Math worksheet for converting improper fractions to mixed numbers.

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, the remainder becomes the new numerator, and the denominator remains 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 = $5$ (since $13 = 8 \times 1 + 5$)
- Mixed number: $1 \frac{5}{8}$

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

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

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

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

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

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

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

- Divide $66 \div 8$:
- Quotient = $8$ (whole number part)
- Remainder = $2$ (since $66 = 8 \times 8 + 2$)
- Mixed number: $8 \frac{2}{8}$ (simplify $\frac{2}{8}$ to $\frac{1}{4}$)
- Final answer: $8 \frac{1}{4}$

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

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

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

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

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

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

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

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

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

- Divide $98 \div 12$:
- Quotient = $8$ (whole number part)
- Remainder = $2$ (since $98 = 12 \times 8 + 2$)
- Mixed number: $8 \frac{2}{12}$ (simplify $\frac{2}{12}$ to $\frac{1}{6}$)
- Final answer: $8 \frac{1}{6}$

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

- Divide $72 \div 10$:
- Quotient = $7$ (whole number part)
- Remainder = $2$ (since $72 = 10 \times 7 + 2$)
- Mixed number: $7 \frac{2}{10}$ (simplify $\frac{2}{10}$ to $\frac{1}{5}$)
- Final answer: $7 \frac{1}{5}$

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

- Divide $38 \div 6$:
- Quotient = $6$ (whole number part)
- Remainder = $2$ (since $38 = 6 \times 6 + 2$)
- Mixed number: $6 \frac{2}{6}$ (simplify $\frac{2}{6}$ to $\frac{1}{3}$)
- Final answer: $6 \frac{1}{3}$

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

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

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

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

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

- Divide $52 \div 6$:
- Quotient = $8$ (whole number part)
- Remainder = $4$ (since $52 = 6 \times 8 + 4$)
- Mixed number: $8 \frac{4}{6}$ (simplify $\frac{4}{6}$ to $\frac{2}{3}$)
- Final answer: $8 \frac{2}{3}$

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Final Answers:

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) $8 \frac{2}{3}$

$$
\boxed{
1) \, 1 \frac{5}{8}, \,
2) \, 5 \frac{4}{5}, \,
3) \, 1 \frac{4}{7}, \,
4) \, 5 \frac{1}{7}, \,
5) \, 8 \frac{1}{4}, \,
6) \, 6 \frac{1}{8}, \,
7) \, 5 \frac{3}{10}, \,
8) \, 6 \frac{1}{6}, \,
9) \, 9 \frac{5}{9}, \,
10) \, 8 \frac{1}{6}, \,
11) \, 7 \frac{1}{5}, \,
12) \, 6 \frac{1}{3}, \,
13) \, 7 \frac{7}{11}, \,
14) \, 4 \frac{4}{9}, \,
15) \, 8 \frac{2}{3}
}
$$