Converting Improper Fractions to Mixed Fractions (A) - Free Printable
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Step-by-step solution for: Converting Improper Fractions to Mixed Fractions (A)
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Show Answer Key & Explanations
Step-by-step solution for: Converting Improper Fractions to Mixed Fractions (A)
The task involves converting improper fractions to mixed fractions. An improper fraction is a fraction where the numerator (top number) is greater than or equal to the denominator (bottom number). A mixed fraction consists of a whole number and a proper fraction.
1. Divide the numerator by the denominator to find the quotient and remainder.
2. The quotient becomes the whole number part of the mixed fraction.
3. The remainder becomes the numerator of the fractional part.
4. The denominator remains the same.
Let’s solve each problem step by step.
---
- Divide 32 by 9:
\( 32 \div 9 = 3 \) remainder \( 5 \).
- Quotient = 3, Remainder = 5.
- Mixed fraction: \( 3 \frac{5}{9} \).
- Divide 67 by 12:
\( 67 \div 12 = 5 \) remainder \( 7 \).
- Quotient = 5, Remainder = 7.
- Mixed fraction: \( 5 \frac{7}{12} \).
- Divide 116 by 15:
\( 116 \div 15 = 7 \) remainder \( 11 \).
- Quotient = 7, Remainder = 11.
- Mixed fraction: \( 7 \frac{11}{15} \).
- Divide 34 by 15:
\( 34 \div 15 = 2 \) remainder \( 4 \).
- Quotient = 2, Remainder = 4.
- Mixed fraction: \( 2 \frac{4}{15} \).
- Divide 25 by 12:
\( 25 \div 12 = 2 \) remainder \( 1 \).
- Quotient = 2, Remainder = 1.
- Mixed fraction: \( 2 \frac{1}{12} \).
- Divide 41 by 6:
\( 41 \div 6 = 6 \) remainder \( 5 \).
- Quotient = 6, Remainder = 5.
- Mixed fraction: \( 6 \frac{5}{6} \).
- Divide 53 by 7:
\( 53 \div 7 = 7 \) remainder \( 4 \).
- Quotient = 7, Remainder = 4.
- Mixed fraction: \( 7 \frac{4}{7} \).
- Divide 25 by 4:
\( 25 \div 4 = 6 \) remainder \( 1 \).
- Quotient = 6, Remainder = 1.
- Mixed fraction: \( 6 \frac{1}{4} \).
- Divide 127 by 15:
\( 127 \div 15 = 8 \) remainder \( 7 \).
- Quotient = 8, Remainder = 7.
- Mixed fraction: \( 8 \frac{7}{15} \).
- Divide 21 by 8:
\( 21 \div 8 = 2 \) remainder \( 5 \).
- Quotient = 2, Remainder = 5.
- Mixed fraction: \( 2 \frac{5}{8} \).
- Divide 15 by 4:
\( 15 \div 4 = 3 \) remainder \( 3 \).
- Quotient = 3, Remainder = 3.
- Mixed fraction: \( 3 \frac{3}{4} \).
- Divide 33 by 10:
\( 33 \div 10 = 3 \) remainder \( 3 \).
- Quotient = 3, Remainder = 3.
- Mixed fraction: \( 3 \frac{3}{10} \).
- Divide 25 by 9:
\( 25 \div 9 = 2 \) remainder \( 7 \).
- Quotient = 2, Remainder = 7.
- Mixed fraction: \( 2 \frac{7}{9} \).
- Divide 38 by 7:
\( 38 \div 7 = 5 \) remainder \( 3 \).
- Quotient = 5, Remainder = 3.
- Mixed fraction: \( 5 \frac{3}{7} \).
- Divide 99 by 10:
\( 99 \div 10 = 9 \) remainder \( 9 \).
- Quotient = 9, Remainder = 9.
- Mixed fraction: \( 9 \frac{9}{10} \).
- Divide 44 by 5:
\( 44 \div 5 = 8 \) remainder \( 4 \).
- Quotient = 8, Remainder = 4.
- Mixed fraction: \( 8 \frac{4}{5} \).
