The homework involves finding equivalent fractions. Can you provide the original questions for problems 1 and 2?

Here are the solutions to the problems:

1. Fill in the boxes to make equivalent fractions.

a) $\frac{4}{8} = \frac{\square}{16}$

Step 1: Find the factor by which the denominator was multiplied.

$$16 \div 8 = 2$$

Step 2: Multiply the numerator by the same factor.

$$4 \times 2 = 8$$

The missing number is $\boxed{8}$.

b) $\frac{3}{7} = \frac{\square}{28}$

Step 1: Find the factor by which the denominator was multiplied.

$$28 \div 7 = 4$$

Step 2: Multiply the numerator by the same factor.

$$3 \times 4 = 12$$

The missing number is $\boxed{12}$.

c) $\frac{2}{5} = \frac{10}{\square}$

Step 1: Find the factor by which the numerator was multiplied.

$$10 \div 2 = 5$$

Step 2: Multiply the denominator by the same factor.

$$5 \times 5 = 25$$

The missing number is $\boxed{25}$.

d) $\frac{8}{7} = \frac{32}{\square}$

Step 1: Find the factor by which the numerator was multiplied.

$$32 \div 8 = 4$$

Step 2: Multiply the denominator by the same factor.

$$7 \times 4 = 28$$

The missing number is $\boxed{28}$.

2. Write the first five equivalent fractions for the following.

a) $\frac{6}{12}$
To find equivalent fractions, multiply the numerator and denominator by 2, 3, 4, 5, and 6.

$$\frac{6 \times 2}{12 \times 2} = \frac{12}{24}$$ $$\frac{6 \times 3}{12 \times 3} = \frac{18}{36}$$ $$\frac{6 \times 4}{12 \times 4} = \frac{24}{48}$$ $$\frac{6 \times 5}{12 \times 5} = \frac{30}{60}$$ $$\frac{6 \times 6}{12 \times 6} = \frac{36}{72}$$

The first five equivalent fractions are $\boxed{\frac{12}{24}, \frac{18}{36}, \frac{24}{48}, \frac{30}{60}, \frac{36}{72}}$.

b) $\frac{5}{6}$
To find equivalent fractions, multiply the numerator and denominator by 2, 3, 4, 5, and 6.

$$\frac{5 \times 2}{6 \times 2} = \frac{10}{12}$$ $$\frac{5 \times 3}{6 \times 3} = \frac{15}{18}$$ $$\frac{5 \times 4}{6 \times 4} = \frac{20}{24}$$ $$\frac{5 \times 5}{6 \times 5} = \frac{25}{30}$$ $$\frac{5 \times 6}{6 \times 6} = \frac{30}{36}$$

The first five equivalent fractions are $\boxed{\frac{10}{12}, \frac{15}{18}, \frac{20}{24}, \frac{25}{30}, \frac{30}{36}}$.

c) $\frac{3}{6}$
To find equivalent fractions, multiply the numerator and denominator by 2, 3, 4, 5, and 6.

$$\frac{3 \times 2}{6 \times 2} = \frac{6}{12}$$ $$\frac{3 \times 3}{6 \times 3} = \frac{9}{18}$$ $$\frac{3 \times 4}{6 \times 4} = \frac{12}{24}$$ $$\frac{3 \times 5}{6 \times 5} = \frac{15}{30}$$ $$\frac{3 \times 6}{6 \times 6} = \frac{18}{36}$$

The first five equivalent fractions are $\boxed{\frac{6}{12}, \frac{9}{18}, \frac{12}{24}, \frac{15}{30}, \frac{18}{36}}$.

d) $\frac{7}{10}$
To find equivalent fractions, multiply the numerator and denominator by 2, 3, 4, 5, and 6.

$$\frac{7 \times 2}{10 \times 2} = \frac{14}{20}$$ $$\frac{7 \times 3}{10 \times 3} = \frac{21}{30}$$ $$\frac{7 \times 4}{10 \times 4} = \frac{28}{40}$$ $$\frac{7 \times 5}{10 \times 5} = \frac{35}{50}$$ $$\frac{7 \times 6}{10 \times 6} = \frac{42}{60}$$

The first five equivalent fractions are $\boxed{\frac{14}{20}, \frac{21}{30}, \frac{28}{40}, \frac{35}{50}, \frac{42}{60}}$.

e) $\frac{2}{5}$
To find equivalent fractions, multiply the numerator and denominator by 2, 3, 4, 5, and 6.

$$\frac{2 \times 2}{5 \times 2} = \frac{4}{10}$$ $$\frac{2 \times 3}{5 \times 3} = \frac{6}{15}$$ $$$$