Fractions Worksheets with Answer Key - Free Printable

Let's solve the problems step by step.

Section A: Add or Subtract the Following. Simplify Your Answers.

#### 1) \(\frac{1}{7} + \frac{3}{7}\)
- Since the denominators are the same, we can add the numerators directly:
\[
\frac{1}{7} + \frac{3}{7} = \frac{1 + 3}{7} = \frac{4}{7}
\]
- The answer is already in simplest form.
\[
\boxed{\frac{4}{7}}
\]

#### 2) \(\frac{2}{5} + \frac{8}{15}\)
- Find a common denominator. The least common multiple of 5 and 15 is 15.
- Convert \(\frac{2}{5}\) to a fraction with a denominator of 15:
\[
\frac{2}{5} = \frac{2 \times 3}{5 \times 3} = \frac{6}{15}
\]
- Now add the fractions:
\[
\frac{6}{15} + \frac{8}{15} = \frac{6 + 8}{15} = \frac{14}{15}
\]
- The answer is already in simplest form.
\[
\boxed{\frac{14}{15}}
\]

#### 3) \(\frac{2}{3} + \frac{1}{4}\)
- Find a common denominator. The least common multiple of 3 and 4 is 12.
- Convert \(\frac{2}{3}\) to a fraction with a denominator of 12:
\[
\frac{2}{3} = \frac{2 \times 4}{3 \times 4} = \frac{8}{12}
\]
- Convert \(\frac{1}{4}\) to a fraction with a denominator of 12:
\[
\frac{1}{4} = \frac{1 \times 3}{4 \times 3} = \frac{3}{12}
\]
- Now add the fractions:
\[
\frac{8}{12} + \frac{3}{12} = \frac{8 + 3}{12} = \frac{11}{12}
\]
- The answer is already in simplest form.
\[
\boxed{\frac{11}{12}}
\]

#### 4) \(\frac{3}{10} - \frac{1}{10}\)
- Since the denominators are the same, we can subtract the numerators directly:
\[
\frac{3}{10} - \frac{1}{10} = \frac{3 - 1}{10} = \frac{2}{10}
\]
- Simplify the fraction:
\[
\frac{2}{10} = \frac{1}{5}
\]
\[
\boxed{\frac{1}{5}}
\]

#### 5) \(\frac{11}{24} - \frac{3}{8}\)
- Find a common denominator. The least common multiple of 24 and 8 is 24.
- Convert \(\frac{3}{8}\) to a fraction with a denominator of 24:
\[
\frac{3}{8} = \frac{3 \times 3}{8 \times 3} = \frac{9}{24}
\]
- Now subtract the fractions:
\[
\frac{11}{24} - \frac{9}{24} = \frac{11 - 9}{24} = \frac{2}{24}
\]
- Simplify the fraction:
\[
\frac{2}{24} = \frac{1}{12}
\]
\[
\boxed{\frac{1}{12}}
\]

#### 6) \(\frac{5}{6} - \frac{1}{16}\)
- Find a common denominator. The least common multiple of 6 and 16 is 48.
- Convert \(\frac{5}{6}\) to a fraction with a denominator of 48:
\[
\frac{5}{6} = \frac{5 \times 8}{6 \times 8} = \frac{40}{48}
\]
- Convert \(\frac{1}{16}\) to a fraction with a denominator of 48:
\[
\frac{1}{16} = \frac{1 \times 3}{16 \times 3} = \frac{3}{48}
\]
- Now subtract the fractions:
\[
\frac{40}{48} - \frac{3}{48} = \frac{40 - 3}{48} = \frac{37}{48}
\]
- The answer is already in simplest form.
\[
\boxed{\frac{37}{48}}
\]

Section B: Multiply or Divide the Following. Simplify Your Answers.

