quivalent fractions

Equivalent fractions are fractions that represent the same value or proportion, even though they may have different numerators and denominators. To find equivalent fractions, you can multiply or divide both the numerator and the denominator of a fraction by the same non-zero number. ### Example: Let's take the fraction \( \frac{1}{2} \). 1. **Multiply by 2:** \[ \frac{1 \times 2}{2 \times 2} = \frac{2}{4} \] So, \( \frac{1}{2} \) is equivalent to \( \frac{2}{4} \). 2. **Multiply by 3:** \[ \frac{1 \times 3}{2 \times 3} = \frac{3}{6} \] So, \( \frac{1}{2} \) is also equivalent to \( \frac{3}{6} \). 3. **Divide by 2:** \[ \frac{2 \div 2}{4 \div 2} = \frac{1}{2} \] This shows that \( \frac{2}{4} \) is equivalent to \( \frac{1}{2} \). ### General Rule: If you have a fraction \( \frac{a}{b} \), you can find equivalent fractions by: - Multiplying: \( \frac{a \times n}{b \times n} \) for any integer \( n \neq 0 \) - Dividing: \( \frac{a \div n}{b \div n} \) for any integer \( n \) that divides both \( a \) and \( b \) ### Conclusion: To create equivalent fractions, simply multiply or divide the numerator and denominator by the same number. This principle can be applied to any fraction to find its equivalents.