Understanding fractions is a big milestone for many learners, and one of the trickiest parts is learning how to work with different denominators. If you've ever tried adding or subtracting fractions with different denominators, you know it’s not as simple as just lining them up and doing the math. To combine these fractions correctly, you need a common denominator. In this post, we’ll explore what a common denominator is, when you need to use one, and how to find it, all with examples to guide you.

What is a Common Denominator?

In a fraction, a denominator is the bottom number. It tells you how many equal parts the whole is divided into. A common denominator is a shared multiple of two or more denominators. We need it any time we add or subtract fractions that don’t already share the same denominator.

For example, if you want to add 1/8 and 5/12:

• The denominators here are 8 and 12. They’re not the same, so we can’t add them yet!
• To add 1/8 + 5/12, we need to find a number that both 8 and 12 can divide into.

How Do You Find a Common Denominator?

Step 1: List Multiples

1. List the multiples of both denominators.
2. Find the smallest number they have in common.

Example:
To find a common denominator for 1/8 and 5/12, let's list the multiples:

• Multiples of 8: 8, 16, 24, 32...
• Multiples of 12: 12, 24, 36, 48...

Here, the Least Common Multiple (LCM) = 24 → So the common denominator is 12!

Step 2: Rewrite Each Fraction with the Common Denominator

Now we convert each fraction:

• 1/8 becomes 3/24 because 8 × 3 = 24, and we multiply the numerator by the same number: 1 × 3 = 3.
• 5/12 becomes 10/24​ because 12 × 2 = 24, and 5 × 2 = 10.

Step 3: Add the Fractions

Now that the denominators match, simply add together 3/24 + 10/24 to equal 13/24.

When Do You Need a Common Denominator?

You need a common denominator any time you’re:

• Adding or subtracting fractions with different denominators.
• Comparing fractions to see which is greater or smaller.

Tips for Finding Common Denominators

1. Look for the least common multiple (LCM) of both denominators.
2. Use times tables to find common multiples faster.
3. If you can’t find the LCM easily, you can always multiply the two denominators together, it may not be the smallest, but it works!
4. • For example: For 1/5 and 1/6, 5 × 6 = 30 → use 30 as a common denominator.

Want to see these strategies in action?

Watch our full video on YouTube for a step-by-step walkthrough and more helpful tips to support your learning:

Remember, fractions don’t have to be frustrating! At TurtlEd, we support K–12 students in building a strong foundation in math, including tricky concepts like finding common denominators. Our approach helps students feel confident and capable every step of the way. Many of our students improve by more than one grade level in just 10 weeks. Contact us to learn how our effective tutoring strategies can help your student thrive in math.