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

Q: How do you compute \frac{4}{5}\times 3?

Treat 3 as \frac{3}{1} and multiply: \frac{4}{5}\times\frac{3}{1}=\frac{12}{5}.

Q: Why do we only multiply the numerator?

Writing 3 as \frac{3}{1} shows multiplication is numerator-by-numerator and denominator-by-denominator: \frac{4\times3}{5\times1}.

Q: What is \frac{12}{5} as a mixed number?

\frac{12}{5}=2\frac{2}{5} because 12 ÷ 5 = 2 remainder 2.

Q: What is \frac{12}{5} as a decimal?

\frac{12}{5}=2.4 (since 12 ÷ 5 = 2.4).

Q: What is \frac{12}{5} as a percent?

2.4 = 240\%, so \frac{12}{5}=240\%.

Q: How can I check my answer quickly?

Convert \frac{4}{5} to 0.8, then 0.8×3 = 2.4, matching \frac{12}{5}.

Answer

Multiply the numerator by 3: \( \frac{4}{5} \times 3 = \frac{12}{5} = 2\frac{2}{5} \).

Detailed Explanation

Write the whole number 3 as a fraction.

Any whole number can be written as a fraction by putting it over 1. So rewrite the problem as:

\[ \dfrac{4}{5} \times 3 = \dfrac{4}{5} \times \dfrac{3}{1} \]
Multiply the numerators and multiply the denominators.

When multiplying fractions, multiply the numerators together and the denominators together:

\[ \dfrac{4}{5} \times \dfrac{3}{1} = \dfrac{4 \times 3}{5 \times 1} = \dfrac{12}{5} \]
Simplify the fraction if possible.

The greatest common divisor of 12 and 5 is 1, so the fraction is already in simplest form.

Final answer as a fraction: \( \dfrac{12}{5} \)

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FAQs

How do you compute \( \frac{4}{5}\times 3\)?

Treat 3 as \( \frac{3}{1}\) and multiply: \( \frac{4}{5}\times\frac{3}{1}=\frac{12}{5}\).

Can I simplify before multiplying?

Check common factors between 3 and 5; none exist, so no cancellation. If there were common factors you can cancel first to simplify.

Why do we only multiply the numerator?

Writing 3 as \( \frac{3}{1}\) shows multiplication is numerator-by-numerator and denominator-by-denominator: \( \frac{4\times3}{5\times1}\).

What is \( \frac{12}{5}\) as a mixed number?

\( \frac{12}{5}=2\frac{2}{5}\) because 12 ÷ 5 = 2 remainder 2.

What is \( \frac{12}{5}\) as a decimal?

\( \frac{12}{5}=2.4\) (since 12 ÷ 5 = 2.4).

What is \( \frac{12}{5}\) as a percent?

\( 2.4 = 240\%\), so \( \frac{12}{5}=240\%\).

What common mistakes should I avoid?

Don’t multiply only the denominator or swap numerator/denominator. Also don’t forget to express whole numbers as fractions like \( \frac{3}{1}\).

How can I check my answer quickly?

Convert \( \frac{4}{5}\) to 0.8, then 0.8×3 = 2.4, matching \( \frac{12}{5}\).

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