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

Let's solve each of the 10 fraction operations step by step.

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1. $\frac{48}{19} - \left(-\frac{31}{11}\right)$

Subtracting a negative is adding:

→ $\frac{48}{19} + \frac{31}{11}$

Find LCD of 19 and 11 → 209

Convert:

$\frac{48 \times 11}{209} = \frac{528}{209}$

$\frac{31 \times 19}{209} = \frac{589}{209}$

Add: $\frac{528 + 589}{209} = \frac{1117}{209}$

Check if reducible: 1117 ÷ 209 ≈ 5.34 → not integer. 209 = 11×19, 1117 not divisible by 11 or 19 → already simplified

✔ Answer: $\frac{1117}{209}$

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2. $\frac{1}{2} - \left(-\frac{15}{8}\right)$

Again, subtracting negative → add:

→ $\frac{1}{2} + \frac{15}{8}$

LCD of 2 and 8 is 8

$\frac{1}{2} = \frac{4}{8}$

→ $\frac{4}{8} + \frac{15}{8} = \frac{19}{8}$

✔ Answer: $\frac{19}{8}$ or $2\frac{3}{8}$

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3. $\frac{11}{10} \div \frac{1}{2}$

Dividing fractions: multiply by reciprocal

→ $\frac{11}{10} \times \frac{2}{1} = \frac{22}{10} = \frac{11}{5}$

✔ Answer: $\frac{11}{5}$ or $2\frac{1}{5}$

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4. $\frac{16}{15} \times \frac{18}{11}$

Multiply numerators and denominators:

→ $\frac{16 \times 18}{15 \times 11} = \frac{288}{165}$

Simplify: divide numerator and denominator by GCD(288,165)

GCD: 288 ÷ 3 = 96, 165 ÷ 3 = 55 → so divide by 3

→ $\frac{96}{55}$

Check: 96 and 55 — 55=5×11, 96=32×3 → no common factors

✔ Answer: $\frac{96}{55}$ or $1\frac{41}{55}$

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5. $\frac{13}{11} - \left(-\frac{1}{7}\right)$

→ $\frac{13}{11} + \frac{1}{7}$

LCD of 11 and 7 = 77

$\frac{13 \times 7}{77} = \frac{91}{77}$

$\frac{1 \times 11}{77} = \frac{11}{77}$

→ $\frac{91 + 11}{77} = \frac{102}{77}$

Simplify? 102 and 77 → 77=7×11, 102=2×3×17 → no common factors

✔ Answer: $\frac{102}{77}$ or $1\frac{25}{77}$

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6. $\left(-\frac{3}{7}\right) \div \left(-\frac{14}{11}\right)$

Divide fractions: multiply by reciprocal

→ $\left(-\frac{3}{7}\right) \times \left(-\frac{11}{14}\right)$

Negative × negative = positive

→ $\frac{3 \times 11}{7 \times 14} = \frac{33}{98}$

Check simplification: 33=3×11, 98=2×49=2×7² → no common factors

✔ Answer: $\frac{33}{98}$

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7. $\left(-\frac{1}{2}\right) \times \frac{20}{7}$

Multiply:

→ $-\frac{1 \times 20}{2 \times 7} = -\frac{20}{14} = -\frac{10}{7}$

✔ Answer: $-\frac{10}{7}$ or $-1\frac{3}{7}$

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8. $\frac{11}{5} + \frac{1}{11}$

LCD of 5 and 11 = 55

$\frac{11 \times 11}{55} = \frac{121}{55}$

$\frac{1 \times 5}{55} = \frac{5}{55}$

→ $\frac{121 + 5}{55} = \frac{126}{55}$

Simplify? 126 and 55 → 55=5×11, 126=2×63=2×3²×7 → no common factors

✔ Answer: $\frac{126}{55}$ or $2\frac{16}{55}$

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9. $\left(-\frac{5}{9}\right) + \frac{5}{6}$

Find LCD of 9 and 6 → 18

$-\frac{5}{9} = -\frac{10}{18}$

$\frac{5}{6} = \frac{15}{18}$

→ $-\frac{10}{18} + \frac{15}{18} = \frac{5}{18}$

✔ Answer: $\frac{5}{18}$

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10. $\left(-\frac{36}{19}\right) + \left(-\frac{45}{19}\right)$

Same denominator → add numerators:

→ $\frac{-36 + (-45)}{19} = \frac{-81}{19}$

Simplify? 81 and 19 → 19 is prime, 81=3⁴ → no common factors

✔ Answer: $-\frac{81}{19}$ or $-4\frac{5}{19}$

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## ✔ Final Answers:

1. $\boxed{\frac{1117}{209}}$
2. $\boxed{\frac{19}{8}}$
3. $\boxed{\frac{11}{5}}$
4. $\boxed{\frac{96}{55}}$
5. $\boxed{\frac{102}{77}}$
6. $\boxed{\frac{33}{98}}$
7. $\boxed{-\frac{10}{7}}$
8. $\boxed{\frac{126}{55}}$
9. $\boxed{\frac{5}{18}}$
10. $\boxed{-\frac{81}{19}}$

Let me know if you’d like these as mixed numbers or decimal approximations too!