How to Add and Subtract Fractions with Unlike Denominators

Adding or subtracting fractions gets tricky when the denominators — the numbers at the bottom — are different. That’s called unlike denominators, and you can’t add or subtract until the denominators match.

Let’s see an addition example:

\[ \frac{1}{6} + \frac{1}{9} \]

You can’t add them yet — the denominators are different!

Here comes a subtraction example:

\[\frac{5}{6} – \frac{1}{3}\]

Again, different denominators mean we need to do some work first.

In this guide, we’ll use addition examples to show you exactly how to handle fractions with unlike denominators.

Plus, you can download our free printable worksheets to help your child practice and build confidence at home.

3 Steps to Operate Fractions

This is the problem we’re working on:

\[ \frac{1}{6} + \frac{1}{9} \]

Step 1: Find the Least Common Denominator (LCD)

The denominators are 6 and 9. To find their Least Common Denominator (LCD), let’s list out the multiples of 6 and 9 and spot the match:

• Multiples of 6: 6, 12, 18, 24, 30, …
• Multiples of 9: 9, 18, 27, 36, …

Look, the first number they have in common is 18. 18 is called the Least Common Denominator (LCD) of 6 and 9, which is the smallest number both denominators can evenly divide into.

Step 2: Convert fractions into like denominators by LCD

We found that the Least Common Denominator (LCD) of 6 and 9 is 18. That means both fractions can be rewritten with a denominator of 18.

Notice: Whatever you multiply the denominator by, you must multiply the numerator by the same number — that’s how we keep the fractions equivalent.

\[\frac{1}{6} = \frac{1 \times 3}{6 \times 3} = \frac{3}{18}\] and \[\frac{1}{9} = \frac{1 \times 2}{9 \times 2} = \frac{2}{18}\]

Step 3: Add or subtract the fractions

\[\frac{1}{6} + \frac{1}{9} = \frac{3}{18} + \frac{2}{18} = \frac{5}{18}\]

And don’t forget — after calculation, always check if the fraction is in the simplest form! In this case, 5/18 is already in the simplest form, so you’re all set!

Let’s practice subtraction using the same denominators for easy understanding.

\[\frac{5}{6} – \frac{1}{3}\]

1. Find the LCD: since 6 is the multiple of 3, 6 is the LCD;
2. Convert fractions into like denominator:

\[\frac{1}{3} = \frac{1 \times 2}{3 \times 2} = \frac{2}{6}\]

3. Subtract the numerator:

\[\frac{5}{6} – \frac{1}{3} = \frac{5}{6} – \frac{2}{6} = \frac{5 – 2}{6} = \frac{3}{6} = \frac{1}{2}\]

Example Problem: Add and Subtract Fractions with Unlike Denominators

Example 1

Problem: Use the model to help you finish the calculation

\[\frac{1}{4} + \frac{3}{8}\]

Solution:

\[\frac{1}{4} = \frac{2}{8}\]

\[\frac{1}{4} + \frac{3}{8} = \frac{2}{8} + \frac{3}{8} = \frac{5}{8}\]

Example 2

Problem: Use the model to help you finish the calculation

\[\frac{2}{5} – \frac{1}{3}\]

Solution:

Least Common Denominator (LCD): 3 × 5 = 15

\[\frac{2}{5} = \frac{2 \times 3}{5 \times 3} = \frac{6}{15}
\quad \text{and} \quad
\frac{1}{3} = \frac{1 \times 5}{3 \times 5} = \frac{5}{15}\]

\[\frac{2}{5} – \frac{1}{3} = \frac{6}{15} – \frac{5}{15} = \frac{1}{15}\]

Want more practice with fractions?

Summary

When adding or subtracting fractions with unlike denominator, you cannot add or subtract fractions with different denominators right away — they must “speak the same language” first:

1. Find the Least Common Multiple (LCD);
2. Convert fractions into like denominator by LCD;
3. Add or subtract the numerators, and simplify!

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