Mixed Numbers to Improper Fractions Worksheet (examples, answers ... - Free Printable
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Step-by-step solution for: Mixed Numbers to Improper Fractions Worksheet (examples, answers ...
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Show Answer Key & Explanations
Step-by-step solution for: Mixed Numbers to Improper Fractions Worksheet (examples, answers ...
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: \( 4 \)
- Fraction: \( \frac{3}{4} \)
Steps:
1. Multiply the whole number by the denominator: \( 4 \times 4 = 16 \)
2. Add the numerator: \( 16 + 3 = 19 \)
3. Write the improper fraction: \( \frac{19}{4} \)
Answer: \( \frac{19}{4} \)
---
- Whole number: \( 3 \)
- Fraction: \( \frac{1}{2} \)
Steps:
1. Multiply the whole number by the denominator: \( 3 \times 2 = 6 \)
2. Add the numerator: \( 6 + 1 = 7 \)
3. Write the improper fraction: \( \frac{7}{2} \)
Answer: \( \frac{7}{2} \)
---
- Whole number: \( 5 \)
- Fraction: \( \frac{3}{5} \)
Steps:
1. Multiply the whole number by the denominator: \( 5 \times 5 = 25 \)
2. Add the numerator: \( 25 + 3 = 28 \)
3. Write the improper fraction: \( \frac{28}{5} \)
Answer: \( \frac{28}{5} \)
---
- Whole number: \( 4 \)
- Fraction: \( \frac{1}{2} \)
Steps:
1. Multiply the whole number by the denominator: \( 4 \times 2 = 8 \)
2. Add the numerator: \( 8 + 1 = 9 \)
3. Write the improper fraction: \( \frac{9}{2} \)
Answer: \( \frac{9}{2} \)
---
- Whole number: \( 3 \)
- Fraction: \( \frac{1}{4} \)
Steps:
1. Multiply the whole number by the denominator: \( 3 \times 4 = 12 \)
2. Add the numerator: \( 12 + 1 = 13 \)
3. Write the improper fraction: \( \frac{13}{4} \)
Answer: \( \frac{13}{4} \)
---
- Whole number: \( 5 \)
- Fraction: \( \frac{3}{4} \)
Steps:
1. Multiply the whole number by the denominator: \( 5 \times 4 = 20 \)
2. Add the numerator: \( 20 + 3 = 23 \)
3. Write the improper fraction: \( \frac{23}{4} \)
Answer: \( \frac{23}{4} \)
---
- Whole number: \( 2 \)
- Fraction: \( \frac{1}{3} \)
Steps:
1. Multiply the whole number by the denominator: \( 2 \times 3 = 6 \)
2. Add the numerator: \( 6 + 1 = 7 \)
3. Write the improper fraction: \( \frac{7}{3} \)
Answer: \( \frac{7}{3} \)
---
- Whole number: \( 7 \)
- Fraction: \( \frac{2}{9} \)
Steps:
1. Multiply the whole number by the denominator: \( 7 \times 9 = 63 \)
2. Add the numerator: \( 63 + 2 = 65 \)
3. Write the improper fraction: \( \frac{65}{9} \)
Answer: \( \frac{65}{9} \)
---
- Whole number: \( 8 \)
- Fraction: \( \frac{3}{7} \)
Steps:
1. Multiply the whole number by the denominator: \( 8 \times 7 = 56 \)
2. Add the numerator: \( 56 + 3 = 59 \)
3. Write the improper fraction: \( \frac{59}{7} \)
Answer: \( \frac{59}{7} \)
---
- Whole number: \( 2 \)
- Fraction: \( \frac{3}{5} \)
Steps:
1. Multiply the whole number by the denominator: \( 2 \times 5 = 10 \)
2. Add the numerator: \( 10 + 3 = 13 \)
3. Write the improper fraction: \( \frac{13}{5} \)
Answer: \( \frac{13}{5} \)
