Converting Mixed Numbers to Improper Fractions | - Free Printable
Educational worksheet: Converting Mixed Numbers to Improper Fractions |. Download and print for classroom or home learning activities.
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Show Answer Key & Explanations
Step-by-step solution for: Converting Mixed Numbers to Improper Fractions |
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Show Answer Key & Explanations
Step-by-step solution for: Converting Mixed Numbers to Improper Fractions |
To convert a mixed number to an improper fraction, follow these steps:
1. Multiply the whole number by the denominator of the fractional part.
2. Add the result to the numerator of the fractional part.
3. Write the sum as the new numerator, keeping the original denominator.
Let's solve each problem step by step.
---
- Whole number: \( 9 \)
- Fraction: \( \frac{1}{9} \)
Steps:
1. Multiply the whole number by the denominator: \( 9 \times 9 = 81 \)
2. Add the numerator: \( 81 + 1 = 82 \)
3. Write the improper fraction: \( \frac{82}{9} \)
Answer: \( \frac{82}{9} \)
---
- Whole number: \( 3 \)
- Fraction: \( \frac{8}{9} \)
Steps:
1. Multiply the whole number by the denominator: \( 3 \times 9 = 27 \)
2. Add the numerator: \( 27 + 8 = 35 \)
3. Write the improper fraction: \( \frac{35}{9} \)
Answer: \( \frac{35}{9} \)
---
- Whole number: \( 8 \)
- Fraction: \( \frac{7}{12} \)
Steps:
1. Multiply the whole number by the denominator: \( 8 \times 12 = 96 \)
2. Add the numerator: \( 96 + 7 = 103 \)
3. Write the improper fraction: \( \frac{103}{12} \)
Answer: \( \frac{103}{12} \)
---
- Whole number: \( 7 \)
- Fraction: \( \frac{7}{9} \)
Steps:
1. Multiply the whole number by the denominator: \( 7 \times 9 = 63 \)
2. Add the numerator: \( 63 + 7 = 70 \)
3. Write the improper fraction: \( \frac{70}{9} \)
Answer: \( \frac{70}{9} \)
---
- Whole number: \( 3 \)
- Fraction: \( \frac{11}{15} \)
Steps:
1. Multiply the whole number by the denominator: \( 3 \times 15 = 45 \)
2. Add the numerator: \( 45 + 11 = 56 \)
3. Write the improper fraction: \( \frac{56}{15} \)
Answer: \( \frac{56}{15} \)
---
- Whole number: \( 3 \)
- Fraction: \( \frac{2}{5} \)
Steps:
1. Multiply the whole number by the denominator: \( 3 \times 5 = 15 \)
2. Add the numerator: \( 15 + 2 = 17 \)
3. Write the improper fraction: \( \frac{17}{5} \)
Answer: \( \frac{17}{5} \)
---
- Whole number: \( 4 \)
- Fraction: \( \frac{2}{7} \)
Steps:
1. Multiply the whole number by the denominator: \( 4 \times 7 = 28 \)
2. Add the numerator: \( 28 + 2 = 30 \)
3. Write the improper fraction: \( \frac{30}{7} \)
Answer: \( \frac{30}{7} \)
---
- Whole number: \( 7 \)
- Fraction: \( \frac{1}{3} \)
Steps:
1. Multiply the whole number by the denominator: \( 7 \times 3 = 21 \)
2. Add the numerator: \( 21 + 1 = 22 \)
3. Write the improper fraction: \( \frac{22}{3} \)
Answer: \( \frac{22}{3} \)
---
- Whole number: \( 5 \)
- Fraction: \( \frac{1}{7} \)
Steps:
1. Multiply the whole number by the denominator: \( 5 \times 7 = 35 \)
2. Add the numerator: \( 35 + 1 = 36 \)
3. Write the improper fraction: \( \frac{36}{7} \)
Answer: \( \frac{36}{7} \)
---
- Whole number: \( 2 \)
- Fraction: \( \frac{7}{10} \)
Steps:
1. Multiply the whole number by the denominator: \( 2 \times 10 = 20 \)
2. Add the numerator: \( 20 + 7 = 27 \)
3. Write the improper fraction: \( \frac{27}{10} \)
Answer: \( \frac{27}{10} \)
---
- Whole number: \( 3 \)
- Fraction: \( \frac{4}{5} \)
Steps:
