Equivalent fractions

Introduction

Equivalent fractions are different fractions that represent the same value or proportion. Understanding equivalent fractions is essential for comparing fractions, adding and subtracting them, and working with decimals.

Definition

Two fractions $\frac{a}{b}$ and $\frac{c}{d}$ are equivalent if:

$$\frac{a}{b} = \frac{c}{d}$$

This can be achieved by multiplying or dividing both the numerator and denominator by the same non-zero number.

Example

Let's find equivalent fractions for $\frac{1}{2}$:

1. Multiply the numerator and denominator by 2: $$\frac{1 \times 2}{2 \times 2} = \frac{2}{4}$$
2. Multiply the numerator and denominator by 3: $$\frac{1 \times 3}{2 \times 3} = \frac{3}{6}$$

Thus, $\frac{1}{2}$, $\frac{2}{4}$, and $\frac{3}{6}$ are all equivalent fractions.

Key Questions

• What are equivalent fractions?
• How can you find equivalent fractions for a given fraction?
• Why are equivalent fractions important in math?

Conclusion

Recognizing and generating equivalent fractions is a fundamental skill in math that helps with various operations involving fractions and decimals.