Fraction addition practice worksheet with problems and instructions.

The image shows a worksheet with problems involving division of fractions. The task is to solve each problem by dividing the given fractions and expressing the answers in simplest form. Below, I will solve each problem step by step.

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Problem 1: \( \frac{1}{3} \div \frac{1}{3} \)

1. Recall the rule for dividing fractions:
To divide two fractions, multiply the first fraction by the reciprocal of the second fraction.
\[
\frac{a}{b} \div \frac{c}{d} = \frac{a}{b} \times \frac{d}{c}
\]

2. Apply the rule:
\[
\frac{1}{3} \div \frac{1}{3} = \frac{1}{3} \times \frac{3}{1}
\]

3. Multiply the fractions:
\[
\frac{1}{3} \times \frac{3}{1} = \frac{1 \times 3}{3 \times 1} = \frac{3}{3} = 1
\]

Answer:
\[
\boxed{1}
\]

---

Problem 2: \( \frac{2}{3} \div \frac{1}{3} \)

1. Apply the rule for dividing fractions:
\[
\frac{2}{3} \div \frac{1}{3} = \frac{2}{3} \times \frac{3}{1}
\]

2. Multiply the fractions:
\[
\frac{2}{3} \times \frac{3}{1} = \frac{2 \times 3}{3 \times 1} = \frac{6}{3} = 2
\]

Answer:
\[
\boxed{2}
\]

---

Problem 3: \( \frac{3}{4} \div \frac{1}{8} \)

1. Apply the rule for dividing fractions:
\[
\frac{3}{4} \div \frac{1}{8} = \frac{3}{4} \times \frac{8}{1}
\]

2. Multiply the fractions:
\[
\frac{3}{4} \times \frac{8}{1} = \frac{3 \times 8}{4 \times 1} = \frac{24}{4} = 6
\]

Answer:
\[
\boxed{6}
\]

---

Problem 4: \( \frac{4}{3} \div \frac{1}{5} \)

1. Apply the rule for dividing fractions:
\[
\frac{4}{3} \div \frac{1}{5} = \frac{4}{3} \times \frac{5}{1}
\]

2. Multiply the fractions:
\[
\frac{4}{3} \times \frac{5}{1} = \frac{4 \times 5}{3 \times 1} = \frac{20}{3}
\]

3. Simplify if possible:
\(\frac{20}{3}\) is already in simplest form.

Answer:
\[
\boxed{\frac{20}{3}}
\]

---

Problem 5: \( \frac{2}{3} \div \frac{1}{4} \)

1. Apply the rule for dividing fractions:
\[
\frac{2}{3} \div \frac{1}{4} = \frac{2}{3} \times \frac{4}{1}
\]

2. Multiply the fractions:
\[
\frac{2}{3} \times \frac{4}{1} = \frac{2 \times 4}{3 \times 1} = \frac{8}{3}
\]

3. Simplify if possible:
\(\frac{8}{3}\) is already in simplest form.

Answer:
\[
\boxed{\frac{8}{3}}
\]

---

Problem 6: \( \frac{2}{3} \div \frac{2}{3} \)

1. Apply the rule for dividing fractions:
\[
\frac{2}{3} \div \frac{2}{3} = \frac{2}{3} \times \frac{3}{2}
\]

2. Multiply the fractions:
\[
\frac{2}{3} \times \frac{3}{2} = \frac{2 \times 3}{3 \times 2} = \frac{6}{6} = 1
\]

Answer:
\[
\boxed{1}
\]

---

Problem 7: \( \frac{8}{9} \div \frac{1}{3} \)

1. Apply the rule for dividing fractions:
\[
\frac{8}{9} \div \frac{1}{3} = \frac{8}{9} \times \frac{3}{1}
\]

2. Multiply the fractions:
\[
\frac{8}{9} \times \frac{3}{1} = \frac{8 \times 3}{9 \times 1} = \frac{24}{9}
\]

3. Simplify the fraction:
\[
\frac{24}{9} = \frac{8}{3} \quad (\text{divide numerator and denominator by } 3)
\]

Answer:
\[
\boxed{\frac{8}{3}}
\]

---

Problem 8: \( \frac{2}{3} \div \frac{7}{8} \)

1. Apply the rule for dividing fractions:
\[
\frac{2}{3} \div \frac{7}{8} = \frac{2}{3} \times \frac{8}{7}
\]

2. Multiply the fractions:
\[
\frac{2}{3} \times \frac{8}{7} = \frac{2 \times 8}{3 \times 7} = \frac{16}{21}
\]

3. Simplify if possible:
\(\frac{16}{21}\) is already in simplest form.

Answer:
\[
\boxed{\frac{16}{21}}
\]

---

Problem 9: \( \frac{9}{4} \div \frac{1}{3} \)

1. Apply the rule for dividing fractions:
\[
\frac{9}{4} \div \frac{1}{3} = \frac{9}{4} \times \frac{3}{1}
\]

2. Multiply the fractions:
\[
\frac{9}{4} \times \frac{3}{1} = \frac{9 \times 3}{4 \times 1} = \frac{27}{4}
\]

3. Simplify if possible:
\(\frac{27}{4}\) is already in simplest form.

Answer:
\[
\boxed{\frac{27}{4}}
\]

---

Problem 10: \( \frac{10}{8} \div \frac{1}{3} \)

1. Simplify the first fraction:
\[
\frac{10}{8} = \frac{5}{4} \quad (\text{divide numerator and denominator by } 2)
\]

2. Apply the rule for dividing fractions:
\[
\frac{5}{4} \div \frac{1}{3} = \frac{5}{4} \times \frac{3}{1}
\]

3. Multiply the fractions:
\[
\frac{5}{4} \times \frac{3}{1} = \frac{5 \times 3}{4 \times 1} = \frac{15}{4}
\]

4. Simplify if possible:
\(\frac{15}{4}\) is already in simplest form.

Answer:
\[
\boxed{\frac{15}{4}}
\]

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Final Answers

\[
\boxed{1, 2, 6, \frac{20}{3}, \frac{8}{3}, 1, \frac{8}{3}, \frac{16}{21}, \frac{27}{4}, \frac{15}{4}}
\]