1. Change the following fractions to 8ths. **a)** Convert $\frac{1}{2}$ to eighths: Multiply numerator and denominator by 4: $$\frac{1}{2} = \frac{1 \times 4}{2 \times 4} = \frac{4}{8}$$ **b)** Convert $\frac{3}{4}$ to eighths: Multiply numerator and denominator by 2: $$\frac{3}{4} = \frac{3 \times 2}{4 \times 2} = \frac{6}{8}$$ **c)** Convert $\frac{3}{8}$ to eighths: Already in eighths: $$\frac{3}{8}$$ 2. Change the following fractions to 16ths. **a)** Convert $\frac{1}{4}$ to sixteenths: Multiply numerator and denominator by 4: $$\frac{1}{4} = \frac{1 \times 4}{4 \times 4} = \frac{4}{16}$$ **b)** Convert $\frac{3}{4}$ to sixteenths: Multiply numerator and denominator by 4: $$\frac{3}{4} = \frac{3 \times 4}{4 \times 4} = \frac{12}{16}$$ **c)** Convert $\frac{1}{2}$ to sixteenths: Multiply numerator and denominator by 8: $$\frac{1}{2} = \frac{1 \times 8}{2 \times 8} = \frac{8}{16}$$ 3. Change the following fractions to 32nds. **a)** Convert $\frac{3}{4}$ to thirty-seconds: Multiply numerator and denominator by 8: $$\frac{3}{4} = \frac{3 \times 8}{4 \times 8} = \frac{24}{32}$$ **b)** Convert $\frac{5}{16}$ to thirty-seconds: Multiply numerator and denominator by 2: $$\frac{5}{16} = \frac{5 \times 2}{16 \times 2} = \frac{10}{32}$$ **c)** Convert $\frac{3}{4}$ to thirty-seconds (same as a): $$\frac{24}{32}$$ 4. Change the following fractions to 64ths. **a)** Convert $\frac{7}{16}$ to sixty-fourths: Multiply numerator and denominator by 4: $$\frac{7}{16} = \frac{7 \times 4}{16 \times 4} = \frac{28}{64}$$ **b)** $\frac{19}{64}$ is already in sixty-fourths. **c)** Convert $\frac{7}{16}$ to sixty-fourths (same as a): $$\frac{28}{64}$$ 5. Which measurement is greater? **a)** Compare $\frac{1}{4}$ and $\frac{15}{64}$: Convert $\frac{1}{4}$ to sixty-fourths: $$\frac{1}{4} = \frac{1 \times 16}{4 \times 16} = \frac{16}{64}$$ Since $16/64 > 15/64$, $\frac{1}{4}$ is greater. **b)** Compare $\frac{3}{32}$ and $\frac{7}{64}$: Convert $\frac{3}{32}$ to sixty-fourths: $$\frac{3}{32} = \frac{3 \times 2}{32 \times 2} = \frac{6}{64}$$ Since $7/64 > 6/64$, $\frac{7}{64}$ is greater. **c)** Compare $\frac{1}{2}$ and $\frac{7}{32}$: Convert $\frac{1}{2}$ to thirty-seconds: $$\frac{1}{2} = \frac{1 \times 16}{2 \times 16} = \frac{16}{32}$$ Since $16/32 > 7/32$, $\frac{1}{2}$ is greater. 6. Arrange these rivets in order from smallest to largest: $\frac{3}{4}$, $\frac{7}{8}$, $\frac{13}{16}$, $\frac{4}{64}$, $\frac{27}{32}$ Convert all to sixty-fourths: $$\frac{3}{4} = \frac{48}{64}, \quad \frac{7}{8} = \frac{56}{64}, \quad \frac{13}{16} = \frac{52}{64}, \quad \frac{4}{64} = \frac{4}{64}, \quad \frac{27}{32} = \frac{54}{64}$$ Order: $$\frac{4}{64} < \frac{48}{64} < \frac{52}{64} < \frac{54}{64} < \frac{56}{64}$$ So: $$\frac{4}{64} < \frac{3}{4} < \frac{13}{16} < \frac{27}{32} < \frac{7}{8}$$ 7. Arrange these rivets in order from smallest to largest: $\frac{7}{16}$, $\frac{3}{8}$, $\frac{9}{32}$, $\frac{21}{64}$, $\frac{1}{4}$ Convert all to sixty-fourths: $$\frac{7}{16} = \frac{28}{64}, \quad \frac{3}{8} = \frac{24}{64}, \quad \frac{9}{32} = \frac{18}{64}, \quad \frac{21}{64} = \frac{21}{64}, \quad \frac{1}{4} = \frac{16}{64}$$ Order: $$\frac{16}{64} < \frac{18}{64} < \frac{21}{64} < \frac{24}{64} < \frac{28}{64}$$ So: $$\frac{1}{4} < \frac{9}{32} < \frac{21}{64} < \frac{3}{8} < \frac{7}{16}$$