---
- Whole number: \( 7 \)
- Fraction: \( \frac{1}{10} \)
Steps:
1. Multiply the whole number by the denominator: \( 7 \times 10 = 70 \)
2. Add the numerator: \( 70 + 1 = 71 \)
3. Write the improper fraction: \( \frac{71}{10} \)
Answer: \( \frac{71}{10} \)
---
- Whole number: \( 4 \)
- Fraction: \( \frac{2}{3} \)
Steps:
1. Multiply the whole number by the denominator: \( 4 \times 3 = 12 \)
2. Add the numerator: \( 12 + 2 = 14 \)
3. Write the improper fraction: \( \frac{14}{3} \)
Answer: \( \frac{14}{3} \)
---
- Whole number: \( 9 \)
- Fraction: \( \frac{1}{3} \)
Steps:
1. Multiply the whole number by the denominator: \( 9 \times 3 = 27 \)
2. Add the numerator: \( 27 + 1 = 28 \)
3. Write the improper fraction: \( \frac{28}{3} \)
Answer: \( \frac{28}{3} \)
---
- 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: \( \frac{22}{3} \)
---
- Whole number: \( 4 \)
- Fraction: \( \frac{8}{9} \)
Steps:
1. Multiply the whole number by the denominator: \( 4 \times 9 = 36 \)
2. Add the numerator: \( 36 + 8 = 44 \)
3. Write the improper fraction: \( \frac{44}{9} \)
Answer: \( \frac{44}{9} \)
---
- Whole number: \( 9 \)
- Fraction: \( \frac{3}{4} \)
Steps:
1. Multiply the whole number by the denominator: \( 9 \times 4 = 36 \)
2. Add the numerator: \( 36 + 3 = 39 \)
3. Write the improper fraction: \( \frac{39}{4} \)
Answer: \( \frac{39}{4} \)
---
- Whole number: \( 5 \)
- Fraction: \( \frac{2}{3} \)
Steps:
1. Multiply the whole number by the denominator: \( 5 \times 3 = 15 \)
2. Add the numerator: \( 15 + 2 = 17 \)
3. Write the improper fraction: \( \frac{17}{3} \)
Answer: \( \frac{17}{3} \)
---
- 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: \( 5 \)
- Fraction: \( \frac{1}{8} \)
Steps:
1. Multiply the whole number by the denominator: \( 5 \times 8 = 40 \)
2. Add the numerator: \( 40 + 1 = 41 \)
3. Write the improper fraction: \( \frac{41}{8} \)
Answer: \( \frac{41}{8} \)
---
- Whole number: \( 6 \)
- Fraction: \( \frac{1}{2} \)
Steps:
1. Multiply the whole number by the denominator: \( 6 \times 2 = 12 \)
2. Add the numerator: \( 12 + 1 = 13 \)
3. Write the improper fraction: \( \frac{13}{2} \)
Answer: \( \frac{13}{2} \)
---
\[
\boxed{
\begin{array}{ll}
4 \frac{3}{4} = \frac{19}{4} & 3 \frac{1}{2} = \frac{7}{2} \\
5 \frac{3}{5} = \frac{28}{5} & 4 \frac{1}{2} = \frac{9}{2} \\
3 \frac{1}{4} = \frac{13}{4} & 5 \frac{3}{4} = \frac{23}{4} \\
2 \frac{1}{3} = \frac{7}{3} & 7 \frac{2}{9} = \frac{65}{9} \\
8 \frac{3}{7} = \frac{59}{7} & 2 \frac{3}{5} = \frac{13}{5} \\
7 \frac{1}{10} = \frac{71}{10} & 4 \frac{2}{3} = \frac{14}{3} \\
9 \frac{1}{3} = \frac{28}{3} & 7 \frac{1}{3} = \frac{22}{3} \\
4 \frac{8}{9} = \frac{44}{9} & 9 \frac{3}{4} = \frac{39}{4} \\
5 \frac{2}{3} = \frac{17}{3} & 3 \frac{2}{5} = \frac{17}{5} \\
5 \frac{1}{8} = \frac{41}{8} & 6 \frac{1}{2} = \frac{13}{2}
\end{array}
}
\]
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. \( 4 \frac{3}{4} \)
- Whole number: \( 4 \)
- Fraction: \( \frac{3}{4} \)
