Improper Fraction to Mixed Number conversion practice worksheet.

To solve the problem of converting improper fractions to mixed numbers, we need to follow these steps:

Steps to Convert an Improper Fraction to a Mixed Number:

1. Divide the numerator by the denominator to find the whole number part.
2. Find the remainder of the division.
3. Write the result as a mixed number: The whole number part is the quotient, and the remainder becomes the numerator of the fractional part, with the original denominator remaining the same.

Let's solve each problem step by step.

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1) $\frac{13}{8}$

- Divide $13 \div 8$:
- Quotient = $1$ (whole number part)
- Remainder = $5$
- Mixed number: $1 \frac{5}{8}$

Answer: $1 \frac{5}{8}$

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2) $\frac{29}{5}$

- Divide $29 \div 5$:
- Quotient = $5$ (whole number part)
- Remainder = $4$
- Mixed number: $5 \frac{4}{5}$

Answer: $5 \frac{4}{5}$

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3) $\frac{11}{7}$

- Divide $11 \div 7$:
- Quotient = $1$ (whole number part)
- Remainder = $4$
- Mixed number: $1 \frac{4}{7}$

Answer: $1 \frac{4}{7}$

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4) $\frac{36}{7}$

- Divide $36 \div 7$:
- Quotient = $5$ (whole number part)
- Remainder = $1$
- Mixed number: $5 \frac{1}{7}$

Answer: $5 \frac{1}{7}$

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5) $\frac{66}{8}$

- Divide $66 \div 8$:
- Quotient = $8$ (whole number part)
- Remainder = $2$
- Mixed number: $8 \frac{2}{8}$
- Simplify $\frac{2}{8}$ to $\frac{1}{4}$
- Final mixed number: $8 \frac{1}{4}$

Answer: $8 \frac{1}{4}$

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6) $\frac{49}{8}$

- Divide $49 \div 8$:
- Quotient = $6$ (whole number part)
- Remainder = $1$
- Mixed number: $6 \frac{1}{8}$

Answer: $6 \frac{1}{8}$

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7) $\frac{53}{10}$

- Divide $53 \div 10$:
- Quotient = $5$ (whole number part)
- Remainder = $3$
- Mixed number: $5 \frac{3}{10}$

Answer: $5 \frac{3}{10}$

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8) $\frac{37}{6}$

- Divide $37 \div 6$:
- Quotient = $6$ (whole number part)
- Remainder = $1$
- Mixed number: $6 \frac{1}{6}$

Answer: $6 \frac{1}{6}$

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9) $\frac{86}{9}$

- Divide $86 \div 9$:
- Quotient = $9$ (whole number part)
- Remainder = $5$
- Mixed number: $9 \frac{5}{9}$

Answer: $9 \frac{5}{9}$

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10) $\frac{98}{12}$

- Divide $98 \div 12$:
- Quotient = $8$ (whole number part)
- Remainder = $2$
- Mixed number: $8 \frac{2}{12}$
- Simplify $\frac{2}{12}$ to $\frac{1}{6}$
- Final mixed number: $8 \frac{1}{6}$

Answer: $8 \frac{1}{6}$

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11) $\frac{72}{10}$

- Divide $72 \div 10$:
- Quotient = $7$ (whole number part)
- Remainder = $2$
- Mixed number: $7 \frac{2}{10}$
- Simplify $\frac{2}{10}$ to $\frac{1}{5}$
- Final mixed number: $7 \frac{1}{5}$

Answer: $7 \frac{1}{5}$

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12) $\frac{38}{6}$

- Divide $38 \div 6$:
- Quotient = $6$ (whole number part)
- Remainder = $2$
- Mixed number: $6 \frac{2}{6}$
- Simplify $\frac{2}{6}$ to $\frac{1}{3}$
- Final mixed number: $6 \frac{1}{3}$

Answer: $6 \frac{1}{3}$

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13) $\frac{84}{11}$

- Divide $84 \div 11$:
- Quotient = $7$ (whole number part)
- Remainder = $7$
- Mixed number: $7 \frac{7}{11}$

Answer: $7 \frac{7}{11}$

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14) $\frac{40}{9}$

- Divide $40 \div 9$:
- Quotient = $4$ (whole number part)
- Remainder = $4$
- Mixed number: $4 \frac{4}{9}$

Answer: $4 \frac{4}{9}$

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15) $\frac{52}{6}$

- Divide $52 \div 6$:
- Quotient = $8$ (whole number part)
- Remainder = $4$
- Mixed number: $8 \frac{4}{6}$
- Simplify $\frac{4}{6}$ to $\frac{2}{3}$
- Final mixed number: $8 \frac{2}{3}$

Answer: $8 \frac{2}{3}$

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Final Answers:

\[
\boxed{
\begin{array}{lll}
1) & 1 \frac{5}{8} & \\
2) & 5 \frac{4}{5} & \\
3) & 1 \frac{4}{7} & \\
4) & 5 \frac{1}{7} & \\
5) & 8 \frac{1}{4} & \\
6) & 6 \frac{1}{8} & \\
7) & 5 \frac{3}{10} & \\
8) & 6 \frac{1}{6} & \\
9) & 9 \frac{5}{9} & \\
10) & 8 \frac{1}{6} & \\
11) & 7 \frac{1}{5} & \\
12) & 6 \frac{1}{3} & \\
13) & 7 \frac{7}{11} & \\
14) & 4 \frac{4}{9} & \\
15) & 8 \frac{2}{3} &
\end{array}
}
\]