Multiplying Fractions: Cross Cancelling - Variation Theory - Free Printable

Let's solve each of these fraction multiplication problems step by step. We'll simplify where possible and follow the rule:

> To multiply two fractions:
> $\frac{a}{b} \times \frac{c}{d} = \frac{a \times c}{b \times d}$

We can also simplify before multiplying by canceling common factors.

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1) $\frac{2}{9} \times \frac{3}{4}$

- Multiply numerators: $2 \times 3 = 6$
- Multiply denominators: $9 \times 4 = 36$
- So: $\frac{6}{36} = \frac{1}{6}$ (simplified)

✔ Answer: $\boxed{\frac{1}{6}}$

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2) $\frac{2}{9} \times \frac{3}{8}$

- Numerator: $2 \times 3 = 6$
- Denominator: $9 \times 8 = 72$
- $\frac{6}{72} = \frac{1}{12}$

✔ Answer: $\boxed{\frac{1}{12}}$

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3) $\frac{4}{9} \times \frac{3}{16}$

- Simplify first:
- 4 and 16: $4 \div 4 = 1$, $16 \div 4 = 4$
- 3 and 9: $3 \div 3 = 1$, $9 \div 3 = 3$
- So: $\frac{1}{3} \times \frac{1}{4} = \frac{1}{12}$

✔ Answer: $\boxed{\frac{1}{12}}$

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4) $\frac{4}{27} \times \frac{3}{16}$

- Simplify:
- 4 and 16: $4 \div 4 = 1$, $16 \div 4 = 4$
- 3 and 27: $3 \div 3 = 1$, $27 \div 3 = 9$
- Now: $\frac{1}{9} \times \frac{1}{4} = \frac{1}{36}$

✔ Answer: $\boxed{\frac{1}{36}}$

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5) $\frac{4}{27} \times \frac{9}{16}$

- Simplify:
- 4 and 16: $4 \div 4 = 1$, $16 \div 4 = 4$
- 9 and 27: $9 \div 9 = 1$, $27 \div 9 = 3$
- So: $\frac{1}{3} \times \frac{1}{4} = \frac{1}{12}$

✔ Answer: $\boxed{\frac{1}{12}}$

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6) $\frac{8}{27} \times \frac{9}{16}$

- Simplify:
- 8 and 16: $8 \div 8 = 1$, $16 \div 8 = 2$
- 9 and 27: $9 \div 9 = 1$, $27 \div 9 = 3$
- So: $\frac{1}{3} \times \frac{1}{2} = \frac{1}{6}$

✔ Answer: $\boxed{\frac{1}{6}}$

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7) $\frac{8}{27} \times \frac{15}{16}$

- Simplify:
- 8 and 16: $8 \div 8 = 1$, $16 \div 8 = 2$
- 15 and 27: both divisible by 3 → $15 \div 3 = 5$, $27 \div 3 = 9$
- So: $\frac{1}{9} \times \frac{5}{2} = \frac{5}{18}$

✔ Answer: $\boxed{\frac{5}{18}}$

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8) $\frac{16}{27} \times \frac{15}{16}$

- Cancel 16 in numerator and denominator:
- $\frac{1}{27} \times 15 = \frac{15}{27} = \frac{5}{9}$

✔ Answer: $\boxed{\frac{5}{9}}$

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9) $\frac{27}{8} \times \frac{16}{15}$

- Simplify:
- 27 and 15: both divisible by 3 → $27 \div 3 = 9$, $15 \div 3 = 5$
- 16 and 8: $16 \div 8 = 2$, $8 \div 8 = 1$
- So: $\frac{9}{1} \times \frac{2}{5} = \frac{18}{5} = 3\frac{3}{5}$

✔ Answer: $\boxed{\frac{18}{5}}$ or $\boxed{3\frac{3}{5}}$

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10) $3\frac{3}{8} \times \frac{16}{15}$

First, convert mixed number to improper fraction:

- $3\frac{3}{8} = \frac{3 \times 8 + 3}{8} = \frac{24 + 3}{8} = \frac{27}{8}$

Now: $\frac{27}{8} \times \frac{16}{15}$

This is same as problem #9!

So: $\frac{27}{8} \times \frac{16}{15} = \frac{18}{5} = 3\frac{3}{5}$

✔ Answer: $\boxed{\frac{18}{5}}$ or $\boxed{3\frac{3}{5}}$

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11) $3\frac{3}{8} \times 1\frac{1}{15}$

Convert both to improper fractions:

- $3\frac{3}{8} = \frac{27}{8}$
- $1\frac{1}{15} = \frac{16}{15}$

Now: $\frac{27}{8} \times \frac{16}{15}$ — again same as #9 and #10!

So: $\frac{18}{5} = 3\frac{3}{5}$

✔ Answer: $\boxed{\frac{18}{5}}$ or $\boxed{3\frac{3}{5}}$

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12) $3\frac{3}{8} \times 1\frac{2}{30}$

First, simplify $1\frac{2}{30}$:

- $\frac{2}{30} = \frac{1}{15}$, so $1\frac{2}{30} = 1\frac{1}{15} = \frac{16}{15}$

So this is same as #11!

Thus: $\frac{27}{8} \times \frac{16}{15} = \frac{18}{5} = 3\frac{3}{5}$

✔ Answer: $\boxed{\frac{18}{5}}$ or $\boxed{3\frac{3}{5}}$

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✔ Final Answers Summary:

| Problem | Answer |
|--------|--------|
| 1) | $\frac{1}{6}$ |
| 2) | $\frac{1}{12}$ |
| 3) | $\frac{1}{12}$ |
| 4) | $\frac{1}{36}$ |
| 5) | $\frac{1}{12}$ |
| 6) | $\frac{1}{6}$ |
| 7) | $\frac{5}{18}$ |
| 8) | $\frac{5}{9}$ |
| 9) | $\frac{18}{5}$ or $3\frac{3}{5}$ |
| 10) | $\frac{18}{5}$ or $3\frac{3}{5}$ |
| 11) | $\frac{18}{5}$ or $3\frac{3}{5}$ |
| 12) | $\frac{18}{5}$ or $3\frac{3}{5}$ |

Let me know if you'd like a visual explanation or simplification steps for any specific one!