1.14: Division Problems
Review 1.6: Problem Solving.
One common type of division problem gives a total amount for several things and asks you to find what the amount would be for one. See Table 1.14.1 for common division problems.
| What the Problem Tells You | What the Problem Asks You To Find |
|---|---|
| kilometres driven in 8 hours (h) | km driven in 1 h |
| cost for 15 kg (or litres, etc.) | cost for one kg |
| pay for 40 hours | pay for one hour |
| rent for one year (12 months) | rent for one month |
| work done in eight hours | work done in one hour |
| kilometres driven on 55 L of gas | km driven on 1 L of gas |
The word per is a Latin word meaning “for each.” For example, “Find the kilometres per hour” may be used to mean, “Find the kilometres driven in one hour.” A slash (/ ) also means per e.g. km/h.
“Find the average” is another way of asking you to find the amount for one.
It may be difficult to decide which number is the dividend and which is the divisor. These suggestions should help:
- Look at the question in the problem. What do you have to find out? Look for the words “per” and “for one.”
- How will the answer be written? That is your clue. If the answer is km/h, the division equation will be total km ÷ h. Study these examples:
- [latex]\text{total of kilometres} \div \text{number of hours} = \text{km/h}[/latex]
- [latex]\text{total of kilometres} \div \text{number of litres} = \text{km/L}[/latex]
- [latex]\text{total cost} \div \text{unit} = \text{cost per unit}[/latex]
- [latex]\text{total pay} \div \text{hours (or days, etc.)} = \text{pay per hour}[/latex]
- [latex]\text{total rent}\div \text{number of months} = \text{rent/month}[/latex]
- [latex]\text{total things done} \div \text{total time} = \text{number done/unit of time}[/latex]
- Do a quick estimate.
- Look at your estimate and re-read the problem. Does your answer make sense?
To find the average, 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.
Average = Total amount number of items that make the total
Example A
You bowled 5 games with scores of 124, 187, 164, 205, 130. What was your average score?
Step 1: Find the total by adding.
[latex]124 + 187 + 164 + 205 + 130 = 810[/latex]
Step 2: Divide the total by number of items.
[latex]810 \div 5 \text{ games} = 162 \text{ per game}[/latex]
Example B
Joan and Rick have been keeping track of their household costs. They want to plan a monthly budget. Their grocery bills over six months were $428, $605, $397, $530, $590, and $474. What is their average monthly grocery cost?
Step 1: Find the total amount.
[latex]$428 + $605 + $397 + $530 + $590 + $474 = $3\,024[/latex]
Step 2: Divide total amount by number of items.
[latex]$3\,024 \div 6 = $504[/latex] average cost per month
Some details to remember:
- 1 minute = 60 seconds
- 1 hour = 60 minutes
- 1 year = 365 days
- 1 year = 12 months
- 1 year = 52 weeks
Keywords that point to division:
- find the average
- separated
- find the ____ per ____
- split
- find the unit price
- shared
Exercise 1
Solve the following word problems. Use the five problem solving steps. Be sure to write down an estimate and check that the estimate makes sense BEFORE you find the actual solution. Check your work using the answer key at the end of the exercise.
- A machine shop can stamp out 360 car parts during an 8-hour working day. How many parts is that per hour?
- Izyan paid $560 for 4 tires. How much did each tire cost?
- Bjork earned $8840 in 4
- How much did he earn each month?
- How much did he earn per week? (4 months is 17 weeks)
- Theron used 9 L of gasoline to drive 207 km. How many kilometres did he drive per litre?
- The total cost of the car Elena bought is $14880, including taxes and interest. She will pay for it in 24 equal payments. How much will each payment be?
- 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 – you must first find the total number of)
- a) Dae-Hyun and Mi-Ok can afford no more than $14940 per year for rent, electricity, and phone. How much can they pay per month?
Exercise 1 Answers
- 45 parts per hour
- $140 per tire
- $2210 per month
- $520 per week
- 23 km/L
- $620 per payment
- $9 per hour
- $1245 per month
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 both numbers have the same units. The answer to the problem will give another unit. This other unit will be asked for in the problem.
Example C
One necklace uses 125 beads. How many necklaces can Susan make for the craft fair if she has 6250 beads?
Step 1: Find how many groups of 125 there are in 6520.
[latex]6\,250\div125=[/latex]
[latex]\begin{array}{r}50\\125\enclose{longdiv}{6250}\\625 \\ \hline 0 \end{array}[/latex]
She can make 50 necklaces.
Example D
If you drive an average speed of 80 km an hour, how many hours will it take you to drive 560 km?
Step 1: Find how many groups of 80 km there are in 560 km.
[latex]56\cancel{0} \div 8\cancel{0} = 7[/latex]
The 560 km trip will take 7 hours.
