Q. What is \( \frac{3}{8} \times \frac{2}{5} \) as a fraction?

Q: How do you multiply fractions?

Multiply numerators and denominators: \frac{a}{b}\times\frac{c}{d}=\frac{ac}{bd} . For these: \frac{3}{8}\times\frac{2}{5}=\frac{6}{40} , then simplify.

Q: What is the final simplified answer?

The product simplified is \frac{3}{20} .

Q: How do I convert \frac{3}{20} to a decimal?

Divide numerator by denominator: \frac{3}{20}=0.15 .

Q: How do I convert \frac{3}{20} to a percent?

How do I convert \frac{3}{20} to a percent?

Q: Can I multiply a fraction by a whole number?

Yes. Treat the whole number n as \frac{n}{1} . Example: 3\times\frac{2}{5}=\frac{3}{1}\times\frac{2}{5}=\frac{6}{5}.

Answer

\(\frac{3}{8}\times\frac{2}{5}=\frac{3\cdot2}{8\cdot5}=\frac{6}{40}=\frac{3}{20}\)

Detailed Explanation

Step 1 — multiply numerators and multiply denominators separately.
\[ \frac{3}{8} \times \frac{2}{5} = \frac{3 \times 2}{8 \times 5} = \frac{6}{40} \]
Step 2 — simplify the fraction by dividing numerator and denominator by their greatest common divisor. The greatest common divisor of 6 and 40 is 2, so divide both by 2:
\[ \frac{6}{40} = \frac{6 \div 2}{40 \div 2} = \frac{3}{20} \]
Alternative (cross-cancellation before multiplying) — notice 2 (numerator) and 8 (denominator) share a common factor 2, so reduce them first:
\[ \frac{3}{8} \times \frac{2}{5} = \frac{3}{4} \times \frac{1}{5} = \frac{3}{4 \times 5} = \frac{3}{20} \]

Final answer: \[ \frac{3}{20} \]

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FAQs

How do you multiply fractions?

Multiply numerators and denominators: \( \frac{a}{b}\times\frac{c}{d}=\frac{ac}{bd} \). For these: \( \frac{3}{8}\times\frac{2}{5}=\frac{6}{40} \), then simplify.

Should I simplify before or after multiplying?

Either works, but simplifying (cross-canceling) first keeps numbers small. Here 2 and 8 cancel: \( \frac{3}{8}\times\frac{2}{5}=\frac{3}{4}\times\frac{1}{5}=\frac{3}{20} \).

What is cross-cancellation?

Canceling common factors between any numerator and any denominator before multiplying. Example: 2 and 8 reduce to 1 and 4, giving \( \frac{3}{4}\times\frac{1}{5}=\frac{3}{20} \).

What is the final simplified answer?

The product simplified is \( \frac{3}{20} \).

How do I convert \( \frac{3}{20} \) to a decimal?

Divide numerator by denominator: \( \frac{3}{20}=0.15 \).

How do I convert \( \frac{3}{20} \) to a percent?

Can I multiply a fraction by a whole number?

Yes. Treat the whole number n as \( \frac{n}{1} \). Example: \(3\times\frac{2}{5}=\frac{3}{1}\times\frac{2}{5}=\frac{6}{5}\).

Why do we multiply numerators and denominators?

Fraction multiplication scales numerators and denominators independently; algebraically \( \frac{a}{b}\times\frac{c}{d}=\frac{ac}{bd} \), which preserves the proportion of the product.

Multiply numerators and denominators.
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