1. Multiply the whole number by the denominator: \( 3 \times 5 = 15 \)
2. Add the numerator: \( 15 + 4 = 19 \)
3. Write the improper fraction: \( \frac{19}{5} \)
Answer: \( \frac{19}{5} \)
---
- Whole number: \( 4 \)
- Fraction: \( \frac{5}{7} \)
Steps:
1. Multiply the whole number by the denominator: \( 4 \times 7 = 28 \)
2. Add the numerator: \( 28 + 5 = 33 \)
3. Write the improper fraction: \( \frac{33}{7} \)
Answer: \( \frac{33}{7} \)
---
- Whole number: \( 3 \)
- Fraction: \( \frac{3}{8} \)
Steps:
1. Multiply the whole number by the denominator: \( 3 \times 8 = 24 \)
2. Add the numerator: \( 24 + 3 = 27 \)
3. Write the improper fraction: \( \frac{27}{8} \)
Answer: \( \frac{27}{8} \)
---
- Whole number: \( 6 \)
- Fraction: \( \frac{1}{8} \)
Steps:
1. Multiply the whole number by the denominator: \( 6 \times 8 = 48 \)
2. Add the numerator: \( 48 + 1 = 49 \)
3. Write the improper fraction: \( \frac{49}{8} \)
Answer: \( \frac{49}{8} \)
---
- Whole number: \( 5 \)
- Fraction: \( \frac{5}{6} \)
Steps:
1. Multiply the whole number by the denominator: \( 5 \times 6 = 30 \)
2. Add the numerator: \( 30 + 5 = 35 \)
3. Write the improper fraction: \( \frac{35}{6} \)
Answer: \( \frac{35}{6} \)
---
- Whole number: \( 7 \)
- Fraction: \( \frac{4}{15} \)
Steps:
1. Multiply the whole number by the denominator: \( 7 \times 15 = 105 \)
2. Add the numerator: \( 105 + 4 = 109 \)
3. Write the improper fraction: \( \frac{109}{15} \)
Answer: \( \frac{109}{15} \)
---
- Whole number: \( 4 \)
- Fraction: \( \frac{2}{9} \)
Steps:
1. Multiply the whole number by the denominator: \( 4 \times 9 = 36 \)
2. Add the numerator: \( 36 + 2 = 38 \)
3. Write the improper fraction: \( \frac{38}{9} \)
Answer: \( \frac{38}{9} \)
---
- Whole number: \( 9 \)
- Fraction: \( \frac{1}{6} \)
Steps:
1. Multiply the whole number by the denominator: \( 9 \times 6 = 54 \)
2. Add the numerator: \( 54 + 1 = 55 \)
3. Write the improper fraction: \( \frac{55}{6} \)
Answer: \( \frac{55}{6} \)
---
- Whole number: \( 7 \)
- Fraction: \( \frac{5}{8} \)
Steps:
1. Multiply the whole number by the denominator: \( 7 \times 8 = 56 \)
2. Add the numerator: \( 56 + 5 = 61 \)
3. Write the improper fraction: \( \frac{61}{8} \)
Answer: \( \frac{61}{8} \)
---
- Whole number: \( 1 \)
- Fraction: \( \frac{5}{9} \)
Steps:
1. Multiply the whole number by the denominator: \( 1 \times 9 = 9 \)
2. Add the numerator: \( 9 + 5 = 14 \)
3. Write the improper fraction: \( \frac{14}{9} \)
Answer: \( \frac{14}{9} \)
---
\[
\boxed{
\begin{aligned}
&9 \frac{1}{9} = \frac{82}{9}, \quad 3 \frac{8}{9} = \frac{35}{9}, \quad 8 \frac{7}{12} = \frac{103}{12}, \quad 7 \frac{7}{9} = \frac{70}{9}, \\
&3 \frac{11}{15} = \frac{56}{15}, \quad 3 \frac{2}{5} = \frac{17}{5}, \quad 4 \frac{2}{7} = \frac{30}{7}, \quad 7 \frac{1}{3} = \frac{22}{3}, \\
&5 \frac{1}{7} = \frac{36}{7}, \quad 2 \frac{7}{10} = \frac{27}{10}, \quad 3 \frac{4}{5} = \frac{19}{5}, \quad 4 \frac{5}{7} = \frac{33}{7}, \\
&3 \frac{3}{8} = \frac{27}{8}, \quad 6 \frac{1}{8} = \frac{49}{8}, \quad 5 \frac{5}{6} = \frac{35}{6}, \quad 7 \frac{4}{15} = \frac{109}{15}, \\
&4 \frac{2}{9} = \frac{38}{9}, \quad 9 \frac{1}{6} = \frac{55}{6}, \quad 7 \frac{5}{8} = \frac{61}{8}, \quad 1 \frac{5}{9} = \frac{14}{9}.
\end{aligned}
}
\]
Steps:
1. Multiply the whole number by the denominator of the fractional part.
2. Add the result to the numerator of the fractional part.
3. Write the sum as the new numerator, keeping the original denominator.
Let's solve each problem step by step.
