How to Simplify Fractions Step-by-Step

Understanding How to Simplify Fractions

Simplifying fractions, also called reducing fractions, means rewriting a fraction in lowest terms. In other words, we want the numerator and denominator to have no common factor greater than 1.

The big idea is simple: divide the numerator and denominator by the same number. When you do this, the value of the fraction stays the same, but the fraction becomes easier to read and work with.

Steps to Simplify Fractions

1. 1. Find the greatest common factor (GCF) of the numerator and denominator.
   2. Divide the numerator by the GCF.
   3. Divide the denominator by the GCF.
   4. Write the new fraction and check that it cannot be reduced again.

Here is a basic example:

Simplify:

\large \frac{24}{36}

Example: Simplifying Fractions

Step 1: Find the greatest common factor.

Factors of 24: 1, 2, 3, 4, 6, 8, 12, 24

Factors of 36: 1, 2, 3, 4, 6, 9, 12, 18, 36

The greatest common factor is 12.

Step 2: Divide the numerator and denominator by the GCF.

\large 24 \div 12=2

\large 36 \div 12=3

Step 3: Write the simplified fraction.

\large \frac{24}{36}=\frac{2}{3}

Another Example: Simplifying Fractions

Simplify:

\large \frac{45}{60}

The GCF of 45 and 60 is 15.

\large 45 \div 15=3

\large 60 \div 15=4

\large \frac{45}{60}=\frac{3}{4}

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Watch How to Simplify Fractions

Watch John simplify fractions step-by-step:

This example shows you how to reduce a larger fraction by first looking for common factors.

Watch Another Simplifying Fractions Example

It always helps to see a second example because this skill really comes down to pattern recognition and practice.

Practice Problems

Try these on your own:

1. \large \frac{18}{30}

2. \large \frac{32}{48}

3. \large \frac{54}{90}

Answers

1. \large \frac{18}{30}=\frac{3}{5}

2. \large \frac{32}{48}=\frac{2}{3}

3. \large \frac{54}{90}=\frac{3}{5}

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Common Mistakes

• Do not subtract the numerator and denominator to simplify a fraction.
• Do not divide only the numerator or only the denominator. You must divide both by the same number.
• If the fraction can still be reduced, keep going until it is in lowest terms.

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