#### 1) \(\frac{2}{7} \times \frac{3}{5}\)
- Multiply the numerators and the denominators:
\[
\frac{2}{7} \times \frac{3}{5} = \frac{2 \times 3}{7 \times 5} = \frac{6}{35}
\]
- The answer is already in simplest form.
\[
\boxed{\frac{6}{35}}
\]

#### 2) \(\frac{5}{8} \times \frac{2}{3}\)
- Multiply the numerators and the denominators:
\[
\frac{5}{8} \times \frac{2}{3} = \frac{5 \times 2}{8 \times 3} = \frac{10}{24}
\]
- Simplify the fraction:
\[
\frac{10}{24} = \frac{5}{12}
\]
\[
\boxed{\frac{5}{12}}
\]

#### 3) \(\frac{8}{9} \times \frac{3}{10}\)
- Multiply the numerators and the denominators:
\[
\frac{8}{9} \times \frac{3}{10} = \frac{8 \times 3}{9 \times 10} = \frac{24}{90}
\]
- Simplify the fraction:
\[
\frac{24}{90} = \frac{4}{15}
\]
\[
\boxed{\frac{4}{15}}
\]

#### 4) \(\frac{9}{11} \div \frac{5}{6}\)
- Dividing by a fraction is the same as multiplying by its reciprocal:
\[
\frac{9}{11} \div \frac{5}{6} = \frac{9}{11} \times \frac{6}{5} = \frac{9 \times 6}{11 \times 5} = \frac{54}{55}
\]
- The answer is already in simplest form.
\[
\boxed{\frac{54}{55}}
\]

#### 5) \(\frac{3}{8} \div \frac{5}{12}\)
- Dividing by a fraction is the same as multiplying by its reciprocal:
\[
\frac{3}{8} \div \frac{5}{12} = \frac{3}{8} \times \frac{12}{5} = \frac{3 \times 12}{8 \times 5} = \frac{36}{40}
\]
- Simplify the fraction:
\[
\frac{36}{40} = \frac{9}{10}
\]
\[
\boxed{\frac{9}{10}}
\]

#### 6) \(\frac{8}{12} \div 4\)
- Write 4 as a fraction: \(4 = \frac{4}{1}\).
- Dividing by a fraction is the same as multiplying by its reciprocal:
\[
\frac{8}{12} \div 4 = \frac{8}{12} \times \frac{1}{4} = \frac{8 \times 1}{12 \times 4} = \frac{8}{48}
\]
- Simplify the fraction:
\[
\frac{8}{48} = \frac{1}{6}
\]
\[
\boxed{\frac{1}{6}}
\]

Section C: Simplify and Leave Your Answers as Mixed Numbers.

#### 1) \(12 + \frac{8}{11}\)
- Combine the whole number and the fraction:
\[
12 + \frac{8}{11} = 12 \frac{8}{11}
\]
\[
\boxed{12 \frac{8}{11}}
\]

#### 2) \(\frac{7}{15} \times 9\)
- Multiply the fraction by the whole number:
\[
\frac{7}{15} \times 9 = \frac{7 \times 9}{15} = \frac{63}{15}
\]
- Simplify the fraction:
\[
\frac{63}{15} = \frac{21}{5}
\]
- Convert to a mixed number:
\[
\frac{21}{5} = 4 \frac{1}{5}
\]
\[
\boxed{4 \frac{1}{5}}
\]

#### 3) \(12 - \frac{8}{3}\)
- Convert 12 to a fraction with a denominator of 3:
\[
12 = \frac{36}{3}
\]
- Subtract the fractions:
\[
\frac{36}{3} - \frac{8}{3} = \frac{36 - 8}{3} = \frac{28}{3}
\]
- Convert to a mixed number:
\[
\frac{28}{3} = 9 \frac{1}{3}
\]
\[
\boxed{9 \frac{1}{3}}
\]

