Fractions on the ACT® Math: Complete Guide

Fractions are another fundamental building block on the ACT® Math section. You've probably worked with fractions before, but on the ACT®, things get more complicated than just addition or subtraction. Let's start with the basics to make sure we've got a solid foundation.

Fraction Addition

Before we start adding fractions, it's important to understand why we need common denominators. When we add or subtract fractions, we're essentially combining or removing parts of a whole. To do this accurately, these parts need to be of the same size - that's where common denominators come in.

Practice Problems

+ = ?

+ = ?

- = ?

Problem 1:

Problem 2:

1. Understand the fractions:

   • means one-half.
   • means one-quarter.

2. Find a common denominator:

   The denominators are 2 and 4. The least common multiple (LCM) of 2 and 4 is 4.

   = =

3. Add the fractions:

   + = =

Problem 3:

1. Understand the fractions:

   • means one-half.
   • means one-quarter.

2. Find a common denominator:

   The denominators are 2 and 4. The least common multiple (LCM) of 2 and 4 is 4.

   = =

3. Subtract the fractions:

   - = =

How do you compare fractions?

Now, let's tackle a more complex problem that you might encounter on the ACT® Math section. Imagine you're given a question where you need to compare fractions. This could be ordering them from least to greatest or simply picking the largest one.

Here's an example:

Sort these fractions from least to greatest:

At first glance, this might seem daunting. We could find the LCM for all denominators, convert each fraction, and then compare. But there's a simpler way: converting fractions to decimals.

Here's how we can approach this step-by-step:

1. Recognize that comparing fractions directly can be tricky.
2. Recall that we can convert fractions to decimals by dividing the numerator by the denominator.
3. Convert each fraction to a decimal.
4. Order the resulting decimals from least to greatest.
5. Match the ordered decimals back to their original fractions.

Let's work through this process:

Now that we have the decimal equivalents, we can easily order them from least to greatest:

And there you have it! We've successfully ordered the fractions from least to greatest.

How Can You Use This on the ACT® Math?

You'll receive several questions that involve fractions. Some will ask you to perform simple arithmetic: adding, subtracting, multiplying, dividing. Those are few. As you progress through the math section into more difficult questions, you'll continue to receive questions involving fractions.

The rules for basic arithmetic with fractions will still undergird all of these questions. Ensure that you're really solid on these rules. When you get to questions above #10 on any given test, you'll find that the ACT® Math section is giving you questions with arithmetic and something else. Maybe it's algebra, probability, or graphs/functions. The work you do on fractions on this page will carry over into a lot of the other sections.