---
1. \( 9 \frac{1}{9} \)
- Whole number: \( 9 \)
- Fraction: \( \frac{1}{9} \)
Steps:
1. Multiply the whole number by the denominator: \( 9 \times 9 = 81 \)
2. Add the numerator: \( 81 + 1 = 82 \)
3. Write the improper fraction: \( \frac{82}{9} \)
Answer: \( \frac{82}{9} \)
---
2. \( 3 \frac{8}{9} \)
- Whole number: \( 3 \)
- Fraction: \( \frac{8}{9} \)
Steps:
1. Multiply the whole number by the denominator: \( 3 \times 9 = 27 \)
2. Add the numerator: \( 27 + 8 = 35 \)
3. Write the improper fraction: \( \frac{35}{9} \)
Answer: \( \frac{35}{9} \)
---
3. \( 8 \frac{7}{12} \)
- Whole number: \( 8 \)
- Fraction: \( \frac{7}{12} \)
Steps:
1. Multiply the whole number by the denominator: \( 8 \times 12 = 96 \)
2. Add the numerator: \( 96 + 7 = 103 \)
3. Write the improper fraction: \( \frac{103}{12} \)
Answer: \( \frac{103}{12} \)
---
4. \( 7 \frac{7}{9} \)
- Whole number: \( 7 \)
- Fraction: \( \frac{7}{9} \)
Steps:
1. Multiply the whole number by the denominator: \( 7 \times 9 = 63 \)
2. Add the numerator: \( 63 + 7 = 70 \)
3. Write the improper fraction: \( \frac{70}{9} \)
Answer: \( \frac{70}{9} \)
---
5. \( 3 \frac{11}{15} \)
- Whole number: \( 3 \)
- Fraction: \( \frac{11}{15} \)
Steps:
1. Multiply the whole number by the denominator: \( 3 \times 15 = 45 \)
2. Add the numerator: \( 45 + 11 = 56 \)
3. Write the improper fraction: \( \frac{56}{15} \)
Answer: \( \frac{56}{15} \)
---
6. \( 3 \frac{2}{5} \)
- Whole number: \( 3 \)
- Fraction: \( \frac{2}{5} \)
Steps:
1. Multiply the whole number by the denominator: \( 3 \times 5 = 15 \)
2. Add the numerator: \( 15 + 2 = 17 \)
3. Write the improper fraction: \( \frac{17}{5} \)
Answer: \( \frac{17}{5} \)
---
7. \( 4 \frac{2}{7} \)
- Whole number: \( 4 \)
- Fraction: \( \frac{2}{7} \)
Steps:
1. Multiply the whole number by the denominator: \( 4 \times 7 = 28 \)
2. Add the numerator: \( 28 + 2 = 30 \)
3. Write the improper fraction: \( \frac{30}{7} \)
Answer: \( \frac{30}{7} \)
---
8. \( 7 \frac{1}{3} \)
- Whole number: \( 7 \)
- Fraction: \( \frac{1}{3} \)
Steps:
1. Multiply the whole number by the denominator: \( 7 \times 3 = 21 \)
2. Add the numerator: \( 21 + 1 = 22 \)
3. Write the improper fraction: \( \frac{22}{3} \)
Answer: \( \frac{22}{3} \)
---
9. \( 5 \frac{1}{7} \)
- Whole number: \( 5 \)
- Fraction: \( \frac{1}{7} \)
Steps:
1. Multiply the whole number by the denominator: \( 5 \times 7 = 35 \)
2. Add the numerator: \( 35 + 1 = 36 \)
3. Write the improper fraction: \( \frac{36}{7} \)
Answer: \( \frac{36}{7} \)
---
10. \( 2 \frac{7}{10} \)
- Whole number: \( 2 \)
- Fraction: \( \frac{7}{10} \)
Steps:
1. Multiply the whole number by the denominator: \( 2 \times 10 = 20 \)
2. Add the numerator: \( 20 + 7 = 27 \)
3. Write the improper fraction: \( \frac{27}{10} \)
Answer: \( \frac{27}{10} \)
---
11. \( 3 \frac{4}{5} \)
- Whole number: \( 3 \)
- Fraction: \( \frac{4}{5} \)
Steps:
1. Multiply the whole number by the denominator: \( 3 \times 5 = 15 \)
2. Add the numerator: \( 15 + 4 = 19 \)
3. Write the improper fraction: \( \frac{19}{5} \)
Answer: \( \frac{19}{5} \)
---
12. \( 4 \frac{5}{7} \)
- Whole number: \( 4 \)
- Fraction: \( \frac{5}{7} \)
Steps:
1. Multiply the whole number by the denominator: \( 4 \times 7 = 28 \)
