Four Operations Fractions Worksheet (with answers) | Teaching ... - Free Printable

Let's solve each part of the problem step by step and simplify the answers to their simplest forms.

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a) \( \frac{2}{8} + \frac{1}{8} \)

- Both fractions have the same denominator, so we can add the numerators directly:
\[
\frac{2}{8} + \frac{1}{8} = \frac{2 + 1}{8} = \frac{3}{8}
\]
- The fraction \( \frac{3}{8} \) is already in its simplest form.

Answer: \( \frac{3}{8} \)

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b) \( \frac{2}{8} - \frac{1}{8} \)

- Both fractions have the same denominator, so we can subtract the numerators directly:
\[
\frac{2}{8} - \frac{1}{8} = \frac{2 - 1}{8} = \frac{1}{8}
\]
- The fraction \( \frac{1}{8} \) is already in its simplest form.

Answer: \( \frac{1}{8} \)

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c) \( \frac{1}{8} \times \frac{1}{2} \)

- To multiply fractions, multiply the numerators and the denominators:
\[
\frac{1}{8} \times \frac{1}{2} = \frac{1 \times 1}{8 \times 2} = \frac{1}{16}
\]
- The fraction \( \frac{1}{16} \) is already in its simplest form.

Answer: \( \frac{1}{16} \)

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d) \( \frac{2}{8} \div \frac{1}{8} \)

- To divide fractions, multiply by the reciprocal of the divisor:
\[
\frac{2}{8} \div \frac{1}{8} = \frac{2}{8} \times \frac{8}{1} = \frac{2 \times 8}{8 \times 1} = \frac{16}{8}
\]
- Simplify \( \frac{16}{8} \):
\[
\frac{16}{8} = 2
\]

Answer: \( 2 \)

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e) \( \frac{2}{6} \div 2 \)

- Dividing by 2 is the same as multiplying by \( \frac{1}{2} \):
\[
\frac{2}{6} \div 2 = \frac{2}{6} \times \frac{1}{2} = \frac{2 \times 1}{6 \times 2} = \frac{2}{12}
\]
- Simplify \( \frac{2}{12} \):
\[
\frac{2}{12} = \frac{1}{6}
\]

Answer: \( \frac{1}{6} \)

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f) \( \frac{2}{8} \times 3 \)

- Multiply the numerator by 3:
\[
\frac{2}{8} \times 3 = \frac{2 \times 3}{8} = \frac{6}{8}
\]
- Simplify \( \frac{6}{8} \):
\[
\frac{6}{8} = \frac{3}{4}
\]

Answer: \( \frac{3}{4} \)

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g) \( 1 \frac{2}{8} + \frac{7}{8} \)

- Convert the mixed number \( 1 \frac{2}{8} \) to an improper fraction:
\[
1 \frac{2}{8} = \frac{8}{8} + \frac{2}{8} = \frac{10}{8}
\]
- Add the fractions:
\[
\frac{10}{8} + \frac{7}{8} = \frac{10 + 7}{8} = \frac{17}{8}
\]
- The fraction \( \frac{17}{8} \) is already in its simplest form. Convert it back to a mixed number:
\[
\frac{17}{8} = 2 \frac{1}{8}
\]

Answer: \( 2 \frac{1}{8} \)

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h) \( \frac{2}{8} \div \frac{3}{5} \)

- To divide fractions, multiply by the reciprocal of the divisor:
\[
\frac{2}{8} \div \frac{3}{5} = \frac{2}{8} \times \frac{5}{3} = \frac{2 \times 5}{8 \times 3} = \frac{10}{24}
\]
- Simplify \( \frac{10}{24} \):
\[
\frac{10}{24} = \frac{5}{12}
\]

Answer: \( \frac{5}{12} \)

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i) \( 3 \frac{5}{12} - \frac{1}{6} \)

- Convert the mixed number \( 3 \frac{5}{12} \) to an improper fraction:
\[
3 \frac{5}{12} = \frac{36}{12} + \frac{5}{12} = \frac{41}{12}
\]
- Find a common denominator for \( \frac{41}{12} \) and \( \frac{1}{6} \). The least common denominator is 12:
\[
\frac{1}{6} = \frac{2}{12}
\]
- Subtract the fractions:
\[
\frac{41}{12} - \frac{2}{12} = \frac{41 - 2}{12} = \frac{39}{12}
\]
- Simplify \( \frac{39}{12} \):
\[
\frac{39}{12} = \frac{13}{4}
\]
- Convert \( \frac{13}{4} \) back to a mixed number:
\[
\frac{13}{4} = 3 \frac{1}{4}
\]

Answer: \( 3 \frac{1}{4} \)

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j) \( \frac{3}{7} \times \frac{12}{63} \)

- Multiply the numerators and the denominators:
\[
\frac{3}{7} \times \frac{12}{63} = \frac{3 \times 12}{7 \times 63} = \frac{36}{441}
\]
- Simplify \( \frac{36}{441} \). The greatest common divisor of 36 and 441 is 9:
\[
\frac{36}{441} = \frac{36 \div 9}{441 \div 9} = \frac{4}{49}
\]

Answer: \( \frac{4}{49} \)

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Final Answers:

\[
\boxed{
\begin{array}{ll}
\text{a)} & \frac{3}{8} \\
\text{b)} & \frac{1}{8} \\
\text{c)} & \frac{1}{16} \\
\text{d)} & 2 \\
\text{e)} & \frac{1}{6} \\
\text{f)} & \frac{3}{4} \\
\text{g)} & 2 \frac{1}{8} \\
\text{h)} & \frac{5}{12} \\
\text{i)} & 3 \frac{1}{4} \\
\text{j)} & \frac{4}{49} \\
\end{array}
}
\]