Questions: 1 4/5 × 3/5 State your answer as a mixed number in simplest form.

Solution Steps

To solve the problem of multiplying a mixed number by a fraction, follow these steps:

1. Convert the mixed number to an improper fraction.
2. Multiply the improper fraction by the given fraction.
3. Simplify the resulting fraction if possible.
4. Convert the simplified fraction back to a mixed number.

The mixed number \( 1 \frac{4}{5} \) can be converted to an improper fraction as follows: \[ 1 \frac{4}{5} = \frac{1 \times 5 + 4}{5} = \frac{9}{5} \]

Next, we multiply the improper fraction \( \frac{9}{5} \) by the fraction \( \frac{3}{5} \): \[ \frac{9}{5} \times \frac{3}{5} = \frac{27}{25} \]

To convert \( \frac{27}{25} \) to a mixed number, we divide the numerator by the denominator: \[ 27 \div 25 = 1 \quad \text{(whole number)} \] The remainder is: \[ 27 - (25 \times 1) = 2 \] Thus, we can express \( \frac{27}{25} \) as the mixed number: \[ 1 \frac{2}{25} \]

Final Answer