text-align: center\">[latex]\\begin{array}{r}12\\\\5\\enclose{longdiv}{60}\\end{array}[\/latex]<\/p>\n<p style=\"text-align: left\">The unit price is $12.<\/p>\n<\/div>\n<\/div>\n<div class=\"textbox textbox--examples\">\n<header class=\"textbox__header\">\n<p class=\"textbox__title\">Example F<\/p>\n<\/header>\n<div class=\"textbox__content\">\n<p>6 L of oil for $18<\/p>\n<p>To find the cost per L, [latex]$18 \\div 6 =[\/latex]<\/p>\n<p style=\"text-align: center\">[latex]\\begin{array}{r}3\\\\6\\enclose{longdiv}{18}\\end{array}[\/latex]<\/p>\n<p>The unit price is $3.<\/p>\n<\/div>\n<\/div>\n<div class=\"textbox textbox--exercises\">\n<header class=\"textbox__header\">\n<p class=\"textbox__title\">Exercise 3<\/p>\n<\/header>\n<div class=\"textbox__content\">\n<p>Solve the cost per unit price. Check your work using the answer key at the end of the exercise.<\/p>\n<ol class=\"twocolumn\" type=\"a\">\n<li>2 CDs for $26<\/li>\n<li>3 cans of dog food for $6<\/li>\n<li>4 air fresheners for $8<\/li>\n<li>2 cat treats for $4<\/li>\n<li>2 pizzas for $22<\/li>\n<li>2 cans of peanuts for $8<\/li>\n<li>2 ice cream for $12<\/li>\n<li>4 boxes of chocolate bars for $48<\/li>\n<li>2 WD-40 for $6<\/li>\n<li>3 paint rollers for $9<\/li>\n<li>4 tie downs for $20<\/li>\n<li>3 boxes of diapers for $51<\/li>\n<li>3 work shirts for $45<\/li>\n<li>8 pairs of socks for $64<\/li>\n<\/ol>\n<p><strong>Answers to Exercise 3<\/strong><\/p>\n<ol class=\"twocolumn\" type=\"a\">\n<li>$13<\/li>\n<li>$2<\/li>\n<li>$2<\/li>\n<li>$2<\/li>\n<li>$11<\/li>\n<li>$4<\/li>\n<li>$6<\/li>\n<li>$12<\/li>\n<li>$3<\/li>\n<li>$3<\/li>\n<li>$5<\/li>\n<li>$17<\/li>\n<li>$15<\/li>\n<li>$8<\/li>\n<\/ol>\n<\/div>\n<\/div>\n<h1>Best Buy<\/h1>\n<p>The <strong>best <\/strong>buy is the <strong>lowest unit price.<\/strong><\/p>\n<div class=\"textbox textbox--examples\">\n<header class=\"textbox__header\">\n<p class=\"textbox__title\">Example G<\/p>\n<\/header>\n<div class=\"textbox__content\">\n<p>You can buy 4 L of canola oil for $8 or 10 L of canola oil for $30. Which is the best buy?<\/p>\n<p>[latex]$8\\div4=[\/latex] can be rewritten and solved: [latex]\\begin{array}{r}2\\\\4\\enclose{longdiv}{8}\\end{array}[\/latex]<\/p>\n<p>[latex]$30 \\div 10 =[\/latex] can be rewritten and solved: [latex]\\begin{array}{r}3\\\\10\\enclose{longdiv}{30}\\end{array}[\/latex]<\/p>\n<p>4 L of canola oil for $8 is a better buy since the unit price is $2 per L, while 10 L for $30 has a unit price of $3 per L.<\/p>\n<\/div>\n<\/div>\n<div class=\"textbox textbox--exercises\">\n<header class=\"textbox__header\">\n<p class=\"textbox__title\">Exercise 4<\/p>\n<\/header>\n<div class=\"textbox__content\">\n<p>Solve the unit price and then underline the best buy. \u00a0Check your work using the answer key at the end of the exercise.<\/p>\n<ol type=\"a\">\n<li>2 L of engine oil for $8 or 5 L of engine oil for $15<\/li>\n<li>4 tires for $240 or 2 tires for $110<\/li>\n<li>6 jars of salad dressing for $24 or 3 jars of salad dressing for $15<\/li>\n<li>7 kg of dog food for $21or 16 kg of dog food for $32<\/li>\n<li>3 DVDs for $54 or 7 DVDs for $119<\/li>\n<li>3 L of laundry soap for $6 or 17 L of laundry soap for $68<\/li>\n<\/ol>\n<p><strong>Answers to Exercise 4<\/strong><\/p>\n<ol class=\"twocolumn\" type=\"a\">\n<li>$4, $3, <span style=\"text-decoration: underline\">5 L for $15<\/span> is the best buy.<\/li>\n<li>$60, $55, <span style=\"text-decoration: underline\">2 tires for $110<\/span>\u00a0is the best buy.<\/li>\n<li>$4, $5, <span style=\"text-decoration: underline\">6 salad dressing for $24<\/span>\u00a0is the best buy.<\/li>\n<li>$3, $2, <span style=\"text-decoration: underline\">16 kg for $32<\/span> is the best buy.