# Proportion

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A proportion is similar to a fraction in that one number is compared to another. The 2 numbers have a fixed relationship. Another way to think about it is to think in terms of groups.  Each group must be the same.

Suppose apples are packed in bags of 7.  So there are 7 apples in one bag. Which means there will be 14 apples in 2 such bags or 35 apples in 5 bags.

We can write in out this way:

1 bag = 7 apples

2 bags = 14 apples

5 bags = 35 apples

As long as we know the proportion, we will be able to work out one number given another.  Using the same example, we will be able to work out how many apples are in 12 bags.  Or how many bags we need if we want 56 apples.

Let’s try another example.

If 2 books cost \$9, how much would 6 such books cost?

2 books = \$9

6 books = \$27

6 books is 3 groups of 2.  So 3 groups of \$9 is \$27.

A proportion refers to 2 numbers that have a fixed relationship like a fraction, ratio, rate or percentage.

### Proportion and Ratio

Let's see how to use proportion to solve a question involving ratio.

Here's the question.

I bought some apples and pears in the ratio of 3 : 5.  How many pears did I buy if I bought 12 apples?

Watch the video to learn how to solve it.

Here is another example.

The ratio of the price of a notebook to the price of a box of pencils is 2 : 5.  Find the price of the notebook if the box of pencils costs \$15.

\$15 is 3 groups of \$5.  So 3 groups of \$2 is \$6