Answer key for the "Converting Fractions (A)" worksheet, displaying solutions to convert improper fractions to mixed numbers.
Answer key for converting improper fractions to mixed numbers, showing solutions for 24 fraction conversion problems.
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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 in the image is to convert improper fractions into 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:
- The quotient becomes the whole number part of the mixed fraction.
- The remainder becomes the numerator of the fractional part.
- The denominator remains the same.
2. Write the result as a mixed fraction:
- Combine the whole number, the remainder (as the new numerator), and the original denominator.
Convert the improper fraction \( \frac{32}{9} \) to a mixed fraction.
- Step 1: Divide 32 by 9.
- \( 32 \div 9 = 3 \) with a remainder of 5.
- Step 2: Write the result.
- The whole number is 3, the remainder is 5, and the denominator remains 9.
- Therefore, \( \frac{32}{9} = 3 \frac{5}{9} \).
Let's go through the conversions step by step for all the given improper fractions.
#### First Row:
1. \( \frac{32}{9} \):
- \( 32 \div 9 = 3 \) remainder 5.
- \( \frac{32}{9} = 3 \frac{5}{9} \).
2. \( \frac{67}{12} \):
- \( 67 \div 12 = 5 \) remainder 7.
- \( \frac{67}{12} = 5 \frac{7}{12} \).
3. \( \frac{116}{15} \):
- \( 116 \div 15 = 7 \) remainder 11.
- \( \frac{116}{15} = 7 \frac{11}{15} \).
4. \( \frac{34}{15} \):
- \( 34 \div 15 = 2 \) remainder 4.
- \( \frac{34}{15} = 2 \frac{4}{15} \).
#### Second Row:
5. \( \frac{25}{12} \):
- \( 25 \div 12 = 2 \) remainder 1.
- \( \frac{25}{12} = 2 \frac{1}{12} \).
6. \( \frac{41}{6} \):
- \( 41 \div 6 = 6 \) remainder 5.
- \( \frac{41}{6} = 6 \frac{5}{6} \).
7. \( \frac{53}{7} \):
- \( 53 \div 7 = 7 \) remainder 4.
- \( \frac{53}{7} = 7 \frac{4}{7} \).
8. \( \frac{25}{4} \):
- \( 25 \div 4 = 6 \) remainder 1.
- \( \frac{25}{4} = 6 \frac{1}{4} \).
#### Third Row:
9. \( \frac{127}{15} \):
- \( 127 \div 15 = 8 \) remainder 7.
- \( \frac{127}{15} = 8 \frac{7}{15} \).
10. \( \frac{21}{8} \):
- \( 21 \div 8 = 2 \) remainder 5.
- \( \frac{21}{8} = 2 \frac{5}{8} \).
11. \( \frac{15}{4} \):
- \( 15 \div 4 = 3 \) remainder 3.
- \( \frac{15}{4} = 3 \frac{3}{4} \).
12. \( \frac{33}{10} \):
- \( 33 \div 10 = 3 \) remainder 3.
- \( \frac{33}{10} = 3 \frac{3}{10} \).
#### Fourth Row:
13. \( \frac{25}{9} \):
- \( 25 \div 9 = 2 \) remainder 7.
- \( \frac{25}{9} = 2 \frac{7}{9} \).
14. \( \frac{38}{7} \):
- \( 38 \div 7 = 5 \) remainder 3.
- \( \frac{38}{7} = 5 \frac{3}{7} \).
15. \( \frac{99}{10} \):
- \( 99 \div 10 = 9 \) remainder 9.
- \( \frac{99}{10} = 9 \frac{9}{10} \).
16. \( \frac{44}{5} \):
- \( 44 \div 5 = 8 \) remainder 4.
- \( \frac{44}{5} = 8 \frac{4}{5} \).
#### Fifth Row:
17. \( \frac{53}{15} \):
- \( 53 \div 15 = 3 \) remainder 8.
- \( \frac{53}{15} = 3 \frac{8}{15} \).
18. \( \frac{41}{8} \):
- \( 41 \div 8 = 5 \) remainder 1.
- \( \frac{41}{8} = 5 \frac{1}{8} \).
19. \( \frac{64}{9} \):
- \( 64 \div 9 = 7 \) remainder 1.