- Divide 53 by 15:
\( 53 \div 15 = 3 \) remainder \( 8 \).
- Quotient = 3, Remainder = 8.
- Mixed fraction: \( 3 \frac{8}{15} \).
- Divide 41 by 8:
\( 41 \div 8 = 5 \) remainder \( 1 \).
- Quotient = 5, Remainder = 1.
- Mixed fraction: \( 5 \frac{1}{8} \).
- Divide 64 by 9:
\( 64 \div 9 = 7 \) remainder \( 1 \).
- Quotient = 7, Remainder = 1.
- Mixed fraction: \( 7 \frac{1}{9} \).
- Divide 57 by 10:
\( 57 \div 10 = 5 \) remainder \( 7 \).
- Quotient = 5, Remainder = 7.
- Mixed fraction: \( 5 \frac{7}{10} \).
- Divide 16 by 7:
\( 16 \div 7 = 2 \) remainder \( 2 \).
- Quotient = 2, Remainder = 2.
- Mixed fraction: \( 2 \frac{2}{7} \).
- Divide 56 by 9:
\( 56 \div 9 = 6 \) remainder \( 2 \).
- Quotient = 6, Remainder = 2.
- Mixed fraction: \( 6 \frac{2}{9} \).
- Divide 21 by 10:
\( 21 \div 10 = 2 \) remainder \( 1 \).
- Quotient = 2, Remainder = 1.
- Mixed fraction: \( 2 \frac{1}{10} \).
- Divide 67 by 8:
\( 67 \div 8 = 8 \) remainder \( 3 \).
- Quotient = 8, Remainder = 3.
- Mixed fraction: \( 8 \frac{3}{8} \).
- Divide 12 by 7:
\( 12 \div 7 = 1 \) remainder \( 5 \).
- Quotient = 1, Remainder = 5.
- Mixed fraction: \( 1 \frac{5}{7} \).
- Divide 83 by 12:
\( 83 \div 12 = 6 \) remainder \( 11 \).
- Quotient = 6, Remainder = 11.
- Mixed fraction: \( 6 \frac{11}{12} \).
- Divide 36 by 7:
\( 36 \div 7 = 5 \) remainder \( 1 \).
- Quotient = 5, Remainder = 1.
- Mixed fraction: \( 5 \frac{1}{7} \).
- Divide 19 by 6:
\( 19 \div 6 = 3 \) remainder \( 1 \).
- Quotient = 3, Remainder = 1.
- Mixed fraction: \( 3 \frac{1}{6} \).
- Divide 13 by 2:
\( 13 \div 2 = 6 \) remainder \( 1 \).
- Quotient = 6, Remainder = 1.
- Mixed fraction: \( 6 \frac{1}{2} \).
- Divide 22 by 3:
\( 22 \div 3 = 7 \) remainder \( 1 \).
- Quotient = 7, Remainder = 1.
- Mixed fraction: \( 7 \frac{1}{3} \).
- Divide 23 by 5:
\( 23 \div 5 = 4 \) remainder \( 3 \).
- Quotient = 4, Remainder = 3.
- Mixed fraction: \( 4 \frac{3}{5} \).
- Divide 20 by 7:
\( 20 \div 7 = 2 \) remainder \( 6 \).
- Quotient = 2, Remainder = 6.
- Mixed fraction: \( 2 \frac{6}{7} \).
- Divide 76 by 15:
\( 76 \div 15 = 5 \) remainder \( 1 \).
- Quotient = 5, Remainder = 1.
- Mixed fraction: \( 5 \frac{1}{15} \).
- Divide 85 by 9:
\( 85 \div 9 = 9 \) remainder \( 4 \).
- Quotient = 9, Remainder = 4.
- Mixed fraction: \( 9 \frac{4}{9} \).
- Divide 80 by 9:
\( 80 \div 9 = 8 \) remainder \( 8 \).
- Quotient = 8, Remainder = 8.
- Mixed fraction: \( 8 \frac{8}{9} \).
- Divide 41 by 12:
\( 41 \div 12 = 3 \) remainder \( 5 \).
