Math worksheet featuring eight fraction equations to solve, with instructions to express answers as fractions or mixed numbers.

Let's solve each equation step by step. We are given proportions (equations with fractions), and we need to find the unknown variable in each case. We'll use cross-multiplication to solve them.

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1. $\frac{2}{7} = \frac{x}{15}$

Cross-multiply:

$$
2 \cdot 15 = 7 \cdot x \Rightarrow 30 = 7x
$$

Now divide both sides by 7:

$$
x = \frac{30}{7}
$$

As a mixed number: $4\frac{2}{7}$

✔ Answer: $\boxed{\frac{30}{7}}$ or $\boxed{4\frac{2}{7}}$

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2. $\frac{2}{p} = \frac{9}{4}$

Cross-multiply:

$$
2 \cdot 4 = 9 \cdot p \Rightarrow 8 = 9p
$$

Divide both sides by 9:

$$
p = \frac{8}{9}
$$

✔ Answer: $\boxed{\frac{8}{9}}$

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3. $\frac{1}{p} = \frac{6}{16}$

First, simplify $\frac{6}{16} = \frac{3}{8}$

So:
$$
\frac{1}{p} = \frac{3}{8}
$$

Cross-multiply:

$$
1 \cdot 8 = 3 \cdot p \Rightarrow 8 = 3p
$$

Divide by 3:

$$
p = \frac{8}{3}
$$

As a mixed number: $2\frac{2}{3}$

✔ Answer: $\boxed{\frac{8}{3}}$ or $\boxed{2\frac{2}{3}}$

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4. $\frac{2}{5} = \frac{1}{n}$

Cross-multiply:

$$
2 \cdot n = 5 \cdot 1 \Rightarrow 2n = 5
$$

Divide by 2:

$$
n = \frac{5}{2}
$$

As a mixed number: $2\frac{1}{2}$

✔ Answer: $\boxed{\frac{5}{2}}$ or $\boxed{2\frac{1}{2}}$

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5. $\frac{y}{8} = \frac{1}{28}$

Cross-multiply:

$$
y \cdot 28 = 8 \cdot 1 \Rightarrow 28y = 8
$$

Divide by 28:

$$
y = \frac{8}{28} = \frac{2}{7}
$$

(Simplified by dividing numerator and denominator by 4)

✔ Answer: $\boxed{\frac{2}{7}}$

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6. $\frac{20}{9} = \frac{8}{c}$

Cross-multiply:

$$
20 \cdot c = 9 \cdot 8 \Rightarrow 20c = 72
$$

Divide by 20:

$$
c = \frac{72}{20} = \frac{18}{5}
$$

(Simplify by dividing numerator and denominator by 4)

As a mixed number: $3\frac{3}{5}$

✔ Answer: $\boxed{\frac{18}{5}}$ or $\boxed{3\frac{3}{5}}$

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7. $\frac{1}{7} = \frac{k}{13}$

Cross-multiply:

$$
1 \cdot 13 = 7 \cdot k \Rightarrow 13 = 7k
$$

Divide by 7:

$$
k = \frac{13}{7}
$$

As a mixed number: $1\frac{6}{7}$

✔ Answer: $\boxed{\frac{13}{7}}$ or $\boxed{1\frac{6}{7}}$

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8. $\frac{5}{k} = \frac{9}{10}$

Cross-multiply:

$$
5 \cdot 10 = 9 \cdot k \Rightarrow 50 = 9k
$$

Divide by 9:

$$
k = \frac{50}{9}
$$

As a mixed number: $5\frac{5}{9}$

✔ Answer: $\boxed{\frac{50}{9}}$ or $\boxed{5\frac{5}{9}}$

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✔ Final Answers:

1. $x = \boxed{\frac{30}{7}}$ or $4\frac{2}{7}$
2. $p = \boxed{\frac{8}{9}}$
3. $p = \boxed{\frac{8}{3}}$ or $2\frac{2}{3}$
4. $n = \boxed{\frac{5}{2}}$ or $2\frac{1}{2}$
5. $y = \boxed{\frac{2}{7}}$
6. $c = \boxed{\frac{18}{5}}$ or $3\frac{3}{5}$
7. $k = \boxed{\frac{13}{7}}$ or $1\frac{6}{7}$
8. $k = \boxed{\frac{50}{9}}$ or $5\frac{5}{9}$

Let me know if you'd like these formatted as a table or printed out!