Steps:
1. Multiply the whole number by the denominator: \( 4 \times 4 = 16 \)
2. Add the numerator: \( 16 + 3 = 19 \)
3. Write the improper fraction: \( \frac{19}{4} \)
Answer: \( \frac{19}{4} \)
---
2. \( 3 \frac{1}{2} \)
- Whole number: \( 3 \)
- Fraction: \( \frac{1}{2} \)
Steps:
1. Multiply the whole number by the denominator: \( 3 \times 2 = 6 \)
2. Add the numerator: \( 6 + 1 = 7 \)
3. Write the improper fraction: \( \frac{7}{2} \)
Answer: \( \frac{7}{2} \)
---
3. \( 5 \frac{3}{5} \)
- Whole number: \( 5 \)
- Fraction: \( \frac{3}{5} \)
Steps:
1. Multiply the whole number by the denominator: \( 5 \times 5 = 25 \)
2. Add the numerator: \( 25 + 3 = 28 \)
3. Write the improper fraction: \( \frac{28}{5} \)
Answer: \( \frac{28}{5} \)
---
4. \( 4 \frac{1}{2} \)
- Whole number: \( 4 \)
- Fraction: \( \frac{1}{2} \)
Steps:
1. Multiply the whole number by the denominator: \( 4 \times 2 = 8 \)
2. Add the numerator: \( 8 + 1 = 9 \)
3. Write the improper fraction: \( \frac{9}{2} \)
Answer: \( \frac{9}{2} \)
---
5. \( 3 \frac{1}{4} \)
- Whole number: \( 3 \)
- Fraction: \( \frac{1}{4} \)
Steps:
1. Multiply the whole number by the denominator: \( 3 \times 4 = 12 \)
2. Add the numerator: \( 12 + 1 = 13 \)
3. Write the improper fraction: \( \frac{13}{4} \)
Answer: \( \frac{13}{4} \)
---
6. \( 5 \frac{3}{4} \)
- Whole number: \( 5 \)
- Fraction: \( \frac{3}{4} \)
Steps:
1. Multiply the whole number by the denominator: \( 5 \times 4 = 20 \)
2. Add the numerator: \( 20 + 3 = 23 \)
3. Write the improper fraction: \( \frac{23}{4} \)
Answer: \( \frac{23}{4} \)
---
7. \( 2 \frac{1}{3} \)
- Whole number: \( 2 \)
- Fraction: \( \frac{1}{3} \)
Steps:
1. Multiply the whole number by the denominator: \( 2 \times 3 = 6 \)
2. Add the numerator: \( 6 + 1 = 7 \)
3. Write the improper fraction: \( \frac{7}{3} \)
Answer: \( \frac{7}{3} \)
---
8. \( 7 \frac{2}{9} \)
- Whole number: \( 7 \)
- Fraction: \( \frac{2}{9} \)
Steps:
1. Multiply the whole number by the denominator: \( 7 \times 9 = 63 \)
2. Add the numerator: \( 63 + 2 = 65 \)
3. Write the improper fraction: \( \frac{65}{9} \)
Answer: \( \frac{65}{9} \)
---
9. \( 8 \frac{3}{7} \)
- Whole number: \( 8 \)
- Fraction: \( \frac{3}{7} \)
Steps:
1. Multiply the whole number by the denominator: \( 8 \times 7 = 56 \)
2. Add the numerator: \( 56 + 3 = 59 \)
3. Write the improper fraction: \( \frac{59}{7} \)
Answer: \( \frac{59}{7} \)
---
10. \( 2 \frac{3}{5} \)
- Whole number: \( 2 \)
- Fraction: \( \frac{3}{5} \)
Steps:
1. Multiply the whole number by the denominator: \( 2 \times 5 = 10 \)
2. Add the numerator: \( 10 + 3 = 13 \)
3. Write the improper fraction: \( \frac{13}{5} \)
Answer: \( \frac{13}{5} \)
---
11. \( 7 \frac{1}{10} \)
- Whole number: \( 7 \)
- Fraction: \( \frac{1}{10} \)
Steps:
1. Multiply the whole number by the denominator: \( 7 \times 10 = 70 \)
2. Add the numerator: \( 70 + 1 = 71 \)
3. Write the improper fraction: \( \frac{71}{10} \)
Answer: \( \frac{71}{10} \)