- Quotient = 3, Remainder = 5.
- Mixed fraction: \( 3 \frac{5}{12} \).
- Divide 6 by 5:
\( 6 \div 5 = 1 \) remainder \( 1 \).
- Quotient = 1, Remainder = 1.
- Mixed fraction: \( 1 \frac{1}{5} \).
- Divide 107 by 15:
\( 107 \div 15 = 7 \) remainder \( 2 \).
- Quotient = 7, Remainder = 2.
- Mixed fraction: \( 7 \frac{2}{15} \).
- Divide 63 by 8:
\( 63 \div 8 = 7 \) remainder \( 7 \).
- Quotient = 7, Remainder = 7.
- Mixed fraction: \( 7 \frac{7}{8} \).
- Divide 37 by 5:
\( 37 \div 5 = 7 \) remainder \( 2 \).
- Quotient = 7, Remainder = 2.
- Mixed fraction: \( 7 \frac{2}{5} \).
---
\[
\boxed{
\begin{array}{cccc}
\frac{32}{9} = 3 \frac{5}{9} & \frac{67}{12} = 5 \frac{7}{12} & \frac{116}{15} = 7 \frac{11}{15} & \frac{34}{15} = 2 \frac{4}{15} \\
\frac{25}{12} = 2 \frac{1}{12} & \frac{41}{6} = 6 \frac{5}{6} & \frac{53}{7} = 7 \frac{4}{7} & \frac{25}{4} = 6 \frac{1}{4} \\
\frac{127}{15} = 8 \frac{7}{15} & \frac{21}{8} = 2 \frac{5}{8} & \frac{15}{4} = 3 \frac{3}{4} & \frac{33}{10} = 3 \frac{3}{10} \\
\frac{25}{9} = 2 \frac{7}{9} & \frac{38}{7} = 5 \frac{3}{7} & \frac{99}{10} = 9 \frac{9}{10} & \frac{44}{5} = 8 \frac{4}{5} \\
\frac{53}{15} = 3 \frac{8}{15} & \frac{41}{8} = 5 \frac{1}{8} & \frac{64}{9} = 7 \frac{1}{9} & \frac{57}{10} = 5 \frac{7}{10} \\
\frac{16}{7} = 2 \frac{2}{7} & \frac{56}{9} = 6 \frac{2}{9} & \frac{21}{10} = 2 \frac{1}{10} & \frac{67}{8} = 8 \frac{3}{8} \\
\frac{12}{7} = 1 \frac{5}{7} & \frac{83}{12} = 6 \frac{11}{12} & \frac{36}{7} = 5 \frac{1}{7} & \frac{19}{6} = 3 \frac{1}{6} \\
\frac{13}{2} = 6 \frac{1}{2} & \frac{22}{3} = 7 \frac{1}{3} & \frac{23}{5} = 4 \frac{3}{5} & \frac{20}{7} = 2 \frac{6}{7} \\
\frac{76}{15} = 5 \frac{1}{15} & \frac{85}{9} = 9 \frac{4}{9} & \frac{80}{9} = 8 \frac{8}{9} & \frac{41}{12} = 3 \frac{5}{12} \\
\frac{6}{5} = 1 \frac{1}{5} & \frac{107}{15} = 7 \frac{2}{15} & \frac{63}{8} = 7 \frac{7}{8} & \frac{37}{5} = 7 \frac{2}{5} \\
\end{array}
}
\]
Steps to Convert an Improper Fraction to a Mixed Fraction:
1. Divide the numerator by the denominator to find the quotient and remainder.
2. The quotient becomes the whole number part of the mixed fraction.
3. The remainder becomes the numerator of the fractional part.
4. The denominator remains the same.
Let’s solve each problem step by step.
---
1. \( \frac{32}{9} \)
- Divide 32 by 9:
\( 32 \div 9 = 3 \) remainder \( 5 \).
- Quotient = 3, Remainder = 5.
- Mixed fraction: \( 3 \frac{5}{9} \).
2. \( \frac{67}{12} \)
- Divide 67 by 12:
\( 67 \div 12 = 5 \) remainder \( 7 \).