#### 4) \(1 \frac{2}{3} - \frac{2}{9}\)
- Convert \(1 \frac{2}{3}\) to an improper fraction:
\[
1 \frac{2}{3} = \frac{3 \times 1 + 2}{3} = \frac{5}{3}
\]
- Find a common denominator. The least common multiple of 3 and 9 is 9.
- Convert \(\frac{5}{3}\) to a fraction with a denominator of 9:
\[
\frac{5}{3} = \frac{5 \times 3}{3 \times 3} = \frac{15}{9}
\]
- Now subtract the fractions:
\[
\frac{15}{9} - \frac{2}{9} = \frac{15 - 2}{9} = \frac{13}{9}
\]
- Convert to a mixed number:
\[
\frac{13}{9} = 1 \frac{4}{9}
\]
\[
\boxed{1 \frac{4}{9}}
\]

#### 5) \(\frac{12}{5} + \frac{4}{6}\)
- Simplify \(\frac{4}{6}\):
\[
\frac{4}{6} = \frac{2}{3}
\]
- Find a common denominator. The least common multiple of 5 and 3 is 15.
- Convert \(\frac{12}{5}\) to a fraction with a denominator of 15:
\[
\frac{12}{5} = \frac{12 \times 3}{5 \times 3} = \frac{36}{15}
\]
- Convert \(\frac{2}{3}\) to a fraction with a denominator of 15:
\[
\frac{2}{3} = \frac{2 \times 5}{3 \times 5} = \frac{10}{15}
\]
- Now add the fractions:
\[
\frac{36}{15} + \frac{10}{15} = \frac{36 + 10}{15} = \frac{46}{15}
\]
- Convert to a mixed number:
\[
\frac{46}{15} = 3 \frac{1}{15}
\]
\[
\boxed{3 \frac{1}{15}}
\]

#### 6) \(10 \div \frac{4}{7}\)
- Dividing by a fraction is the same as multiplying by its reciprocal:
\[
10 \div \frac{4}{7} = 10 \times \frac{7}{4} = \frac{10 \times 7}{4} = \frac{70}{4}
\]
- Simplify the fraction:
\[
\frac{70}{4} = \frac{35}{2}
\]
- Convert to a mixed number:
\[
\frac{35}{2} = 17 \frac{1}{2}
\]
\[
\boxed{17 \frac{1}{2}}
\]

Extension: Solve the Following:

\[
\frac{2}{10} \left[ \left( \frac{1}{12} + \frac{3}{4} \right) \div \frac{4}{7} \right]
\]

#### Step 1: Simplify \(\frac{1}{12} + \frac{3}{4}\)
- Find a common denominator. The least common multiple of 12 and 4 is 12.
- Convert \(\frac{3}{4}\) to a fraction with a denominator of 12:
\[
\frac{3}{4} = \frac{3 \times 3}{4 \times 3} = \frac{9}{12}
\]
- Now add the fractions:
\[
\frac{1}{12} + \frac{9}{12} = \frac{1 + 9}{12} = \frac{10}{12}
\]
- Simplify the fraction:
\[
\frac{10}{12} = \frac{5}{6}
\]

#### Step 2: Divide \(\frac{5}{6}\) by \(\frac{4}{7}\)
- Dividing by a fraction is the same as multiplying by its reciprocal:
\[
\frac{5}{6} \div \frac{4}{7} = \frac{5}{6} \times \frac{7}{4} = \frac{5 \times 7}{6 \times 4} = \frac{35}{24}
\]

#### Step 3: Multiply \(\frac{2}{10}\) by \(\frac{35}{24}\)
- Simplify \(\frac{2}{10}\):
\[
\frac{2}{10} = \frac{1}{5}
\]
- Multiply the fractions:
\[
\frac{1}{5} \times \frac{35}{24} = \frac{1 \times 35}{5 \times 24} = \frac{35}{120}
\]
- Simplify the fraction:
\[
\frac{35}{120} = \frac{7}{24}
\]

The final answer is:
\[
\boxed{\frac{7}{24}}
\]

Final Answer:

\[
\boxed{\frac{7}{24}}
\]