Convert mixed numbers to improper fractions with this educational worksheet.
Worksheet for converting mixed numbers to improper fractions with math problems and geometric background design.
JPG
1000×1310
121.3 KB
Free · Personal Use
Quality Assured by Worksheets Library Team
Reviewed for educational accuracy and age-appropriateness
ID: #558892
⭐
Show Answer Key & Explanations
Step-by-step solution for: Converting Mixed Numbers to Improper Fractions interactive ...
▼
Show Answer Key & Explanations
Step-by-step solution for: Converting Mixed Numbers to Improper Fractions interactive ...
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 turning mixed numbers into improper fractions worksheet.