- Quotient = 5, Remainder = 7.
- Mixed fraction: \( 5 \frac{7}{12} \).
3. \( \frac{116}{15} \)
- Divide 116 by 15:
\( 116 \div 15 = 7 \) remainder \( 11 \).
- Quotient = 7, Remainder = 11.
- Mixed fraction: \( 7 \frac{11}{15} \).
4. \( \frac{34}{15} \)
- Divide 34 by 15:
\( 34 \div 15 = 2 \) remainder \( 4 \).
- Quotient = 2, Remainder = 4.
- Mixed fraction: \( 2 \frac{4}{15} \).
5. \( \frac{25}{12} \)
- Divide 25 by 12:
\( 25 \div 12 = 2 \) remainder \( 1 \).
- Quotient = 2, Remainder = 1.
- Mixed fraction: \( 2 \frac{1}{12} \).
6. \( \frac{41}{6} \)
- Divide 41 by 6:
\( 41 \div 6 = 6 \) remainder \( 5 \).
- Quotient = 6, Remainder = 5.
- Mixed fraction: \( 6 \frac{5}{6} \).
7. \( \frac{53}{7} \)
- Divide 53 by 7:
\( 53 \div 7 = 7 \) remainder \( 4 \).
- Quotient = 7, Remainder = 4.
- Mixed fraction: \( 7 \frac{4}{7} \).
8. \( \frac{25}{4} \)
- Divide 25 by 4:
\( 25 \div 4 = 6 \) remainder \( 1 \).
- Quotient = 6, Remainder = 1.
- Mixed fraction: \( 6 \frac{1}{4} \).
9. \( \frac{127}{15} \)
- Divide 127 by 15:
\( 127 \div 15 = 8 \) remainder \( 7 \).
- Quotient = 8, Remainder = 7.
- Mixed fraction: \( 8 \frac{7}{15} \).
10. \( \frac{21}{8} \)
- Divide 21 by 8:
\( 21 \div 8 = 2 \) remainder \( 5 \).
- Quotient = 2, Remainder = 5.
- Mixed fraction: \( 2 \frac{5}{8} \).
11. \( \frac{15}{4} \)
- Divide 15 by 4:
\( 15 \div 4 = 3 \) remainder \( 3 \).
- Quotient = 3, Remainder = 3.
- Mixed fraction: \( 3 \frac{3}{4} \).
12. \( \frac{33}{10} \)
- Divide 33 by 10:
\( 33 \div 10 = 3 \) remainder \( 3 \).
- Quotient = 3, Remainder = 3.
- Mixed fraction: \( 3 \frac{3}{10} \).
13. \( \frac{25}{9} \)
- Divide 25 by 9:
\( 25 \div 9 = 2 \) remainder \( 7 \).
- Quotient = 2, Remainder = 7.
- Mixed fraction: \( 2 \frac{7}{9} \).
14. \( \frac{38}{7} \)
- Divide 38 by 7:
\( 38 \div 7 = 5 \) remainder \( 3 \).
- Quotient = 5, Remainder = 3.
- Mixed fraction: \( 5 \frac{3}{7} \).
15. \( \frac{99}{10} \)
- Divide 99 by 10:
\( 99 \div 10 = 9 \) remainder \( 9 \).
- Quotient = 9, Remainder = 9.
- Mixed fraction: \( 9 \frac{9}{10} \).
16. \( \frac{44}{5} \)
- Divide 44 by 5:
\( 44 \div 5 = 8 \) remainder \( 4 \).
- Quotient = 8, Remainder = 4.
- Mixed fraction: \( 8 \frac{4}{5} \).
17. \( \frac{53}{15} \)
- Divide 53 by 15:
\( 53 \div 15 = 3 \) remainder \( 8 \).
- Quotient = 3, Remainder = 8.
- Mixed fraction: \( 3 \frac{8}{15} \).
18. \( \frac{41}{8} \)
- Divide 41 by 8:
\( 41 \div 8 = 5 \) remainder \( 1 \).
- Quotient = 5, Remainder = 1.