- \( \frac{64}{9} = 7 \frac{1}{9} \).
20. \( \frac{57}{10} \):
- \( 57 \div 10 = 5 \) remainder 7.
- \( \frac{57}{10} = 5 \frac{7}{10} \).
#### Sixth Row:
21. \( \frac{16}{7} \):
- \( 16 \div 7 = 2 \) remainder 2.
- \( \frac{16}{7} = 2 \frac{2}{7} \).
22. \( \frac{56}{9} \):
- \( 56 \div 9 = 6 \) remainder 2.
- \( \frac{56}{9} = 6 \frac{2}{9} \).
23. \( \frac{21}{10} \):
- \( 21 \div 10 = 2 \) remainder 1.
- \( \frac{21}{10} = 2 \frac{1}{10} \).
24. \( \frac{67}{8} \):
- \( 67 \div 8 = 8 \) remainder 3.
- \( \frac{67}{8} = 8 \frac{3}{8} \).
#### Seventh Row:
25. \( \frac{12}{7} \):
- \( 12 \div 7 = 1 \) remainder 5.
- \( \frac{12}{7} = 1 \frac{5}{7} \).
26. \( \frac{83}{12} \):
- \( 83 \div 12 = 6 \) remainder 11.
- \( \frac{83}{12} = 6 \frac{11}{12} \).
27. \( \frac{36}{7} \):
- \( 36 \div 7 = 5 \) remainder 1.
- \( \frac{36}{7} = 5 \frac{1}{7} \).
28. \( \frac{19}{6} \):
- \( 19 \div 6 = 3 \) remainder 1.
- \( \frac{19}{6} = 3 \frac{1}{6} \).
#### Eighth Row:
29. \( \frac{13}{2} \):
- \( 13 \div 2 = 6 \) remainder 1.
- \( \frac{13}{2} = 6 \frac{1}{2} \).
30. \( \frac{22}{3} \):
- \( 22 \div 3 = 7 \) remainder 1.
- \( \frac{22}{3} = 7 \frac{1}{3} \).
31. \( \frac{23}{5} \):
- \( 23 \div 5 = 4 \) remainder 3.
- \( \frac{23}{5} = 4 \frac{3}{5} \).
32. \( \frac{20}{7} \):
- \( 20 \div 7 = 2 \) remainder 6.
- \( \frac{20}{7} = 2 \frac{6}{7} \).
#### Ninth Row:
33. \( \frac{76}{15} \):
- \( 76 \div 15 = 5 \) remainder 1.
- \( \frac{76}{15} = 5 \frac{1}{15} \).
34. \( \frac{85}{9} \):
- \( 85 \div 9 = 9 \) remainder 4.
- \( \frac{85}{9} = 9 \frac{4}{9} \).
35. \( \frac{80}{9} \):
- \( 80 \div 9 = 8 \) remainder 8.
- \( \frac{80}{9} = 8 \frac{8}{9} \).
36. \( \frac{41}{12} \):
- \( 41 \div 12 = 3 \) remainder 5.
- \( \frac{41}{12} = 3 \frac{5}{12} \).
#### Tenth Row:
37. \( \frac{6}{5} \):
- \( 6 \div 5 = 1 \) remainder 1.
- \( \frac{6}{5} = 1 \frac{1}{5} \).
38. \( \frac{107}{15} \):
- \( 107 \div 15 = 7 \) remainder 2.
- \( \frac{107}{15} = 7 \frac{2}{15} \).
39. \( \frac{63}{8} \):
- \( 63 \div 8 = 7 \) remainder 7.
- \( \frac{63}{8} = 7 \frac{7}{8} \).
40. \( \frac{37}{5} \):
- \( 37 \div 5 = 7 \) remainder 2.
