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Visualizing Equivalent Fractions

Look at a fraction wall.

One strip divided into 2 parts ( $\frac{1}{2}$ ).
One strip divided into 4 parts ( $\frac{1}{4}$ ).

You will see that one piece of $\frac{1}{2}$ is the exact same length as two pieces of $\frac{1}{4}$ .

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

These are equivalent fractions. They denote the same length but use different fractional units.

Creating Equivalent Fractions

To find an equivalent fraction, multiply the numerator and denominator by the same number.

\frac{3}{4} = \frac{3 \times 2}{4 \times 2} = \frac{6}{8}

\frac{3}{4} = \frac{3 \times 10}{4 \times 10} = \frac{30}{40}

Lowest Terms (Simplest Form)

A fraction is in its lowest terms if the numerator and denominator have no common factor except 1. To simplify a fraction, divide the numerator and denominator by their highest common factor.

Example: Reduce $\frac{16}{20}$ . Common factor is 4.

\frac{16 \div 4}{20 \div 4} = \frac{4}{5}

$\frac{4}{5}$ is the simplest form.