Adding Subtracting Multiplying and Dividing Fractions Worksheets ... - Free Printable

Problem: Solving the given fraction operations

The worksheet involves adding, subtracting, multiplying, and dividing fractions. Let's solve each problem step by step.

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#### 1. Adding Fractions

Problem 1: $\frac{25}{19} + \frac{2}{38}$

- Step 1: Find a common denominator.
- The denominators are 19 and 38. The least common denominator (LCD) is 38.
- Step 2: Rewrite each fraction with the common denominator.
- $\frac{25}{19} = \frac{25 \times 2}{19 \times 2} = \frac{50}{38}$
- $\frac{2}{38}$ remains $\frac{2}{38}$.
- Step 3: Add the fractions.
- $\frac{50}{38} + \frac{2}{38} = \frac{50 + 2}{38} = \frac{52}{38}$
- Step 4: Simplify the result.
- $\frac{52}{38} = \frac{26}{19}$ (dividing numerator and denominator by 2).

Answer: $\boxed{\frac{26}{19}}$

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Problem 2: $\frac{16}{15} + \frac{12}{25}$

- Step 1: Find a common denominator.
- The denominators are 15 and 25. The LCD is 75.
- Step 2: Rewrite each fraction with the common denominator.
- $\frac{16}{15} = \frac{16 \times 5}{15 \times 5} = \frac{80}{75}$
- $\frac{12}{25} = \frac{12 \times 3}{25 \times 3} = \frac{36}{75}$
- Step 3: Add the fractions.
- $\frac{80}{75} + \frac{36}{75} = \frac{80 + 36}{75} = \frac{116}{75}$
- Step 4: Simplify the result.
- $\frac{116}{75}$ is already in simplest form.

Answer: $\boxed{\frac{116}{75}}$

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Problem 3: $\frac{11}{24} + \frac{5}{32}$

- Step 1: Find a common denominator.
- The denominators are 24 and 32. The LCD is 96.
- Step 2: Rewrite each fraction with the common denominator.
- $\frac{11}{24} = \frac{11 \times 4}{24 \times 4} = \frac{44}{96}$
- $\frac{5}{32} = \frac{5 \times 3}{32 \times 3} = \frac{15}{96}$
- Step 3: Add the fractions.
- $\frac{44}{96} + \frac{15}{96} = \frac{44 + 15}{96} = \frac{59}{96}$
- Step 4: Simplify the result.
- $\frac{59}{96}$ is already in simplest form.

Answer: $\boxed{\frac{59}{96}}$

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#### 2. Subtracting Fractions

Problem 4: $\frac{13}{6} - \frac{3}{26}$

- Step 1: Find a common denominator.
- The denominators are 6 and 26. The LCD is 78.
- Step 2: Rewrite each fraction with the common denominator.
- $\frac{13}{6} = \frac{13 \times 13}{6 \times 13} = \frac{169}{78}$
- $\frac{3}{26} = \frac{3 \times 3}{26 \times 3} = \frac{9}{78}$
- Step 3: Subtract the fractions.
- $\frac{169}{78} - \frac{9}{78} = \frac{169 - 9}{78} = \frac{160}{78}$
- Step 4: Simplify the result.
- $\frac{160}{78} = \frac{80}{39}$ (dividing numerator and denominator by 2).

Answer: $\boxed{\frac{80}{39}}$

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Problem 5: $\frac{20}{42} - \frac{5}{18}$

- Step 1: Find a common denominator.
- The denominators are 42 and 18. The LCD is 126.
- Step 2: Rewrite each fraction with the common denominator.
- $\frac{20}{42} = \frac{20 \times 3}{42 \times 3} = \frac{60}{126}$
- $\frac{5}{18} = \frac{5 \times 7}{18 \times 7} = \frac{35}{126}$
- Step 3: Subtract the fractions.
- $\frac{60}{126} - \frac{35}{126} = \frac{60 - 35}{126} = \frac{25}{126}$
- Step 4: Simplify the result.
- $\frac{25}{126}$ is already in simplest form.

Answer: $\boxed{\frac{25}{126}}$

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Problem 6: $\frac{17}{18} - \frac{4}{45}$

- Step 1: Find a common denominator.
- The denominators are 18 and 45. The LCD is 90.
- Step 2: Rewrite each fraction with the common denominator.
- $\frac{17}{18} = \frac{17 \times 5}{18 \times 5} = \frac{85}{90}$
- $\frac{4}{45} = \frac{4 \times 2}{45 \times 2} = \frac{8}{90}$
- Step 3: Subtract the fractions.
- $\frac{85}{90} - \frac{8}{90} = \frac{85 - 8}{90} = \frac{77}{90}$
- Step 4: Simplify the result.
- $\frac{77}{90}$ is already in simplest form.