- \( \frac{37}{5} = 7 \frac{2}{5} \).
\[
\boxed{
\begin{array}{llll}
\frac{32}{9} = 3 \frac{5}{9} & \frac{67}{12} = 5 \frac{7}{12} & \frac{116}{15} = 7 \frac{11}{15} & \frac{34}{15} = 2 \frac{4}{15} \\
\frac{25}{12} = 2 \frac{1}{12} & \frac{41}{6} = 6 \frac{5}{6} & \frac{53}{7} = 7 \frac{4}{7} & \frac{25}{4} = 6 \frac{1}{4} \\
\frac{127}{15} = 8 \frac{7}{15} & \frac{21}{8} = 2 \frac{5}{8} & \frac{15}{4} = 3 \frac{3}{4} & \frac{33}{10} = 3 \frac{3}{10} \\
\frac{25}{9} = 2 \frac{7}{9} & \frac{38}{7} = 5 \frac{3}{7} & \frac{99}{10} = 9 \frac{9}{10} & \frac{44}{5} = 8 \frac{4}{5} \\
\frac{53}{15} = 3 \frac{8}{15} & \frac{41}{8} = 5 \frac{1}{8} & \frac{64}{9} = 7 \frac{1}{9} & \frac{57}{10} = 5 \frac{7}{10} \\
\frac{16}{7} = 2 \frac{2}{7} & \frac{56}{9} = 6 \frac{2}{9} & \frac{21}{10} = 2 \frac{1}{10} & \frac{67}{8} = 8 \frac{3}{8} \\
\frac{12}{7} = 1 \frac{5}{7} & \frac{83}{12} = 6 \frac{11}{12} & \frac{36}{7} = 5 \frac{1}{7} & \frac{19}{6} = 3 \frac{1}{6} \\
\frac{13}{2} = 6 \frac{1}{2} & \frac{22}{3} = 7 \frac{1}{3} & \frac{23}{5} = 4 \frac{3}{5} & \frac{20}{7} = 2 \frac{6}{7} \\
\frac{76}{15} = 5 \frac{1}{15} & \frac{85}{9} = 9 \frac{4}{9} & \frac{80}{9} = 8 \frac{8}{9} & \frac{41}{12} = 3 \frac{5}{12} \\
\frac{6}{5} = 1 \frac{1}{5} & \frac{107}{15} = 7 \frac{2}{15} & \frac{63}{8} = 7 \frac{7}{8} & \frac{37}{5} = 7 \frac{2}{5} \\
\end{array}
}
\]
Steps to Convert an Improper Fraction to a Mixed Fraction:
1. Divide the numerator by the denominator:
- The quotient becomes the whole number part of the mixed fraction.
- The remainder becomes the numerator of the fractional part.
- The denominator remains the same.
2. Write the result as a mixed fraction:
- Combine the whole number, the remainder (as the new numerator), and the original denominator.
Example:
Convert the improper fraction \( \frac{32}{9} \) to a mixed fraction.
- Step 1: Divide 32 by 9.
- \( 32 \div 9 = 3 \) with a remainder of 5.
- Step 2: Write the result.
- The whole number is 3, the remainder is 5, and the denominator remains 9.
- Therefore, \( \frac{32}{9} = 3 \frac{5}{9} \).
Solution for Each Problem:
Let's go through the conversions step by step for all the given improper fractions.
#### First Row:
1. \( \frac{32}{9} \):
- \( 32 \div 9 = 3 \) remainder 5.
- \( \frac{32}{9} = 3 \frac{5}{9} \).
2. \( \frac{67}{12} \):
- \( 67 \div 12 = 5 \) remainder 7.
- \( \frac{67}{12} = 5 \frac{7}{12} \).
3. \( \frac{116}{15} \):
- \( 116 \div 15 = 7 \) remainder 11.
- \( \frac{116}{15} = 7 \frac{11}{15} \).
4. \( \frac{34}{15} \):
- \( 34 \div 15 = 2 \) remainder 4.
- \( \frac{34}{15} = 2 \frac{4}{15} \).
#### Second Row:
5. \( \frac{25}{12} \):
- \( 25 \div 12 = 2 \) remainder 1.
- \( \frac{25}{12} = 2 \frac{1}{12} \).
6. \( \frac{41}{6} \):
- \( 41 \div 6 = 6 \) remainder 5.
- \( \frac{41}{6} = 6 \frac{5}{6} \).
7. \( \frac{53}{7} \):
- \( 53 \div 7 = 7 \) remainder 4.
- \( \frac{53}{7} = 7 \frac{4}{7} \).
