Reducing Fractions

Part 01

What Does "Reducing" Mean?

Reducing (or simplifying) a fraction means rewriting it in a simpler form — using smaller numbers — without changing its value. The fraction still represents the same amount, just with fewer pieces.

      4
      
      8

=

1 2

Think of it like pizza! If you eat 4 out of 8 slices, that's the same as eating 1 out of 2 halves. Same amount of pizza — just described differently.

4 / 8

4 out of 8 slices eaten

=

1 / 2

1 out of 2 halves eaten

Bar model: 4/8 is the same as 1/2

1/8

1/2

      Both bars show the same amount filled — 4/8 and 1/2 are equal!
    

Part 02

The Fast Way: Using the GCF

The quickest way to reduce a fraction in one step is to find the Greatest Common Factor (GCF) — the biggest number that divides evenly into both the numerator and the denominator — and divide both parts by it.

What's a Factor?

A factor is a number that divides evenly into another number with no remainder. For example, the factors of 12 are: 1, 2, 3, 4, 6, and 12.

Let's find the GCF of 8 and 12:

Factors of 8: 1, 2, 4, 8
Factors of 12: 1, 2, 3, 4, 6, 12

The numbers they share are 1, 2, and 4. The greatest one is 4 — so the GCF of 8 and 12 is 4. Divide both parts by 4:

÷ 4
      
÷ 4

=

2 3

Visual: 8/12 = 2/3

      ■ 8 out of 12 =
      ■ 2 out of 3 — same amount!
    

Part 03

Don't Know the GCF? No Problem!

Sometimes the GCF isn't obvious — especially with bigger numbers. That's totally fine! You can reduce step by step by dividing by any common factor you spot. Keep going until the fraction can't be reduced any further.

💡 The Key Idea

You don't need to find the biggest factor on the first try. As long as you keep dividing by common factors, you'll always reach the simplest form — it just might take a few steps instead of one.

Here are some quick divisibility tests that help you spot common factors:

÷ 2

Both numbers are even

Even = ends in 0, 2, 4, 6, or 8
Ex: 18 and 24 → both even ✓

÷ 3

Sum of the digits is divisible by 3

Ex: 24 → 2+4 = 6, and 6÷3 = 2 ✓
Ex: 15 → 1+5 = 6 ✓

÷ 5

Both numbers end in 0 or 5

Ex: 15 and 25 → both end in 5 ✓
Ex: 30 and 50 → both end in 0 ✓

÷ 10

Both numbers end in 0

Ex: 30 and 60 → both end in 0 ✓

Let's try reducing 24/36 step by step — without figuring out the GCF first:

1

Are both numbers even? Yes! Divide by 2.

            24
            
            36

→

            24 ÷ 2
            
            36 ÷ 2

=

12 18

2

Still both even? Divide by 2 again.

12 18

→

            12 ÷ 2
            
            18 ÷ 2

=

6 9

3

6 is even but 9 is odd — can't divide by 2. Try 3!

6 → digits sum to 6 (÷3 ✓) 9 → digits sum to 9 (÷3 ✓)

6 9

→

            6 ÷ 3
            
            9 ÷ 3

=

2 3

✓

Done! 2 and 3 share no common factors except 1.

We got 2/3 — the same answer we'd get using the GCF (which was 12). It just took a few more steps!

Part 04

Try It: Reduce Step by Step

Here's a fraction to simplify. Pick a number to divide by at each step. Keep going until you can't reduce any further!

Interactive Reduction

Reduce this fraction:

Pick a number that divides evenly into both:

Part 05

More Examples

Example 1: Reduce 6/9

Both digit sums divisible by 3 → GCF is 3

÷ 3
      
÷ 3

=

2 3

Example 2: Reduce 15/20

Both end in 5 or 0 → divisible by 5

÷ 5
      
÷ 5

=

3 4

Example 3: Reduce 10/30

Both end in 0 → divisible by 10, or step by step: ÷2 → 5/15, then ÷5 → 1/3

÷ 10
      
÷ 10

=

1 3

💡 What If It's Already Reduced?

Some fractions can't be simplified any further — like 3/7 or 5/8. If the only factor they share is 1, the fraction is already in simplest form!

Your Turn!

Practice Problems

Reduce each fraction to its simplest form. You can use the GCF or divide step by step — whichever you prefer!

Score: 0 / 0

Problem 1

Reduce this fraction:

Enter the fully reduced fraction below.

Reduced fraction: