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Real Life Proportion Problems. What is a proportion problem and how do you solve it?

Updated on July 23, 2012

A basic proportion problem is when you have 2 different quantities, and when one quantity gets larger the other quantity increases by the same amount. Here are 3 simple steps to help you solve a basic proportion problem:

Step 1 Summarise the proportion problem.

Step 2 Divide the same 2 quantities that you are given in the question.

Step 3 Multiply the other quantity by the answer from step 2.

Let’s take a look at some examples:

Example 1

If 3 apples cost 34p, work out the cost of 12 apples?

Step 1 Summarise the proportion problem.

3 apples = 34p

12 apples = ? p

Step 2 Divide the same 2 quantities that you are given in the question.

Since you have both amounts of apples, divide these quantities:

12 ÷ 3 = 4

Step 3 Multiply the other quantity by the answer from step 2.

Since the amount of apples is 4 times larger, the price of the apples will also be 4 times larger:

34 × 4 = 136p

So the price of the 4 apples is £1.36

Example 2

If £5 (UK pounds) is worth $8 (American dollars), what is £45 in American dollars?

Step 1 Summarise the proportion problem.

£5 = $8

£45 = $?

Step 2 Divide the same 2 quantities that you are given in the question.

Since you given both pound values, divide these quantities:

45 ÷ 5 = 9

Step 3 Multiply the other quantity by the answer from step 2.

Since the amount of UK pounds is 9 times larger, the amount of American dollars will also be 9 times larger:

8 × 9 = $72

So £45 is the same as $72.

Example 3

Convert 48 kilometres into miles. You may use the conversion 5 miles is equal to 8 kilometres.

Step 1 Summarise the proportion problem.

5 miles = 8 kilometres

? miles = 48 kilometres

Step 2 Divide the same 2 quantities that you are given in the question.

Since you given the kilometre amounts, divide these quantities:

48 ÷ 8 = 6

Step 3 Multiply the other quantity by the answer from step 2.

Since the kilometres amount is 6 times larger, the amount of miles will also be 6 times larger:

5 × 6 = 30 miles

So 48 kilometres is the same as 30 miles.

Example 4

If 4 gallons of fuel cost £20, work out the cost of 14 gallons of fuel.

Step 1 Summarise the proportion problem.

4 gallons = £20

14 gallons = £?

Step 2 Divide the same 2 quantities that you are given in the question.

Since you given the two gallon amounts, divide these quantities:

14 ÷ 4 = 3.5

Step 3 Multiply the other quantity by the answer from step 2.

Since the gallons amount is 3.5 times larger, the price will also be 3.5 times larger:

20 × 3.5 = £70

So 14 gallons of fuel will be worth £70.

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  • SidKemp profile image

    Sid Kemp 5 years ago from Boca Raton, Florida (near Miami and Palm Beach)

    These are good examples. I think they might be a little easier if you kept the units of measure in your descriptions. For example, if 4 gallons of gas costs 20 pounds, then 1 gallon of gas costs 5 pounds, or gas is 5 pounds/gallon. Keeping the conversion ratio in your notes allows you to solve all similar problems. Voted up and useful.