Multiplying and dividing fractions - Free Printable

Let’s solve each problem step by step. Remember:

- To multiply fractions: multiply numerators (top numbers) and denominators (bottom numbers). Then simplify if needed.
- To divide fractions: flip the second fraction (reciprocal), then multiply.

We’ll go row by row, left to right.

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Row 1:

1. \( \frac{1}{2} \times \frac{5}{4} = \frac{1 \times 5}{2 \times 4} = \frac{5}{8} \)

2. \( \frac{1}{4} \times \frac{5}{3} = \frac{1 \times 5}{4 \times 3} = \frac{5}{12} \)

3. \( \frac{10}{3} \times \frac{11}{6} = \frac{10 \times 11}{3 \times 6} = \frac{110}{18} \)
Simplify: divide numerator and denominator by 2 → \( \frac{55}{9} \)
Or as mixed number: \( 6 \frac{1}{9} \) — but since instructions don’t specify, we’ll leave as improper fraction unless it simplifies nicely. Actually, let’s check: 110 ÷ 2 = 55, 18 ÷ 2 = 9 → yes, \( \frac{55}{9} \)

Wait — maybe they want simplified fractions? Let’s keep going and simplify all at end if needed. But for now, we’ll write simplified forms.

Actually, better to simplify immediately when possible.

But 55/9 is already simplified.

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Row 2:

4. \( \frac{1}{6} \div \frac{8}{11} = \frac{1}{6} \times \frac{11}{8} = \frac{1 \times 11}{6 \times 8} = \frac{11}{48} \)

5. \( \frac{11}{2} \div \frac{1}{2} = \frac{11}{2} \times \frac{2}{1} = \frac{11 \times 2}{2 \times 1} = \frac{22}{2} = 11 \)

6. \( \frac{1}{2} \div \frac{1}{2} = \frac{1}{2} \times \frac{2}{1} = \frac{2}{2} = 1 \)

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Row 3:

7. \( \frac{1}{3} \div \frac{13}{9} = \frac{1}{3} \times \frac{9}{13} = \frac{1 \times 9}{3 \times 13} = \frac{9}{39} \)
Simplify: divide top and bottom by 3 → \( \frac{3}{13} \)

8. \( \frac{4}{3} \div \frac{11}{12} = \frac{4}{3} \times \frac{12}{11} = \frac{4 \times 12}{3 \times 11} = \frac{48}{33} \)
Simplify: divide by 3 → \( \frac{16}{11} \)

9. \( \frac{14}{9} \times \frac{7}{10} = \frac{14 \times 7}{9 \times 10} = \frac{98}{90} \)
Simplify: divide by 2 → \( \frac{49}{45} \)

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Row 4:

10. \( \frac{13}{4} \div \frac{1}{2} = \frac{13}{4} \times \frac{2}{1} = \frac{13 \times 2}{4 \times 1} = \frac{26}{4} \)
Simplify: divide by 2 → \( \frac{13}{2} \)

11. \( \frac{1}{3} \times \frac{20}{9} = \frac{1 \times 20}{3 \times 9} = \frac{20}{27} \)

12. \( \frac{15}{8} \times \frac{7}{6} = \frac{15 \times 7}{8 \times 6} = \frac{105}{48} \)
Simplify: divide by 3 → \( \frac{35}{16} \)

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Row 5:

13. \( \frac{17}{6} \div \frac{3}{5} = \frac{17}{6} \times \frac{5}{3} = \frac{17 \times 5}{6 \times 3} = \frac{85}{18} \)

14. \( \frac{13}{7} \times \frac{14}{11} = \frac{13 \times 14}{7 \times 11} \)
Notice: 14 and 7 can cancel → 14 ÷ 7 = 2, so becomes \( \frac{13 \times 2}{1 \times 11} = \frac{26}{11} \)

15. \( \frac{3}{2} \times \frac{4}{9} = \frac{3 \times 4}{2 \times 9} = \frac{12}{18} \)
Simplify: divide by 6 → \( \frac{2}{3} \)

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Now let’s list all answers in order (left to right, top to bottom):

1. \( \frac{5}{8} \)
2. \( \frac{5}{12} \)
3. \( \frac{55}{9} \)
4. \( \frac{11}{48} \)
5. \( 11 \)
6. \( 1 \)
7. \( \frac{3}{13} \)
8. \( \frac{16}{11} \)
9. \( \frac{49}{45} \)
10. \( \frac{13}{2} \)
11. \( \frac{20}{27} \)
12. \( \frac{35}{16} \)
13. \( \frac{85}{18} \)
14. \( \frac{26}{11} \)
15. \( \frac{2}{3} \)

Double-check a few tricky ones:

- #3: \( \frac{10}{3} \times \frac{11}{6} = \frac{110}{18} = \frac{55}{9} \) ✔
- #8: \( \frac{4}{3} \times \frac{12}{11} = \frac{48}{33} = \frac{16}{11} \) ✔
- #9: \( \frac{14}{9} \times \frac{7}{10} = \frac{98}{90} = \frac{49}{45} \) ✔
- #12: \( \frac{15}{8} \times \frac{7}{6} = \frac{105}{48} = \frac{35}{16} \) ✔
- #14: Cancel 14 and 7 → 13×2 / 11 = 26/11 ✔
- #15: 12/18 = 2/3 ✔

All correct.

Final Answer:
\(\frac{5}{8}, \frac{5}{12}, \frac{55}{9}, \frac{11}{48}, 11, 1, \frac{3}{13}, \frac{16}{11}, \frac{49}{45}, \frac{13}{2}, \frac{20}{27}, \frac{35}{16}, \frac{85}{18}, \frac{26}{11}, \frac{2}{3}\)