2. Add the numerator: \( 28 + 5 = 33 \)
3. Write the improper fraction: \( \frac{33}{7} \)
Answer: \( \frac{33}{7} \)
---
13. \( 3 \frac{3}{8} \)
- Whole number: \( 3 \)
- Fraction: \( \frac{3}{8} \)
Steps:
1. Multiply the whole number by the denominator: \( 3 \times 8 = 24 \)
2. Add the numerator: \( 24 + 3 = 27 \)
3. Write the improper fraction: \( \frac{27}{8} \)
Answer: \( \frac{27}{8} \)
---
14. \( 6 \frac{1}{8} \)
- Whole number: \( 6 \)
- Fraction: \( \frac{1}{8} \)
Steps:
1. Multiply the whole number by the denominator: \( 6 \times 8 = 48 \)
2. Add the numerator: \( 48 + 1 = 49 \)
3. Write the improper fraction: \( \frac{49}{8} \)
Answer: \( \frac{49}{8} \)
---
15. \( 5 \frac{5}{6} \)
- Whole number: \( 5 \)
- Fraction: \( \frac{5}{6} \)
Steps:
1. Multiply the whole number by the denominator: \( 5 \times 6 = 30 \)
2. Add the numerator: \( 30 + 5 = 35 \)
3. Write the improper fraction: \( \frac{35}{6} \)
Answer: \( \frac{35}{6} \)
---
16. \( 7 \frac{4}{15} \)
- Whole number: \( 7 \)
- Fraction: \( \frac{4}{15} \)
Steps:
1. Multiply the whole number by the denominator: \( 7 \times 15 = 105 \)
2. Add the numerator: \( 105 + 4 = 109 \)
3. Write the improper fraction: \( \frac{109}{15} \)
Answer: \( \frac{109}{15} \)
---
17. \( 4 \frac{2}{9} \)
- Whole number: \( 4 \)
- Fraction: \( \frac{2}{9} \)
Steps:
1. Multiply the whole number by the denominator: \( 4 \times 9 = 36 \)
2. Add the numerator: \( 36 + 2 = 38 \)
3. Write the improper fraction: \( \frac{38}{9} \)
Answer: \( \frac{38}{9} \)
---
18. \( 9 \frac{1}{6} \)
- Whole number: \( 9 \)
- Fraction: \( \frac{1}{6} \)
Steps:
1. Multiply the whole number by the denominator: \( 9 \times 6 = 54 \)
2. Add the numerator: \( 54 + 1 = 55 \)
3. Write the improper fraction: \( \frac{55}{6} \)
Answer: \( \frac{55}{6} \)
---
19. \( 7 \frac{5}{8} \)
- Whole number: \( 7 \)
- Fraction: \( \frac{5}{8} \)
Steps:
1. Multiply the whole number by the denominator: \( 7 \times 8 = 56 \)
2. Add the numerator: \( 56 + 5 = 61 \)
3. Write the improper fraction: \( \frac{61}{8} \)
Answer: \( \frac{61}{8} \)
---
20. \( 1 \frac{5}{9} \)
- Whole number: \( 1 \)
- Fraction: \( \frac{5}{9} \)
Steps:
1. Multiply the whole number by the denominator: \( 1 \times 9 = 9 \)
2. Add the numerator: \( 9 + 5 = 14 \)
3. Write the improper fraction: \( \frac{14}{9} \)
Answer: \( \frac{14}{9} \)
---
Final Answers:
\[
\boxed{
\begin{aligned}
&9 \frac{1}{9} = \frac{82}{9}, \quad 3 \frac{8}{9} = \frac{35}{9}, \quad 8 \frac{7}{12} = \frac{103}{12}, \quad 7 \frac{7}{9} = \frac{70}{9}, \\
&3 \frac{11}{15} = \frac{56}{15}, \quad 3 \frac{2}{5} = \frac{17}{5}, \quad 4 \frac{2}{7} = \frac{30}{7}, \quad 7 \frac{1}{3} = \frac{22}{3}, \\
&5 \frac{1}{7} = \frac{36}{7}, \quad 2 \frac{7}{10} = \frac{27}{10}, \quad 3 \frac{4}{5} = \frac{19}{5}, \quad 4 \frac{5}{7} = \frac{33}{7}, \\
&3 \frac{3}{8} = \frac{27}{8}, \quad 6 \frac{1}{8} = \frac{49}{8}, \quad 5 \frac{5}{6} = \frac{35}{6}, \quad 7 \frac{4}{15} = \frac{109}{15}, \\
&4 \frac{2}{9} = \frac{38}{9}, \quad 9 \frac{1}{6} = \frac{55}{6}, \quad 7 \frac{5}{8} = \frac{61}{8}, \quad 1 \frac{5}{9} = \frac{14}{9}.
\end{aligned}
}
\]
Parent Tip: Review the logic above to help your child master the concept of changing mixed numbers to improper fractions worksheet.