---
12. \( 4 \frac{2}{3} \)
- Whole number: \( 4 \)
- Fraction: \( \frac{2}{3} \)
Steps:
1. Multiply the whole number by the denominator: \( 4 \times 3 = 12 \)
2. Add the numerator: \( 12 + 2 = 14 \)
3. Write the improper fraction: \( \frac{14}{3} \)
Answer: \( \frac{14}{3} \)
---
13. \( 9 \frac{1}{3} \)
- Whole number: \( 9 \)
- Fraction: \( \frac{1}{3} \)
Steps:
1. Multiply the whole number by the denominator: \( 9 \times 3 = 27 \)
2. Add the numerator: \( 27 + 1 = 28 \)
3. Write the improper fraction: \( \frac{28}{3} \)
Answer: \( \frac{28}{3} \)
---
14. \( 7 \frac{1}{3} \)
- 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: \( \frac{22}{3} \)
---
15. \( 4 \frac{8}{9} \)
- Whole number: \( 4 \)
- Fraction: \( \frac{8}{9} \)
Steps:
1. Multiply the whole number by the denominator: \( 4 \times 9 = 36 \)
2. Add the numerator: \( 36 + 8 = 44 \)
3. Write the improper fraction: \( \frac{44}{9} \)
Answer: \( \frac{44}{9} \)
---
16. \( 9 \frac{3}{4} \)
- Whole number: \( 9 \)
- Fraction: \( \frac{3}{4} \)
Steps:
1. Multiply the whole number by the denominator: \( 9 \times 4 = 36 \)
2. Add the numerator: \( 36 + 3 = 39 \)
3. Write the improper fraction: \( \frac{39}{4} \)
Answer: \( \frac{39}{4} \)
---
17. \( 5 \frac{2}{3} \)
- Whole number: \( 5 \)
- Fraction: \( \frac{2}{3} \)
Steps:
1. Multiply the whole number by the denominator: \( 5 \times 3 = 15 \)
2. Add the numerator: \( 15 + 2 = 17 \)
3. Write the improper fraction: \( \frac{17}{3} \)
Answer: \( \frac{17}{3} \)
---
18. \( 3 \frac{2}{5} \)
- 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: \( \frac{17}{5} \)
---
19. \( 5 \frac{1}{8} \)
- Whole number: \( 5 \)
- Fraction: \( \frac{1}{8} \)
Steps:
1. Multiply the whole number by the denominator: \( 5 \times 8 = 40 \)
2. Add the numerator: \( 40 + 1 = 41 \)
3. Write the improper fraction: \( \frac{41}{8} \)
Answer: \( \frac{41}{8} \)
---
20. \( 6 \frac{1}{2} \)
- Whole number: \( 6 \)
- Fraction: \( \frac{1}{2} \)
Steps:
1. Multiply the whole number by the denominator: \( 6 \times 2 = 12 \)
2. Add the numerator: \( 12 + 1 = 13 \)
3. Write the improper fraction: \( \frac{13}{2} \)
Answer: \( \frac{13}{2} \)
---
Final Answers:
\[
\boxed{
\begin{array}{ll}
4 \frac{3}{4} = \frac{19}{4} & 3 \frac{1}{2} = \frac{7}{2} \\
5 \frac{3}{5} = \frac{28}{5} & 4 \frac{1}{2} = \frac{9}{2} \\
3 \frac{1}{4} = \frac{13}{4} & 5 \frac{3}{4} = \frac{23}{4} \\
2 \frac{1}{3} = \frac{7}{3} & 7 \frac{2}{9} = \frac{65}{9} \\
8 \frac{3}{7} = \frac{59}{7} & 2 \frac{3}{5} = \frac{13}{5} \\
7 \frac{1}{10} = \frac{71}{10} & 4 \frac{2}{3} = \frac{14}{3} \\
9 \frac{1}{3} = \frac{28}{3} & 7 \frac{1}{3} = \frac{22}{3} \\
4 \frac{8}{9} = \frac{44}{9} & 9 \frac{3}{4} = \frac{39}{4} \\
5 \frac{2}{3} = \frac{17}{3} & 3 \frac{2}{5} = \frac{17}{5} \\
5 \frac{1}{8} = \frac{41}{8} & 6 \frac{1}{2} = \frac{13}{2}
\end{array}
}
\]
Parent Tip: Review the logic above to help your child master the concept of mixed number to improper fraction worksheet.
