Topic F: Division Problems
Review Topic F: Problem Solving in Adult Literacy Fundamentals Mathematics: Book Two.
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.
| Problems may tell you… | and ask 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 then the division equation will be total km ÷ h. Study these examples:
- [latex]\text{total of kilometres} \div \text{number of hours} = km/h[/latex]
- [latex]\text{total of kilometres} \div \text{number of litres} = 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 divided by the 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?
- Find the total by adding [latex]124 + 187 + 164 + 205 + 130 = 810[/latex]
- 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 for six months were $428, $605, $397, $530, $590, and $474. What is their average monthly grocery cost?
- Find the total amount.
$428 + $605 + $397 + $530 + $590 + $474 = $3024
- Divide total amount by number of items.
$3024 ÷ 6 = $504 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
Key words that point to division:
- Find the average
- Separated
- Find the ____ per ___