8. \( \frac{25}{4} \):
- \( 25 \div 4 = 6 \) remainder 1.
- \( \frac{25}{4} = 6 \frac{1}{4} \).
#### Third Row:
9. \( \frac{127}{15} \):
- \( 127 \div 15 = 8 \) remainder 7.
- \( \frac{127}{15} = 8 \frac{7}{15} \).
10. \( \frac{21}{8} \):
- \( 21 \div 8 = 2 \) remainder 5.
- \( \frac{21}{8} = 2 \frac{5}{8} \).
11. \( \frac{15}{4} \):
- \( 15 \div 4 = 3 \) remainder 3.
- \( \frac{15}{4} = 3 \frac{3}{4} \).
12. \( \frac{33}{10} \):
- \( 33 \div 10 = 3 \) remainder 3.
- \( \frac{33}{10} = 3 \frac{3}{10} \).
#### Fourth Row:
13. \( \frac{25}{9} \):
- \( 25 \div 9 = 2 \) remainder 7.
- \( \frac{25}{9} = 2 \frac{7}{9} \).
14. \( \frac{38}{7} \):
- \( 38 \div 7 = 5 \) remainder 3.
- \( \frac{38}{7} = 5 \frac{3}{7} \).
15. \( \frac{99}{10} \):
- \( 99 \div 10 = 9 \) remainder 9.
- \( \frac{99}{10} = 9 \frac{9}{10} \).
16. \( \frac{44}{5} \):
- \( 44 \div 5 = 8 \) remainder 4.
- \( \frac{44}{5} = 8 \frac{4}{5} \).
#### Fifth Row:
17. \( \frac{53}{15} \):
- \( 53 \div 15 = 3 \) remainder 8.
- \( \frac{53}{15} = 3 \frac{8}{15} \).
18. \( \frac{41}{8} \):
- \( 41 \div 8 = 5 \) remainder 1.
- \( \frac{41}{8} = 5 \frac{1}{8} \).
19. \( \frac{64}{9} \):
- \( 64 \div 9 = 7 \) remainder 1.
- \( \frac{64}{9} = 7 \frac{1}{9} \).
20. \( \frac{57}{10} \):
- \( 57 \div 10 = 5 \) remainder 7.
- \( \frac{57}{10} = 5 \frac{7}{10} \).
#### Sixth Row:
21. \( \frac{16}{7} \):
- \( 16 \div 7 = 2 \) remainder 2.
- \( \frac{16}{7} = 2 \frac{2}{7} \).
22. \( \frac{56}{9} \):
- \( 56 \div 9 = 6 \) remainder 2.
- \( \frac{56}{9} = 6 \frac{2}{9} \).
23. \( \frac{21}{10} \):
- \( 21 \div 10 = 2 \) remainder 1.
- \( \frac{21}{10} = 2 \frac{1}{10} \).
24. \( \frac{67}{8} \):
- \( 67 \div 8 = 8 \) remainder 3.
- \( \frac{67}{8} = 8 \frac{3}{8} \).
#### Seventh Row:
25. \( \frac{12}{7} \):
- \( 12 \div 7 = 1 \) remainder 5.
- \( \frac{12}{7} = 1 \frac{5}{7} \).
26. \( \frac{83}{12} \):
- \( 83 \div 12 = 6 \) remainder 11.
- \( \frac{83}{12} = 6 \frac{11}{12} \).
27. \( \frac{36}{7} \):
- \( 36 \div 7 = 5 \) remainder 1.
- \( \frac{36}{7} = 5 \frac{1}{7} \).
28. \( \frac{19}{6} \):
- \( 19 \div 6 = 3 \) remainder 1.
- \( \frac{19}{6} = 3 \frac{1}{6} \).
#### Eighth Row:
29. \( \frac{13}{2} \):
- \( 13 \div 2 = 6 \) remainder 1.
- \( \frac{13}{2} = 6 \frac{1}{2} \).
30. \( \frac{22}{3} \):
- \( 22 \div 3 = 7 \) remainder 1.
- \( \frac{22}{3} = 7 \frac{1}{3} \).
31. \( \frac{23}{5} \):
- \( 23 \div 5 = 4 \) remainder 3.
