Math Snap

STEP 1

1. We are dealing with division of fractions.
2. Division of a fraction by a whole number can be rewritten as multiplication by the reciprocal of the whole number.
3. We need to solve each division problem and find the corresponding value for each $\square$.

STEP 2

1. Rewrite the division as multiplication by the reciprocal.
2. Perform the multiplication.
3. Simplify the fraction if necessary.

STEP 3

For part (a), rewrite $\frac{1}{5} \div 7$ as multiplication by the reciprocal of $7$.
$$\frac{1}{5} \div 7 = \frac{1}{5} \times \frac{1}{7}$$

STEP 4

Perform the multiplication for part (a).
$$\frac{1}{5} \times \frac{1}{7} = \frac{1 \times 1}{5 \times 7} = \frac{1}{35}$$

STEP 5

For part (b), the answer is $\frac{1}{35}$.
$$\boxed{\frac{1}{35}}$$

STEP 6

For part (c), rewrite $\frac{1}{4} \div 9$ as multiplication by the reciprocal of $9$.
$$\frac{1}{4} \div 9 = \frac{1}{4} \times \frac{1}{9}$$

STEP 7

Perform the multiplication for part (c).
$$\frac{1}{4} \times \frac{1}{9} = \frac{1 \times 1}{4 \times 9} = \frac{1}{36}$$

STEP 8

For part (c), the answer is $\frac{1}{36}$.
$$\boxed{\frac{1}{36}}$$

STEP 9

For part (d), rewrite $\frac{1}{7} \div 6$ as multiplication by the reciprocal of $6$.
$$\frac{1}{7} \div 6 = \frac{1}{7} \times \frac{1}{6}$$

STEP 10

Perform the multiplication for part (d).
$$\frac{1}{7} \times \frac{1}{6} = \frac{1 \times 1}{7 \times 6} = \frac{1}{42}$$

STEP 11

For part (d), the answer is $\frac{1}{42}$.
$$\boxed{\frac{1}{42}}$$

STEP 12

For part (e), rewrite $\frac{4}{9} \div 7$ as multiplication by the reciprocal of $7$.
$$\frac{4}{9} \div 7 = \frac{4}{9} \times \frac{1}{7}$$

STEP 13

Perform the multiplication for part (e).
$$\frac{4}{9} \times \frac{1}{7} = \frac{4 \times 1}{9 \times 7} = \frac{4}{63}$$

For part (e), the answer is $\frac{4}{63}$.
$$\boxed{\frac{4}{63}}$$