Question

Multiply 4/9
by 1 3/4
. Write the answer in simplest form.

Answer 1

To multiply \( \frac{4}{9} \) by \( 1 \frac{3}{4} \), we first convert the mixed number \( 1 \frac{3}{4} \) into an improper fraction.

1. Convert \( 1 \frac{3}{4} \):
\[
1 \frac{3}{4} = \frac{4 \times 1 + 3}{4} = \frac{4 + 3}{4} = \frac{7}{4}
\]

2. Now, multiply \( \frac{4}{9} \) by \( \frac{7}{4} \):
\[
\frac{4}{9} \times \frac{7}{4} = \frac{4 \times 7}{9 \times 4} = \frac{28}{36}
\]

3. Simplify \( \frac{28}{36} \):
- Find the greatest common divisor (GCD) of 28 and 36. The GCD is 4.
- Divide both the numerator and denominator by 4:
\[
\frac{28 \div 4}{36 \div 4} = \frac{7}{9}
\]

Thus, the answer in simplest form is \( \frac{7}{9} \).