- Mixed fraction: \( 5 \frac{1}{8} \).
19. \( \frac{64}{9} \)
- Divide 64 by 9:
\( 64 \div 9 = 7 \) remainder \( 1 \).
- Quotient = 7, Remainder = 1.
- Mixed fraction: \( 7 \frac{1}{9} \).
20. \( \frac{57}{10} \)
- Divide 57 by 10:
\( 57 \div 10 = 5 \) remainder \( 7 \).
- Quotient = 5, Remainder = 7.
- Mixed fraction: \( 5 \frac{7}{10} \).
21. \( \frac{16}{7} \)
- Divide 16 by 7:
\( 16 \div 7 = 2 \) remainder \( 2 \).
- Quotient = 2, Remainder = 2.
- Mixed fraction: \( 2 \frac{2}{7} \).
22. \( \frac{56}{9} \)
- Divide 56 by 9:
\( 56 \div 9 = 6 \) remainder \( 2 \).
- Quotient = 6, Remainder = 2.
- Mixed fraction: \( 6 \frac{2}{9} \).
23. \( \frac{21}{10} \)
- Divide 21 by 10:
\( 21 \div 10 = 2 \) remainder \( 1 \).
- Quotient = 2, Remainder = 1.
- Mixed fraction: \( 2 \frac{1}{10} \).
24. \( \frac{67}{8} \)
- Divide 67 by 8:
\( 67 \div 8 = 8 \) remainder \( 3 \).
- Quotient = 8, Remainder = 3.
- Mixed fraction: \( 8 \frac{3}{8} \).
25. \( \frac{12}{7} \)
- Divide 12 by 7:
\( 12 \div 7 = 1 \) remainder \( 5 \).
- Quotient = 1, Remainder = 5.
- Mixed fraction: \( 1 \frac{5}{7} \).
26. \( \frac{83}{12} \)
- Divide 83 by 12:
\( 83 \div 12 = 6 \) remainder \( 11 \).
- Quotient = 6, Remainder = 11.
- Mixed fraction: \( 6 \frac{11}{12} \).
27. \( \frac{36}{7} \)
- Divide 36 by 7:
\( 36 \div 7 = 5 \) remainder \( 1 \).
- Quotient = 5, Remainder = 1.
- Mixed fraction: \( 5 \frac{1}{7} \).
28. \( \frac{19}{6} \)
- Divide 19 by 6:
\( 19 \div 6 = 3 \) remainder \( 1 \).
- Quotient = 3, Remainder = 1.
- Mixed fraction: \( 3 \frac{1}{6} \).
29. \( \frac{13}{2} \)
- Divide 13 by 2:
\( 13 \div 2 = 6 \) remainder \( 1 \).
- Quotient = 6, Remainder = 1.
- Mixed fraction: \( 6 \frac{1}{2} \).
30. \( \frac{22}{3} \)
- Divide 22 by 3:
\( 22 \div 3 = 7 \) remainder \( 1 \).
- Quotient = 7, Remainder = 1.
- Mixed fraction: \( 7 \frac{1}{3} \).
31. \( \frac{23}{5} \)
- Divide 23 by 5:
\( 23 \div 5 = 4 \) remainder \( 3 \).
- Quotient = 4, Remainder = 3.
- Mixed fraction: \( 4 \frac{3}{5} \).
32. \( \frac{20}{7} \)
- Divide 20 by 7:
\( 20 \div 7 = 2 \) remainder \( 6 \).
- Quotient = 2, Remainder = 6.
- Mixed fraction: \( 2 \frac{6}{7} \).
33. \( \frac{76}{15} \)
- Divide 76 by 15:
\( 76 \div 15 = 5 \) remainder \( 1 \).
- Quotient = 5, Remainder = 1.
- Mixed fraction: \( 5 \frac{1}{15} \).
34. \( \frac{85}{9} \)
- Divide 85 by 9:
\( 85 \div 9 = 9 \) remainder \( 4 \).
- Quotient = 9, Remainder = 4.
- Mixed fraction: \( 9 \frac{4}{9} \).
