Equivalent Fractions

An equivalent fraction is found by scaling a fraction.

To do this, multiply the numerator and denominator by the same number.

$Scaling a fraction by multiplying numerator and denominator$ $Equivalent fractions for one quarter with missing values$

$Another example of scaling a fraction$

Examples

$Equivalent fractions for one half with missing values$

$Equivalent fractions for one third with missing values$

Visual Fractions

These fractions all represent parts of a whole:

\[ \frac{1}{2},\ \frac{1}{4},\ \frac{1}{8},\ \frac{1}{16},\ \frac{1}{32},\ \frac{1}{64} \]

$Diagram showing halves, quarters, eighths, and smaller fractions$

Cutting a whole into two equal parts gives two halves.

\[ \frac{1}{2} + \frac{1}{2} = 1 \text{ whole} \] \[ \text{so } 2 \times \frac{1}{2} = 1 \]

Cutting a whole into four equal parts gives four quarters.

\[ \frac{1}{4} + \frac{1}{4} + \frac{1}{4} + \frac{1}{4} = 1 \text{ whole} \] \[ \text{so } 4 \times \frac{1}{4} = 1 \]

Cutting a half into two equal parts gives two quarters.

\[ \frac{1}{4} + \frac{1}{4} = \frac{1}{2} \] \[ \text{so } \frac{2}{4} = \frac{1}{2} \]

\[ \frac{1}{2} = \frac{2}{4} = \frac{3}{6} = \frac{4}{8} = \frac{5}{10} \]

Cutting a whole into eight equal parts gives eight eighths.

\[ 8 \times \frac{1}{8} = 1 \]

These fractions are based on thirds:

\[ \frac{1}{3},\ \frac{1}{6},\ \frac{1}{9} \]

These fractions are based on fifths:

\[ \frac{1}{5},\ \frac{1}{10},\ \frac{1}{20} \]