# Finding the Ratio: A Guide for Fifth Grade Math Students

Students are not usually introduced to ratios until sixth grade, but fifth grade students typically have the foundational skills necessary to understand them. Keep reading for a simple introduction to ratios!

If you're familiar with fractions, you'll be able to understand how ratios work as well. You already know that a fraction is a way of expressing a certain number of parts out of a whole, or a portion of the total number of objects in a group. For example, if you have 17 pieces of candy and you give away 11 of them, you've given away 11/17 of your candy. You can also say that the ratio of candy given away to the total amount of candy is 11/17 or 11:17.

### Ratios as Rules

Now, imagine that you doubled the amount of candy you had to 34 pieces, and then you doubled the amount you gave away to 22 pieces. You could say that you gave away 22/34 of your candy, but it would be more appropriate to reduce that fraction to 11/17. Likewise, if you tripled both amounts (11 and 17) to 33 and 51, you would give away 33/51 of your candy. You could still reduce this fraction to 11/17.

In fact, in any case where you multiply the numerator (11) and the denominator (17) by the same number, you'll wind up with a fraction that reduces to 11/17. This is true because in every instance, you're still giving away 11 pieces of candy for every 17 pieces that you have. No matter how many groups of 17 pieces you have, the rule is still the same.

This example illustrates the difference between a fraction and a ratio. A fraction just expresses a specific instance; a ratio can represent a specific instance, or it can express a general rule about the relationship between two things. In this case, the ratio of candy given away to the total number of pieces is always 11:17 or 11/17, whether you have 17 pieces or 51.

### Finding Ratios

When you write a ratio, you start by identifying the two things that are related. For example, you could write a ratio representing the number of items you get for a certain price or the number of girls to boys. Next, identify the amounts. The question you're answering might tell you that you can buy two bracelets for \$1.50, or it might tell you that a school has a ratio of three girls for every two boys.

Ratios are normally written from left to right. For example, if a school has three girls for every two boys, the ratio is 3:2. However, if the ratio is stated the other way (two boys for every three girls), it is written the opposite way (2:3).

You can also write any ratio as a fraction. Fractional ratios are read from top to bottom. For instance, two boys to three girls would be 2/3, and two bracelets for \$1.50 would be 2/1.50.

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