Circle all the factors for each number.

Since 1 is greater than $\frac{1}{10}$. $1 > \frac{1}{10}$ Answer: $\boxed{>}$

• 8) Compare $\frac{4}{7}$ and $\frac{4}{5}$

$$
\frac{4}{7} < \frac{4}{5}
$$
**Answer:** $\boxed{<}$

• 9) Compare $\frac{4}{8}$ and $\frac{1}{2}$

$$
\frac{1}{2} = \frac{1}{2}
$$
**Answer:** $\boxed{=}$

• 10) Compare $\frac{1}{9}$ and $\frac{1}{5}$

$$
\frac{1}{9} < \frac{1}{5}
$$
**Answer:** $\boxed{<}$

• 11) Compare $\frac{2}{5}$ and $\frac{2}{9}$

$$
\frac{2}{5} > \frac{2}{9}
$$
**Answer:** $\boxed{>}$

• 12) Compare $\frac{2}{3}$ and $\frac{6}{9}$

$$
\frac{2}{3} = \frac{2}{3}
$$
**Answer:** $\boxed{=}$

• 13) Fill in the boxes to make the statement correct: $\frac{\square}{8} > \frac{\square}{4}$

The common denominator for 8 and 4 is 8. $\frac{\square}{4} = \frac{\square \times 2}{4 \times 2} = \frac{2 \times \square}{8}$

Then $A > 2 \times 1$, so $A > 2$. The smallest integer for $A$ is 3. $\frac{3}{8} > \frac{1}{4}$ Answer: $\boxed{3}$ and $\boxed{1}$ (Other valid answers exist, e.g., $\frac{5}{8} > \frac{2}{4}$)

• 14) Fill in the boxes to make the statement correct: $\frac{\square}{5} > \frac{\square}{10}$

The common denominator for 5 and 10 is 10. $\frac{\square}{5} = \frac{\square \times 2}{5 \times 2} = \frac{2 \times \square}{10}$

Then $2 \times 1 > B$, so $2 > B$. The smallest integer for $B$ is 1. $\frac{1}{5} > \frac{1}{10}$ Answer: $\boxed{1}$ and $\boxed{1}$ (Other valid answers exist, e.g., $\frac{2}{5} > \frac{3}{10}$)

• 15) Fill in the boxes to make the statement correct: $\frac{\square}{3} = \frac{\square}{6}$

The common denominator for 3 and 6 is 6. $\frac{\square}{3} = \frac{\square \times 2}{3 \times 2} = \frac{2 \times \square}{6}$

Then $B = 2 \times 1$, so $B=2$. $\frac{1}{3} = \frac{2}{6}$ Answer: $\boxed{1}$ and $\boxed{2}$ (Other valid answers exist, e.g., $\frac{2}{3} = \frac{4}{6}$)

Fraction challenge!

• 16, 17, 18) Write three fractions between $\frac{7}{8}$ and 1.

Let's use 32 as a common denominator. $\frac{7}{8} = \frac{7 \times 4}{8 \times 4} = \frac{28}{32}$ $\frac{8}{8} = \frac{8 \times 4}{8 \times 4} = \frac{32}{32}$

$\frac{30}{32}$ can be simplified to $\frac{15}{16}$.
Answer: * 16) $\boxed{\frac{29}{32}}$ * 17) $\boxed{\frac{15}{16}}$ * 18) $\boxed{\frac{31}{32}}$