Improper Fractions Worksheets - Math Monks - Free Printable

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. The quotient becomes the whole number part of the mixed number.
3. The remainder becomes the numerator of the fractional part.
4. The denominator remains the same.

Let's solve each problem step by step.

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Problem 1: $\frac{31}{5}$

- Divide $31 \div 5$:
- Quotient = $6$
- Remainder = $1$
- Mixed number: $6 \frac{1}{5}$

Problem 2: $\frac{66}{7}$

- Divide $66 \div 7$:
- Quotient = $9$
- Remainder = $3$
- Mixed number: $9 \frac{3}{7}$

Problem 3: $\frac{72}{7}$

- Divide $72 \div 7$:
- Quotient = $10$
- Remainder = $2$
- Mixed number: $10 \frac{2}{7}$

Problem 4: $\frac{98}{9}$

- Divide $98 \div 9$:
- Quotient = $10$
- Remainder = $8$
- Mixed number: $10 \frac{8}{9}$

Problem 5: $\frac{55}{8}$

- Divide $55 \div 8$:
- Quotient = $6$
- Remainder = $7$
- Mixed number: $6 \frac{7}{8}$

Problem 6: $\frac{85}{7}$

- Divide $85 \div 7$:
- Quotient = $12$
- Remainder = $1$
- Mixed number: $12 \frac{1}{7}$

Problem 7: $\frac{68}{10}$

- Divide $68 \div 10$:
- Quotient = $6$
- Remainder = $8$
- Simplify the fraction $\frac{8}{10}$ to $\frac{4}{5}$.
- Mixed number: $6 \frac{4}{5}$

Problem 8: $\frac{61}{3}$

- Divide $61 \div 3$:
- Quotient = $20$
- Remainder = $1$
- Mixed number: $20 \frac{1}{3}$

Problem 9: $\frac{84}{5}$

- Divide $84 \div 5$:
- Quotient = $16$
- Remainder = $4$
- Mixed number: $16 \frac{4}{5}$

Problem 10: $\frac{56}{9}$

- Divide $56 \div 9$:
- Quotient = $6$
- Remainder = $2$
- Mixed number: $6 \frac{2}{9}$

Problem 11: $\frac{33}{4}$

- Divide $33 \div 4$:
- Quotient = $8$
- Remainder = $1$
- Mixed number: $8 \frac{1}{4}$

Problem 12: $\frac{27}{4}$

- Divide $27 \div 4$:
- Quotient = $6$
- Remainder = $3$
- Mixed number: $6 \frac{3}{4}$

Problem 13: $\frac{36}{7}$

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

Problem 14: $\frac{59}{8}$

- Divide $59 \div 8$:
- Quotient = $7$
- Remainder = $3$
- Mixed number: $7 \frac{3}{8}$

Problem 15: $\frac{19}{4}$

- Divide $19 \div 4$:
- Quotient = $4$
- Remainder = $3$
- Mixed number: $4 \frac{3}{4}$

Problem 16: $\frac{17}{2}$

- Divide $17 \div 2$:
- Quotient = $8$
- Remainder = $1$
- Mixed number: $8 \frac{1}{2}$

Problem 17: $\frac{51}{8}$

- Divide $51 \div 8$:
- Quotient = $6$
- Remainder = $3$
- Mixed number: $6 \frac{3}{8}$

Problem 18: $\frac{20}{7}$

- Divide $20 \div 7$:
- Quotient = $2$
- Remainder = $6$
- Mixed number: $2 \frac{6}{7}$

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Final Answers:

\[
\boxed{
\begin{array}{lll}
1. & 6 \frac{1}{5} & 2. & 9 \frac{3}{7} & 3. & 10 \frac{2}{7} \\
4. & 10 \frac{8}{9} & 5. & 6 \frac{7}{8} & 6. & 12 \frac{1}{7} \\
7. & 6 \frac{4}{5} & 8. & 20 \frac{1}{3} & 9. & 16 \frac{4}{5} \\
10. & 6 \frac{2}{9} & 11. & 8 \frac{1}{4} & 12. & 6 \frac{3}{4} \\
13. & 5 \frac{1}{7} & 14. & 7 \frac{3}{8} & 15. & 4 \frac{3}{4} \\
16. & 8 \frac{1}{2} & 17. & 6 \frac{3}{8} & 18. & 2 \frac{6}{7} \\
\end{array}
}
\]