Math worksheet for practicing operations with fractions, including addition, subtraction, multiplication, and division.

Let's solve each of the 10 fraction problems step by step. I'll go through them one at a time, showing the work and simplifying where needed.

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1. $\frac{7}{3} \times \frac{13}{8}$

Multiply numerators and denominators:

$$
\frac{7 \times 13}{3 \times 8} = \frac{91}{24}
$$

This is an improper fraction. Convert to mixed number:

$$
91 \div 24 = 3 \text{ remainder } 19 \Rightarrow 3\frac{19}{24}
$$

✔ Answer: $ \boxed{3\frac{19}{24}} $

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2. $\frac{9}{8} + \frac{5}{7}$

Find the least common denominator (LCD) of 8 and 7: it's 56.

Convert both fractions:

$$
\frac{9}{8} = \frac{9 \times 7}{8 \times 7} = \frac{63}{56}, \quad \frac{5}{7} = \frac{5 \times 8}{7 \times 8} = \frac{40}{56}
$$

Add:

$$
\frac{63}{56} + \frac{40}{56} = \frac{103}{56}
$$

Convert to mixed number:

$$
103 \div 56 = 1 \text{ remainder } 47 \Rightarrow 1\frac{47}{56}
$$

✔ Answer: $ \boxed{1\frac{47}{56}} $

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3. $\frac{9}{3} - \frac{1}{6}$

Simplify $\frac{9}{3} = 3$

Now subtract:

$$
3 - \frac{1}{6} = \frac{18}{6} - \frac{1}{6} = \frac{17}{6}
$$

Convert to mixed number:

$$
17 \div 6 = 2 \text{ remainder } 5 \Rightarrow 2\frac{5}{6}
$$

✔ Answer: $ \boxed{2\frac{5}{6}} $

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4. $\frac{23}{14} + \frac{20}{19}$

Find LCD of 14 and 19: since they are coprime, LCD = $14 \times 19 = 266$

Convert:

$$
\frac{23}{14} = \frac{23 \times 19}{266} = \frac{437}{266}, \quad \frac{20}{19} = \frac{20 \times 14}{266} = \frac{280}{266}
$$

Add:

$$
\frac{437 + 280}{266} = \frac{717}{266}
$$

Check if reducible: GCF of 717 and 266?

Try dividing: 717 ÷ 266 ≈ 2.69 → not divisible evenly.

Check GCF:
717 ÷ 3 = 239 → 717 = 3 × 239
266 ÷ 2 = 133 → 266 = 2 × 7 × 19
No common factors → already simplified.

Convert to mixed number:

$$
717 \div 266 = 2 \text{ remainder } 185 \Rightarrow 2\frac{185}{266}
$$

✔ Answer: $ \boxed{2\frac{185}{266}} $

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5. $\frac{20}{5} - \frac{15}{14}$

Simplify $\frac{20}{5} = 4$

Now: $4 - \frac{15}{14} = \frac{56}{14} - \frac{15}{14} = \frac{41}{14}$

Convert to mixed number:

$$
41 \div 14 = 2 \text{ remainder } 13 \Rightarrow 2\frac{13}{14}
$$

✔ Answer: $ \boxed{2\frac{13}{14}} $

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6. $\frac{5}{11} + \frac{26}{11}$

Same denominator:

$$
\frac{5 + 26}{11} = \frac{31}{11}
$$

Convert:

$$
31 \div 11 = 2 \text{ remainder } 9 \Rightarrow 2\frac{9}{11}
$$

✔ Answer: $ \boxed{2\frac{9}{11}} $

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7. $\frac{1}{7} \times \frac{29}{18}$

Multiply:

$$
\frac{1 \times 29}{7 \times 18} = \frac{29}{126}
$$

Check if reducible: 29 is prime, doesn't divide 126 → already simplified.

✔ Answer: $ \boxed{\frac{29}{126}} $

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8. $\frac{43}{19} \div \frac{2}{3}$

Dividing fractions: multiply by reciprocal:

$$
\frac{43}{19} \times \frac{3}{2} = \frac{43 \times 3}{19 \times 2} = \frac{129}{38}
$$

Convert to mixed number:

$$
129 \div 38 = 3 \text{ remainder } 15 \Rightarrow 3\frac{15}{38}
$$

✔ Answer: $ \boxed{3\frac{15}{38}} $

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9. $\frac{37}{7} - \frac{5}{2}$

LCD of 7 and 2 is 14.

Convert:

$$
\frac{37}{7} = \frac{37 \times 2}{14} = \frac{74}{14}, \quad \frac{5}{2} = \frac{5 \times 7}{14} = \frac{35}{14}
$$

Subtract:

$$
\frac{74 - 35}{14} = \frac{39}{14}
$$

Convert:

$$
39 \div 14 = 2 \text{ remainder } 11 \Rightarrow 2\frac{11}{14}
$$

✔ Answer: $ \boxed{2\frac{11}{14}} $

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10. $\frac{2}{5} + \frac{2}{5}$

Same denominator:

$$
\frac{2 + 2}{5} = \frac{4}{5}
$$

✔ Answer: $ \boxed{\frac{4}{5}} $

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✔ Final Answers:

1. $3\frac{19}{24}$
2. $1\frac{47}{56}$
3. $2\frac{5}{6}$
4. $2\frac{185}{266}$
5. $2\frac{13}{14}$
6. $2\frac{9}{11}$
7. $\frac{29}{126}$
8. $3\frac{15}{38}$
9. $2\frac{11}{14}$
10. $\frac{4}{5}$

Let me know if you'd like these as decimals or further explained!