Let’s solve each mixed number conversion step by step.
We convert a mixed number like \( a \frac{b}{c} \) to an improper fraction by:
1. Multiplying the whole number (a) by the denominator (c).
2. Adding the numerator (b) to that result.
3. Writing the sum over the original denominator (c).
So:
\[
a \frac{b}{c} = \frac{a \times c + b}{c}
\]
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Left Column:
1. \( 3 \frac{1}{2} \) → already done: \( \frac{7}{2} \)
2. \( 1 \frac{2}{3} \)
→ Calculation: \( \frac{3}{3} + \frac{2}{3} = \frac{5}{3} \)
→ Improper Fraction: \( \frac{5}{3} \)
3. \( 2 \frac{1}{5} \)
→ Calculation: \( \frac{10}{5} + \frac{1}{5} = \frac{11}{5} \)
→ Improper Fraction: \( \frac{11}{5} \)
4. \( 3 \frac{1}{4} \)
→ Calculation: \( \frac{12}{4} + \frac{1}{4} = \frac{13}{4} \)
→ Improper Fraction: \( \frac{13}{4} \)
5. \( 1 \frac{3}{7} \)
→ Calculation: \( \frac{7}{7} + \frac{3}{7} = \frac{10}{7} \)
→ Improper Fraction: \( \frac{10}{7} \)
6. \( 5 \frac{1}{6} \)
→ Calculation: \( \frac{30}{6} + \frac{1}{6} = \frac{31}{6} \)
→ Improper Fraction: \( \frac{31}{6} \)
7. \( 4 \frac{2}{5} \)
→ Calculation: \( \frac{20}{5} + \frac{2}{5} = \frac{22}{5} \)
→ Improper Fraction: \( \frac{22}{5} \)
8. \( 3 \frac{1}{4} \) — same as #4 → \( \frac{13}{4} \)
9. \( 2 \frac{7}{10} \)
→ Calculation: \( \frac{20}{10} + \frac{7}{10} = \frac{27}{10} \)
→ Improper Fraction: \( \frac{27}{10} \)
---
Right Column:
1. \( 2 \frac{3}{4} \)
→ Calculation: \( \frac{8}{4} + \frac{3}{4} = \frac{11}{4} \)
→ Improper Fraction: \( \frac{11}{4} \)
2. \( 4 \frac{1}{3} \)
→ Calculation: \( \frac{12}{3} + \frac{1}{3} = \frac{13}{3} \)
→ Improper Fraction: \( \frac{13}{3} \)
3. \( 2 \frac{3}{5} \)
→ Calculation: \( \frac{10}{5} + \frac{3}{5} = \frac{13}{5} \)
→ Improper Fraction: \( \frac{13}{5} \)
4. \( 3 \frac{2}{7} \)
→ Calculation: \( \frac{21}{7} + \frac{2}{7} = \frac{23}{7} \)
→ Improper Fraction: \( \frac{23}{7} \)
5. \( 6 \frac{1}{11} \)
→ Calculation: \( \frac{66}{11} + \frac{1}{11} = \frac{67}{11} \)
→ Improper Fraction: \( \frac{67}{11} \)
6. \( 7 \frac{3}{10} \)
→ Calculation: \( \frac{70}{10} + \frac{3}{10} = \frac{73}{10} \)
→ Improper Fraction: \( \frac{73}{10} \)
7. \( 4 \frac{5}{12} \)
→ Calculation: \( \frac{48}{12} + \frac{5}{12} = \frac{53}{12} \)
→ Improper Fraction: \( \frac{53}{12} \)
8. \( 9 \frac{2}{3} \)
→ Calculation: \( \frac{27}{3} + \frac{2}{3} = \frac{29}{3} \)
→ Improper Fraction: \( \frac{29}{3} \)
9. \( 11 \frac{2}{9} \)
→ Calculation: \( \frac{99}{9} + \frac{2}{9} = \frac{101}{9} \)
→ Improper Fraction: \( \frac{101}{9} \)
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Final Answer:
Left Column Improper Fractions (top to bottom):
\( \frac{7}{2}, \frac{5}{3}, \frac{11}{5}, \frac{13}{4}, \frac{10}{7}, \frac{31}{6}, \frac{22}{5}, \frac{13}{4}, \frac{27}{10} \)
Right Column Improper Fractions (top to bottom):
\( \frac{11}{4}, \frac{13}{3}, \frac{13}{5}, \frac{23}{7}, \frac{67}{11}, \frac{73}{10}, \frac{53}{12}, \frac{29}{3}, \frac{101}{9} \)
Parent Tip: Review the logic above to help your child master the concept of improper fractions to mixed numbers worksheet 5th grade.
