Equivalent Fractions

What Are Equivalent Fractions?

Fractions that look different but have the same value:

$\frac{1}{2} = \frac{2}{4} = \frac{3}{6} = \frac{4}{8}$

All of these equal one-half!

Creating Equivalent Fractions

Method 1: Multiply

Multiply both numerator and denominator by the same number:

$\frac{2}{3} = \frac{2 \times 2}{3 \times 2} = \frac{4}{6}$

$\frac{2}{3} = \frac{2 \times 5}{3 \times 5} = \frac{10}{15}$

Method 2: Divide (Simplifying)

Divide both numerator and denominator by the same number:

$\frac{6}{8} = \frac{6 \div 2}{8 \div 2} = \frac{3}{4}$

Simplest Form

A fraction is in simplest form when the numerator and denominator have no common factors except 1:

• $\frac{3}{4}$ is in simplest form
• $\frac{6}{8}$ is NOT (it can simplify to $\frac{3}{4}$)

Why Is This Useful?

• Comparing fractions
• Adding and subtracting fractions
• Understanding the same amount in different ways