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Minh Nguyen

ACT Math: How to Solve Ratio Problems

There are a few key concepts to get down in order to ace ACT Math ratios. Let’s go right into how the ACT will test you on ratios and break it down for you.

Ratio Basics

A ratio tells you the proportional quantity of one thing relative to another.

Make sure not to get ratios confused with fractions. Fractions tell you the proportional quantity of something relative to its whole. Ratios expressed as fractions do not tell you the whole.

One instance where you need to use the concept of ratios involves baking. If you want to make double the amount of cookies that a recipe will yield, then you need to double the quantity of each ingredient.



ACT Math: Dealing With Ratios

You might see ratios written in fraction form, colon form, or in plain English. Whatever the case may be, you can treat them all the same way. In the case of the fraction form, do not get it confused with a regular fraction! The denominator of a ratio is not necessarily equivalent to the denominator of a ratio.

For example, the ratio 12/8, 12:8, and 12 to 8 are all the same. Like fractions, you should reduce ratios down to simplest terms – in this case, it is 3/2. Keep your numbers manageable, especially when you need to look for the lowest common multiple later on in the multi-step ratio section.

On the test, ratios will be clearly spelled out for you. If you are looking at a ratio problem, you’ll know it because the test makers will make it obvious.

The important part lies in knowing how to manipulate ratios to get to your answer. The two main things you need to know are proportions and multi-step ratios.


You’ll find that these are very common on the ACT. Thankfully, they are also easy to solve.

You will usually be given a ratio along with a hypothetical quantity of one of the things on the original ratio. The key is to set up two ratios and cross-multiply as you would two fractions to solve for the missing fourth quantity.

If you have a ratio of 3 cats to 2 dogs, how many cats do you have if you have 20 dogs? You could use mental math or set up two fractions to get 30 cats as your answer.

Multi-Step Ratios

These are a little bit more involved, but shouldn’t pose much of a threat to your score one you learn about how to go about solving them.

Here you’ll be given two ratios and three different types of quantities: a, b, and c. The two ratios given compare a to b and b to c. You’ll then be asked to figure out the ratio of a to c.

In order to solve, you need to figure out the least common multiple of the two b’s and multiply the respective a’s accordingly. Now with your b’s equal to each other, simply take the values of your a and c and create a new ratio.

For example, if a:b is 2:3 and b:c is 6:9, then what is a:c? Here we need to multiply our first ratio by 2 in order to get 4:6. Since our b from the first and second ratio match, we can take our a and c and form a new ratio.

Our answer is 4:9.

About Minh Nguyen

Minh's passion for helping students succeed grew during his time as a career counselor at the University of California, Irvine. Now, he's helping students all over the world by spilling SAT/ACT secrets through blog posts on Magoosh. When he's not busy tutoring or writing, he enjoys playing guitar, traveling, and talking about himself in third-person.

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