SSAT Prep
Back to Fractions

Simplifying Fractions

Simplifying a fraction means shrinking the numbers without changing the amount. 2/4 and 1/2 are the same size slice!

Explain what it means to simplify a fraction
Use common factors (or GCF) to reduce fractions to simplest form
Check that numerator and denominator are relatively prime
Handle proper, improper, and mixed-number fractions

Why Learn This?

Smaller numbers are easier to compare and compute with.

Tests (like SSAT) expect answers in simplest form.

It's like cleaning your desk—same stuff, less mess.

Key Vocabulary

NUMERATOR

Top number of a fraction (how many parts).

DENOMINATOR

Bottom number (total equal parts).

FACTOR

A number that divides another number evenly.

COMMON FACTOR

A number that divides both numerator and denominator.

GCF

Greatest Common Factor—the largest common factor.

SIMPLEST FORM

A fraction whose numerator and denominator share no common factor > 1.

How to Simplify

  1. 1

    Look at the numerator and denominator.

  2. 2

    Find a number that divides both (try 2, 3, 5… or find the GCF).

  3. 3

    Divide the top and bottom by that number.

  4. 4

    Repeat until no common factor remains (or divide once by the GCF).

  5. 5

    Optional check: Use a prime-factor tree to confirm there's nothing left to cancel.

Pro Tips

If both numbers are even, divide by 2 first.

If digits sum to a multiple of 3, divide by 3.

Numbers ending in 0 or 5 are divisible by 5.

Use the GCF for a one-step simplify.

Real-World Examples

Pizza
4/8

Both numbers divide by 4 → 1/2 (half a pizza).

4 ÷ 4 = 1

8 ÷ 4 = 2

Result = 1/2

Soccer team shoes
10/15

Divide by 5 → 2/3.

10 ÷ 5 = 2

15 ÷ 5 = 3

Result = 2/3

Notebook pages
12/20

GCF is 4 → 3/5.

12 ÷ 4 = 3

20 ÷ 4 = 5

Result = 3/5

Common Mistakes to Avoid

Only divide one part (top or bottom). You must divide BOTH.

Subtracting numbers instead of dividing to simplify.

Thinking 3/9 = 3/6 because both contain a 3 (you need common factors, not digit matching).

Practice Problems

Write each answer in simplest form. If improper, you may keep it as a simplified improper fraction or convert to a mixed number.

Focus: Divide by 2, 3, 5; obvious GCF; proper fractions

Problem E1
6/12
💡 Both numbers divide by 6.
Problem E2
9/12
💡 Digits of 9 and 12 sum to multiples of 3.
Problem E3
10/25
💡 Both end in 0 or 5.
Problem E4
8/20
Problem E5
14/21
Problem E6
15/20

Challenge Yourself

Create your own real-life fraction (pizza, time used, pages read) and simplify it.

Explain why dividing both top and bottom by the SAME nonzero number keeps the value unchanged.

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