Equivalent & Simplified Fractions

Equivalent Fractions

Equivalent fractions

What are equivalent fractions?

• Equivalent fractions are two fractions that represent the same amount

  • They are different ways of writing the same thing

  • For example, $\frac{1}{2}$ and $\frac{6}{12}$ are equivalent fractions

How do I find an equivalent fraction?

• To find an equivalent fraction, multiply the top and bottom of a fraction by the same number

  • $\frac{5}{6}$ is equivalent to $\frac{5\times 2}{6\times 2}=\frac{10}{12}$ and $\frac{5\times 3}{6\times 3}=\frac{15}{18}$ and $\frac{5\times 4}{6\times 4}=\frac{20}{24}$etc.

  • For each fraction, there are an infinite number of equivalent fractions

Simplifying Fractions

Simplifying fractions

What is a simplified fraction?

• A simplified fraction is a fraction that is written using the smallest possible integer values

  • Simplifying turns a fraction into an 'easier' equivalent fraction

• If both the numerator and denominator can be divided by the same number (called a common factor), the fraction can be simplified

• Simplifying is also called cancelling a fraction

How do I simplify fractions?

• To simplify the fraction, divide the top and bottom by the common factor

• $\frac{12}{18}=\frac{12÷6}{18÷6}=\frac{2}{3}$

• $\frac{25}{45}=\frac{25÷5}{45÷5}=\frac{5}{9}$