- \( \frac{23}{5} = 4 \frac{3}{5} \).
32. \( \frac{20}{7} \):
- \( 20 \div 7 = 2 \) remainder 6.
- \( \frac{20}{7} = 2 \frac{6}{7} \).
#### Ninth Row:
33. \( \frac{76}{15} \):
- \( 76 \div 15 = 5 \) remainder 1.
- \( \frac{76}{15} = 5 \frac{1}{15} \).
34. \( \frac{85}{9} \):
- \( 85 \div 9 = 9 \) remainder 4.
- \( \frac{85}{9} = 9 \frac{4}{9} \).
35. \( \frac{80}{9} \):
- \( 80 \div 9 = 8 \) remainder 8.
- \( \frac{80}{9} = 8 \frac{8}{9} \).
36. \( \frac{41}{12} \):
- \( 41 \div 12 = 3 \) remainder 5.
- \( \frac{41}{12} = 3 \frac{5}{12} \).
#### Tenth Row:
37. \( \frac{6}{5} \):
- \( 6 \div 5 = 1 \) remainder 1.
- \( \frac{6}{5} = 1 \frac{1}{5} \).
38. \( \frac{107}{15} \):
- \( 107 \div 15 = 7 \) remainder 2.
- \( \frac{107}{15} = 7 \frac{2}{15} \).
39. \( \frac{63}{8} \):
- \( 63 \div 8 = 7 \) remainder 7.
- \( \frac{63}{8} = 7 \frac{7}{8} \).
40. \( \frac{37}{5} \):
- \( 37 \div 5 = 7 \) remainder 2.
- \( \frac{37}{5} = 7 \frac{2}{5} \).
Final Answer:
\[
\boxed{
\begin{array}{llll}
\frac{32}{9} = 3 \frac{5}{9} & \frac{67}{12} = 5 \frac{7}{12} & \frac{116}{15} = 7 \frac{11}{15} & \frac{34}{15} = 2 \frac{4}{15} \\
\frac{25}{12} = 2 \frac{1}{12} & \frac{41}{6} = 6 \frac{5}{6} & \frac{53}{7} = 7 \frac{4}{7} & \frac{25}{4} = 6 \frac{1}{4} \\
\frac{127}{15} = 8 \frac{7}{15} & \frac{21}{8} = 2 \frac{5}{8} & \frac{15}{4} = 3 \frac{3}{4} & \frac{33}{10} = 3 \frac{3}{10} \\
\frac{25}{9} = 2 \frac{7}{9} & \frac{38}{7} = 5 \frac{3}{7} & \frac{99}{10} = 9 \frac{9}{10} & \frac{44}{5} = 8 \frac{4}{5} \\
\frac{53}{15} = 3 \frac{8}{15} & \frac{41}{8} = 5 \frac{1}{8} & \frac{64}{9} = 7 \frac{1}{9} & \frac{57}{10} = 5 \frac{7}{10} \\
\frac{16}{7} = 2 \frac{2}{7} & \frac{56}{9} = 6 \frac{2}{9} & \frac{21}{10} = 2 \frac{1}{10} & \frac{67}{8} = 8 \frac{3}{8} \\
\frac{12}{7} = 1 \frac{5}{7} & \frac{83}{12} = 6 \frac{11}{12} & \frac{36}{7} = 5 \frac{1}{7} & \frac{19}{6} = 3 \frac{1}{6} \\
\frac{13}{2} = 6 \frac{1}{2} & \frac{22}{3} = 7 \frac{1}{3} & \frac{23}{5} = 4 \frac{3}{5} & \frac{20}{7} = 2 \frac{6}{7} \\
\frac{76}{15} = 5 \frac{1}{15} & \frac{85}{9} = 9 \frac{4}{9} & \frac{80}{9} = 8 \frac{8}{9} & \frac{41}{12} = 3 \frac{5}{12} \\
\frac{6}{5} = 1 \frac{1}{5} & \frac{107}{15} = 7 \frac{2}{15} & \frac{63}{8} = 7 \frac{7}{8} & \frac{37}{5} = 7 \frac{2}{5} \\
\end{array}
}
\]
Parent Tip: Review the logic above to help your child master the concept of improper fractions to mixed number worksheet.