<\/li>\n<li>$18, $17, <span style=\"text-decoration: underline\">7 DVDs for $119<\/span> is the best buy.<\/li>\n<li>$2, $4, <span style=\"text-decoration: underline\">3 L for $6<\/span> is the best buy.<\/li>\n<\/ol>\n<\/div>\n<\/div>\n<h1 class=\"page-break-before\">Topic F: Self Test<\/h1>\n<p><strong>Mark\u00a0 \/12\u00a0 \u00a0Aim\u00a0 10\/12<\/strong><\/p>\n<ol type=\"A\">\n<li>Solve these problems. (12 marks) <strong>2 marks each \u2013 1 for correct method, 1 for correct solution.<\/strong>\n<ol type=\"a\">\n<li>Enrique drove the 1 920 km from Dease Lake to Creston in 24 hours. What was his average speed in kilometres per hour?<\/li>\n<li>The Evergreen Company employs 26 people. Its total payroll for last month was $84 162.\u00a0 What was the average monthly pay cheque per person?<\/li>\n<li>The proud gardener grew a total crop of 135 cucumbers on 15 plants. What was the average crop per plant?<\/li>\n<li>In a recent truckload sale, electric stoves were sold for $432. The gross income from the stove sale was $42<span style=\"margin-left: 0.25em\">336<\/span>.\u00a0 How many stoves were sold?<\/li>\n<li>The 39 farmers in Jones Valley had a total income last year of $2<span style=\"margin-left: 0.25em\">905<\/span><span style=\"margin-left: 0.25em\">500<\/span>. What was their average income?<\/li>\n<li>A store has an inventory (stock on hand) of chairs with a total value of $1<span style=\"margin-left: 0.25em\">738<\/span>. Each chair is to be sold at $79.\u00a0 How many of these chairs are there?<\/li>\n<\/ol>\n<\/li>\n<\/ol>\n<h2>Answers to Topic E Self-Test<\/h2>\n<ol type=\"A\">\n<li>Give an estimated quotient. Show your work.\n<ol class=\"twocolumn\" type=\"a\">\n<li>80 km\/h<\/li>\n<li>$3<span style=\"margin-left: 0.25em\">237<\/span> per month<\/li>\n<li>9 cucumbers per plant<\/li>\n<li>98 stoves<\/li>\n<li>$74<span style=\"margin-left: 0.25em\">500<\/span><\/li>\n<li>22 chairs<\/li>\n<\/ol>\n<\/li>\n<\/ol>\n","protected":false},"author":999,"menu_order":7,"template":"","meta":{"pb_show_title":"on","pb_short_title":"","pb_subtitle":"","pb_authors":[],"pb_section_license":""},"chapter-type":[],"contributor":[],"license":[],"class_list":["post-52","chapter","type-chapter","status-publish","hentry"],"part":35,"_links":{"self":[{"href":"https:\/\/pressbooks.bccampus.ca\/math023\/wp-json\/pressbooks\/v2\/chapters\/52","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/pressbooks.bccampus.ca\/math023\/wp-json\/pressbooks\/v2\/chapters"}],"about":[{"href":"https:\/\/pressbooks.bccampus.ca\/math023\/wp-json\/wp\/v2\/types\/chapter"}],"author":[{"embeddable":true,"href":"https:\/\/pressbooks.bccampus.ca\/math023\/wp-json\/wp\/v2\/users\/999"}],"version-history":[{"count":3,"href":"https:\/\/pressbooks.bccampus.ca\/math023\/wp-json\/pressbooks\/v2\/chapters\/52\/revisions"}],"predecessor-version":[{"id":219,"href":"https:\/\/pressbooks.bccampus.ca\/math023\/wp-json\/pressbooks\/v2\/chapters\/52\/revisions\/219"}],"part":[{"href":"https:\/\/pressbooks.bccampus.ca\/math023\/wp-json\/pressbooks\/v2\/parts\/35"}],"metadata":[{"href":"https:\/\/pressbooks.bccampus.ca\/math023\/wp-json\/pressbooks\/v2\/chapters\/52\/metadata\/"}],"wp:attachment":[{"href":"https:\/\/pressbooks.bccampus.ca\/math023\/wp-json\/wp\/v2\/media?parent=52"}],"wp:term":[{"taxonomy":"chapter-type","embeddable":true,"href":"https:\/\/pressbooks.bccampus.ca\/math023\/wp-json\/pressbooks\/v2\/chapter-type?post=52"},{"taxonomy":"contributor","embeddable":true,"href":"https:\/\/pressbooks.bccampus.ca\/math023\/wp-json\/wp\/v2\/contributor?post=52"},{"taxonomy":"license","embeddable":true,"href":"https:\/\/pressbooks.bccampus.ca\/math023\/wp-json\/wp\/v2\/license?post=52"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}