Exercise 2
Pay attention to wording and situations as you solve the following word problems. Use the 5 problem-solving steps. Be sure to write down an estimate and check that the estimate makes sense BEFORE you find the actual solution.
- A train travels 90 km per hour. How many hours will it take the train to go 540 km?
- A car gets 16 km per litre of gasoline. How many litres will the car need to go 128 km?
- About 8 m is needed for one parking space. How many parking spaces can be made along a street that is 232 m long?
- 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? How much?
- The Skating Club members decided to sell homemade fudge to raise money. The boxes they bought will hold 45 pieces of fudge. If everyone makes a double batch of fudge they will have 2590 pieces. How many boxes can they fill? How many pieces of fudge are left over for them to eat?
- 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!)
Exercise 2 Answers
- 6 hours
- 8 L
- 29 parking spaces
- 7 problems, yes, 4 min
- 57 boxes, 25 pieces left over
- 8 buses, 10 empty seats
Unit Pricing
A unit price is the price for one of something. To find the unit price, divide the total cost by the number of things bought.
Example E
5 shirts cost $60
To find the cost per shirt:
[latex]$60 \div 5 =[/latex]
[latex]\begin{array}{r}12\\5\enclose{longdiv}{60}\end{array}[/latex]
The unit price is $12.
Example F
6 L of oil for $18
To find the cost per L:
[latex]$18 \div 6 =[/latex]
[latex]\begin{array}{r}3\\6\enclose{longdiv}{18}\end{array}[/latex]
The unit price is $3.
Exercise 3
Solve the cost per unit price.
- 2 CDs for $26
- 3 cans of dog food for $6
- 4 air fresheners for $8
- 2 cat treats for $4
- 2 pizzas for $22
- 2 cans of peanuts for $8
- 2 ice cream for $12
- 4 boxes of chocolate bars for $48
- 2 WD-40 for $6
- 3 paint rollers for $9
- 4 tie downs for $20
- 3 boxes of diapers for $51
- 3 work shirts for $45
- 8 pairs of socks for $64
Exercise 3 Answers
- $13
- $2
- $2
- $2
- $11
- $4
- $6
- $12
- $3
- $3
- $5
- $17
- $15
- $8
Best Buy
The best buy is the lowest unit price.
Example G
You can buy 4 L of canola oil for $8 or 10 L for $30. Which is the best buy?
Step 1: [latex]$8\div4=[/latex] can be rewritten and solved:
[latex]\begin{array}{r}2\\4\enclose{longdiv}{8}\end{array}[/latex]
Step 2: [latex]$30 \div 10 =[/latex] can be rewritten and solved:
[latex]\begin{array}{r}3\\10\enclose{longdiv}{30}\end{array}[/latex]
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.
Exercise 4
Solve the unit price and then underline the best buy.
- 2 L of engine oil for $8 or 5 L of engine oil for $15.
- 4 tires for $240 or 2 tires for $110.
- 6 jars of salad dressing for $24 or 3 jars of salad dressing for $15.
- 7 kg of dog food for $21 or 16 kg for $32.
- 3 DVDs for $54 or 7 DVDs for $119.
- 3 L of laundry soap for $6 or 17 L of laundry soap for $68.
Exercise 4 Answers
- $4, $3, 5 L for $15 is the best buy.
- $60, $55, 2 tires for $110 is the best buy.
- $4, $5, 6 salad dressing for $24 is the best buy.
- $3, $2, 16 kg for $32 is the best buy.
- $18, $17, 7 DVDs for $119 is the best buy.
- $2, $4, 3 L for $6 is the best buy.
1.14: Practice Questions
- Solve the following word problems.
- Enrique drove the 1 920 km from Dease Lake to Creston in 24 hours. What was his average speed in kilometres per hour?
- The Evergreen Company employs 26 people. Its total payroll for last month was $84162. What was the average monthly pay cheque per person?
- The proud gardener grew a total crop of 135 cucumbers on 15 plants. What was the average crop per plant?
- In a recent truckload sale, electric stoves were sold for $432. The gross income from the stove sale was $42336. How many stoves were sold?
- The 39 farmers in Jones Valley had a total income last year of $2905500. What was their average income?
- A store has an inventory (stock on hand) of chairs with a total value of $1738. Each chair is to be sold at $79. How many of these chairs are there?
1.14: Practice Answers
- Solve these problems.
- 80 km/h
- $3237 per month
- 9 cucumbers per plant
- 98 stoves
- $74500
- 22 chairs
Attribution
This chapter has been adapted from Topic F: Division Problems in Adult Literacy Fundamental Mathematics: Book 3 – 2nd Edition (BCcampus) by Wendy Tagami and Liz Girard (2023), which is under a CC BY 4.0 license.
