Q.
\( \frac{2}{3} \times \frac{4}{5} \) as a fraction

Answer

\( \frac{2}{3}\times\frac{4}{5}=\frac{2\cdot4}{3\cdot5}=\frac{8}{15} \)

Multiply numerators and denominators; the final result is \( \frac{8}{15} \).

Detailed Explanation

Problem: Multiply the fractions \( \frac{2}{3} \) and \( \frac{4}{5} \).

Write the product as a single fraction. When multiplying fractions, multiply the numerators together and the denominators together. So:

\[ \frac{2}{3} \times \frac{4}{5} = \frac{2 \times 4}{3 \times 5} \]
Compute the products in numerator and denominator separately.

Numerator: \(2 \times 4 = 8\).

Denominator: \(3 \times 5 = 15\).

Thus the product is \( \frac{8}{15} \).
Simplify the fraction if possible. Find the greatest common divisor of 8 and 15. The divisors of 8 are 1, 2, 4, 8; the divisors of 15 are 1, 3, 5, 15. The only common divisor is 1, so the fraction is already in lowest terms.

You can also check cancellation before multiplying: \(\gcd(2,5)=1\) and \(\gcd(4,3)=1\), so no cross-cancellation is possible.

\( \frac{8}{15} \)

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FAQs

What is \frac{2}{3} \times \frac{4}{5} as a fraction?

\frac{8}{15}. Multiply numerators and denominators: (2\times4)/(3\times5)=8/15, already in lowest terms.

How do you multiply two fractions?

Multiply numerators and multiply denominators: \frac{a}{b}\times\frac{c}{d}=\frac{ac}{bd}. Then reduce by any common factor (GCD).

Should I simplify before or after multiplying?

Either works. Simplifying before (cross-cancel) often makes arithmetic easier; after multiplying, divide numerator and denominator by their GCD to reduce.

Can I cancel 2 and 4 in this problem?

No. Cancellation is allowed only between a numerator and a denominator. Here 2 and 4 are both numerators, so you cannot cancel them.

What is \frac{8}{15} as a decimal and percent?

Decimal: 0.5333\ldots (0.5\overline{3}). Percent: approximately 53.333\ldots\%.

How do you multiply when one factor is a whole number, e.g., 3\times\frac{2}{5}?

Convert the whole number to a fraction: 3=\frac{3}{1}. Then \frac{3}{1}\times\frac{2}{5}=\frac{6}{5}, which equals 1\frac{1}{5}.

What about multiplying negative fractions?

Multiply absolute values normally; determine sign separately. Same sign gives positive, different signs give negative. Example: -\frac{2}{3}\times\frac{4}{5}=-\frac{8}{15}.

How do you handle improper fractions and turn the result into a mixed number?

Multiply to get an improper fraction, simplify, then divide numerator by denominator. Quotient is whole part; remainder over divisor is fractional part (e.g., \frac{20}{15}=\frac{4}{3}=1\frac{1}{3}).

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Q. \( \frac{2}{3} \times \frac{4}{5} \) as a fraction