Adding and Subtracting Fractions

Adding and Subtracting Fractions 🍰

A fraction has two parts:

• The numerator is the top number — it tells you how many pieces you have.
• The denominator is the bottom number — it tells you what size the pieces are.

When two fractions have the same denominator, the pieces are all the same size, so you can just add or subtract the tops:

$\frac{2}{8} + \frac{3}{8} = \frac{5}{8}$

But what about $\frac{1}{2} + \frac{1}{3}$? The pieces are different sizes — halves and thirds. You can't just add , because a half and a third are not the same thing!

Unlike denominators means the bottom numbers are different. Before we can add or subtract, we have to make the pieces match.

The Big Idea: A Common Denominator 🔑

To add or subtract fractions with unlike denominators, we rewrite them so they share the same denominator. This shared bottom number is called a common denominator.

The trick is to use equivalent fractions — fractions that look different but have the same value. If you multiply the top and bottom by the same number, the value does not change:

$\frac{1}{2} = \frac{1 \times 3}{2 \times 3} = \frac{3}{6}$

The 4 Steps ✏️

Here is the full recipe for adding or subtracting fractions with unlike denominators:

Step	What you do	Example: $\frac{1}{4} + \frac{1}{6}$

Quick Check ✅

Let's make sure the main idea is clear.

Worked Example: Adding 📝

Solve $\frac{1}{3} + \frac{1}{4}$

Guided Practice — Choose the Answer 🎯

Find a common denominator, then add or subtract the tops.

Build the Answer 🧩

You are solving $\frac{1}{4} + \frac{2}{3}$. Choose the correct common denominator, then choose the final answer.

Fractions in the Real World 🌎

Adding and subtracting fractions with unlike denominators happens all the time.

🥣 Baking

A recipe needs $\frac{1}{2}$ cup of sugar and $\frac{1}{4}$ cup of brown sugar. How much sugar in all?

Review: What You Learned 🌟

You can now add and subtract fractions even when the denominators are different. Here is the whole idea in one table:

Step	What to do	Example: $\frac{2}{3} - \frac{1}{4}$