Question

1/9 x 4 1/5 write the answer in simplest form

Answer 1

To multiply the mixed number \(4 \frac{1}{5}\) by \(\frac{1}{9}\), we first convert the mixed number to an improper fraction.

1. Convert \(4 \frac{1}{5}\) to an improper fraction:
\[
4 \frac{1}{5} = \frac{4 \times 5 + 1}{5} = \frac{20 + 1}{5} = \frac{21}{5}
\]

2. Now, multiply \(\frac{1}{9}\) by \(\frac{21}{5}\):
\[
\frac{1}{9} \times \frac{21}{5} = \frac{1 \times 21}{9 \times 5} = \frac{21}{45}
\]

3. Simplify \(\frac{21}{45}\):
- Find the greatest common divisor (GCD) of 21 and 45. The GCD is 3.
- Divide both the numerator and denominator by their GCD:
\[
\frac{21 \div 3}{45 \div 3} = \frac{7}{15}
\]

The answer in simplest form is \(\frac{7}{15}\).