35. \( \frac{80}{9} \)
- Divide 80 by 9:
\( 80 \div 9 = 8 \) remainder \( 8 \).
- Quotient = 8, Remainder = 8.
- Mixed fraction: \( 8 \frac{8}{9} \).
36. \( \frac{41}{12} \)
- Divide 41 by 12:
\( 41 \div 12 = 3 \) remainder \( 5 \).
- Quotient = 3, Remainder = 5.
- Mixed fraction: \( 3 \frac{5}{12} \).
37. \( \frac{6}{5} \)
- Divide 6 by 5:
\( 6 \div 5 = 1 \) remainder \( 1 \).
- Quotient = 1, Remainder = 1.
- Mixed fraction: \( 1 \frac{1}{5} \).
38. \( \frac{107}{15} \)
- Divide 107 by 15:
\( 107 \div 15 = 7 \) remainder \( 2 \).
- Quotient = 7, Remainder = 2.
- Mixed fraction: \( 7 \frac{2}{15} \).
39. \( \frac{63}{8} \)
- Divide 63 by 8:
\( 63 \div 8 = 7 \) remainder \( 7 \).
- Quotient = 7, Remainder = 7.
- Mixed fraction: \( 7 \frac{7}{8} \).
40. \( \frac{37}{5} \)
- Divide 37 by 5:
\( 37 \div 5 = 7 \) remainder \( 2 \).
- Quotient = 7, Remainder = 2.
- Mixed fraction: \( 7 \frac{2}{5} \).
---
Final Answer:
\[
\boxed{
\begin{array}{cccc}
\frac{32}{9} = 3 \frac{5}{9} & \frac{67}{12} = 5 \frac{7}{12} & \frac{116}{15} = 7 \frac{11}{15} & \frac{34}{15} = 2 \frac{4}{15} \\
\frac{25}{12} = 2 \frac{1}{12} & \frac{41}{6} = 6 \frac{5}{6} & \frac{53}{7} = 7 \frac{4}{7} & \frac{25}{4} = 6 \frac{1}{4} \\
\frac{127}{15} = 8 \frac{7}{15} & \frac{21}{8} = 2 \frac{5}{8} & \frac{15}{4} = 3 \frac{3}{4} & \frac{33}{10} = 3 \frac{3}{10} \\
\frac{25}{9} = 2 \frac{7}{9} & \frac{38}{7} = 5 \frac{3}{7} & \frac{99}{10} = 9 \frac{9}{10} & \frac{44}{5} = 8 \frac{4}{5} \\
\frac{53}{15} = 3 \frac{8}{15} & \frac{41}{8} = 5 \frac{1}{8} & \frac{64}{9} = 7 \frac{1}{9} & \frac{57}{10} = 5 \frac{7}{10} \\
\frac{16}{7} = 2 \frac{2}{7} & \frac{56}{9} = 6 \frac{2}{9} & \frac{21}{10} = 2 \frac{1}{10} & \frac{67}{8} = 8 \frac{3}{8} \\
\frac{12}{7} = 1 \frac{5}{7} & \frac{83}{12} = 6 \frac{11}{12} & \frac{36}{7} = 5 \frac{1}{7} & \frac{19}{6} = 3 \frac{1}{6} \\
\frac{13}{2} = 6 \frac{1}{2} & \frac{22}{3} = 7 \frac{1}{3} & \frac{23}{5} = 4 \frac{3}{5} & \frac{20}{7} = 2 \frac{6}{7} \\
\frac{76}{15} = 5 \frac{1}{15} & \frac{85}{9} = 9 \frac{4}{9} & \frac{80}{9} = 8 \frac{8}{9} & \frac{41}{12} = 3 \frac{5}{12} \\
\frac{6}{5} = 1 \frac{1}{5} & \frac{107}{15} = 7 \frac{2}{15} & \frac{63}{8} = 7 \frac{7}{8} & \frac{37}{5} = 7 \frac{2}{5} \\
\end{array}
}
\]
Parent Tip: Review the logic above to help your child master the concept of improper fractions to mixed numbers free worksheet.
