1. The problem is to find equivalent fractions for each given fraction by multiplying numerator and denominator by the same number. 2. The rule for equivalent fractions is: $$\frac{a}{b} \times \frac{n}{n} = \frac{a \times n}{b \times n}$$ where $n$ is any nonzero integer. 3. For $\frac{1}{2}$, multiply numerator and denominator by 2: $$\frac{1}{2} \times \frac{2}{2} = \frac{1 \times 2}{2 \times 2} = \frac{2}{4}$$ 4. For $\frac{3}{4}$, multiply numerator and denominator by 2: $$\frac{3}{4} \times \frac{2}{2} = \frac{3 \times 2}{4 \times 2} = \frac{6}{8}$$ 5. For $\frac{4}{5}$, multiply numerator and denominator by 2: $$\frac{4}{5} \times \frac{2}{2} = \frac{4 \times 2}{5 \times 2} = \frac{8}{10}$$ 6. For $\frac{2}{3}$, multiply numerator and denominator by 2: $$\frac{2}{3} \times \frac{2}{2} = \frac{2 \times 2}{3 \times 2} = \frac{4}{6}$$ Each fraction is multiplied by $\frac{2}{2}$ to get an equivalent fraction with doubled denominator and numerator, matching the shaded parts in the graphs. Final answers: - $\frac{1}{2} = \frac{2}{4}$ - $\frac{3}{4} = \frac{6}{8}$ - $\frac{4}{5} = \frac{8}{10}$ - $\frac{2}{3} = \frac{4}{6}$