Answer: $\boxed{\frac{77}{90}}$

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#### 3. Multiplying Fractions

Problem 7: $\frac{10}{24} \times \frac{9}{16}$

- Step 1: Multiply the numerators and the denominators.
- Numerator: $10 \times 9 = 90$
- Denominator: $24 \times 16 = 384$
- Result: $\frac{90}{384}$
- Step 2: Simplify the fraction.
- Both 90 and 384 are divisible by 6.
- $\frac{90 \div 6}{384 \div 6} = \frac{15}{64}$

Answer: $\boxed{\frac{15}{64}}$

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Problem 8: $\frac{13}{15} \times \frac{6}{7}$

- Step 1: Multiply the numerators and the denominators.
- Numerator: $13 \times 6 = 78$
- Denominator: $15 \times 7 = 105$
- Result: $\frac{78}{105}$
- Step 2: Simplify the fraction.
- Both 78 and 105 are divisible by 3.
- $\frac{78 \div 3}{105 \div 3} = \frac{26}{35}$

Answer: $\boxed{\frac{26}{35}}$

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Problem 9: $\frac{23}{8} \times \frac{14}{11}$

- Step 1: Multiply the numerators and the denominators.
- Numerator: $23 \times 14 = 322$
- Denominator: $8 \times 11 = 88$
- Result: $\frac{322}{88}$
- Step 2: Simplify the fraction.
- Both 322 and 88 are divisible by 2.
- $\frac{322 \div 2}{88 \div 2} = \frac{161}{44}$

Answer: $\boxed{\frac{161}{44}}$

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#### 4. Dividing Fractions

Problem 10: $3\frac{1}{2} \div 2\frac{3}{4}$

- Step 1: Convert mixed numbers to improper fractions.
- $3\frac{1}{2} = \frac{7}{2}$
- $2\frac{3}{4} = \frac{11}{4}$
- Step 2: Divide the fractions by multiplying by the reciprocal.
- $\frac{7}{2} \div \frac{11}{4} = \frac{7}{2} \times \frac{4}{11}$
- Step 3: Multiply the numerators and the denominators.
- Numerator: $7 \times 4 = 28$
- Denominator: $2 \times 11 = 22$
- Result: $\frac{28}{22}$
- Step 4: Simplify the fraction.
- Both 28 and 22 are divisible by 2.
- $\frac{28 \div 2}{22 \div 2} = \frac{14}{11}$

Answer: $\boxed{\frac{14}{11}}$

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Problem 11: $1\frac{4}{11} \div 2\frac{1}{4}$

- Step 1: Convert mixed numbers to improper fractions.
- $1\frac{4}{11} = \frac{15}{11}$
- $2\frac{1}{4} = \frac{9}{4}$
- Step 2: Divide the fractions by multiplying by the reciprocal.
- $\frac{15}{11} \div \frac{9}{4} = \frac{15}{11} \times \frac{4}{9}$
- Step 3: Multiply the numerators and the denominators.
- Numerator: $15 \times 4 = 60$
- Denominator: $11 \times 9 = 99$
- Result: $\frac{60}{99}$
- Step 4: Simplify the fraction.
- Both 60 and 99 are divisible by 3.
- $\frac{60 \div 3}{99 \div 3} = \frac{20}{33}$

Answer: $\boxed{\frac{20}{33}}$

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Problem 12: $2\frac{1}{10} \div 1\frac{7}{18}$

- Step 1: Convert mixed numbers to improper fractions.
- $2\frac{1}{10} = \frac{21}{10}$
- $1\frac{7}{18} = \frac{25}{18}$
- Step 2: Divide the fractions by multiplying by the reciprocal.
- $\frac{21}{10} \div \frac{25}{18} = \frac{21}{10} \times \frac{18}{25}$
- Step 3: Multiply the numerators and the denominators.
- Numerator: $21 \times 18 = 378$
- Denominator: $10 \times 25 = 250$
- Result: $\frac{378}{250}$
- Step 4: Simplify the fraction.
- Both 378 and 250 are divisible by 2.
- $\frac{378 \div 2}{250 \div 2} = \frac{189}{125}$

Answer: $\boxed{\frac{189}{125}}$

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Final Answers:

1. $\boxed{\frac{26}{19}}$
2. $\boxed{\frac{116}{75}}$
3. $\boxed{\frac{59}{96}}$
4. $\boxed{\frac{80}{39}}$
5. $\boxed{\frac{25}{126}}$
6. $\boxed{\frac{77}{90}}$
7. $\boxed{\frac{15}{64}}$
8. $\boxed{\frac{26}{35}}$
9. $\boxed{\frac{161}{44}}$
10. $\boxed{\frac{14}{11}}$
11. $\boxed{\frac{20}{33}}$
12. $\boxed{\frac{189}{125}}$