Math · Fractions

Adding & Subtracting Fractions

Learn how to combine and take away fractions — even when the denominators are different. We'll walk through each step, show you how it works visually, and then you can try it yourself!

Part 01

Quick Review: Parts of a Fraction

A fraction has two parts. The numerator (top number) tells you how many parts you have. The denominator (bottom number) tells you how many equal parts make up the whole.

3 4

Think of it like pizza! 🍕

If a pizza is cut into 4 equal slices and you eat 3 of them, you've eaten 3/4 of the pizza.

Part 02

Adding Fractions with the Same Denominator

When fractions already have the same denominator, adding is easy! Just add the numerators and keep the denominator the same.

1 6
+
3 6
=
4 6
Visual: sixths
1/6
1/6
1/6
1/6
1/6
1/6
1 piece + 3 pieces = 4 pieces out of 6

Subtracting works the same way — subtract the numerators and keep the denominator:

5 8
2 8
=
3 8
Part 03

What If the Denominators Are Different?

You can't add or subtract fractions that have different denominators directly — it's like trying to add apples and oranges. You need to find a common denominator first so the pieces are all the same size.

💡 What's a Common Denominator?

A common denominator is a number that both denominators divide into evenly. The easiest one to use is the Least Common Denominator (LCD) — the smallest number that works.

Let's walk through an example step by step:

1 3
+
1 4
1

Find the Least Common Denominator

List multiples of each denominator until you find a match.
Multiples of 3: 3, 6, 9, 12, 15…
Multiples of 4: 4, 8, 12, 16…
The LCD is 12.

2

Build Equivalent Fractions

Multiply the numerator and denominator of each fraction by whatever turns the denominator into 12.

1 × 4 3 × 4
=
4 12
1 × 3 4 × 3
=
3 12
3

Add the Numerators

Now that the denominators match, add the numerators:

4 12
+
3 12
=
7 12
Visual: twelfths
4/12 (= 1/3) + 3/12 (= 1/4) = 7/12
Part 04

Subtracting with Different Denominators

Subtracting works the same way — find the common denominator, build equivalent fractions, then subtract the numerators.

3 4
1 3
1

Find the LCD

Multiples of 4: 4, 8, 12
Multiples of 3: 3, 6, 9, 12
The LCD is 12.

2

Build Equivalent Fractions

3 × 3 4 × 3
=
9 12
1 × 4 3 × 4
=
4 12
3

Subtract the Numerators

9 12
4 12
=
5 12
Visual: twelfths — subtraction
9/12 (= 3/4) − 4/12 (= 1/3) = 5/12
Part 05

Don't Forget to Simplify!

After adding or subtracting, check if your answer can be simplified (reduced). A fraction is simplified when the numerator and denominator have no common factors other than 1.

Example: Simplifying 4/6

Both 4 and 6 can be divided by 2:

4 ÷ 2 6 ÷ 2
=
2 3

To simplify, find the Greatest Common Factor (GCF) of the numerator and denominator, and divide both by it.

Your Turn!

Practice Problems

Work through each problem step by step. Enter the common denominator, the equivalent numerators, and the final answer.

Problem 1 — Addition

Solve this problem:

+

First, find the common denominator. Then fill in the equivalent fractions and your final answer.


Equivalent fractions:
1st fraction
+
2nd fraction
=
answer
Problem 2 — Subtraction

Solve this problem:

Find the common denominator, fill in the equivalent fractions, then subtract.


Equivalent fractions:
1st fraction
2nd fraction
=
answer