Multiply 2/3 by 1 1/4. Write answer in simplest form.

Answer 1

To multiply \( \frac{2}{3} \) by \( 1 \frac{1}{4} \), we first need to convert the mixed number \( 1 \frac{1}{4} \) into an improper fraction.

1. Convert \( 1 \frac{1}{4} \):

   • Multiply the whole number (1) by the denominator (4): \( 1 \times 4 = 4 \).
   • Add the numerator (1): \( 4 + 1 = 5 \).
   • Therefore, \( 1 \frac{1}{4} = \frac{5}{4} \).

2. Now, multiply \( \frac{2}{3} \) by \( \frac{5}{4} \): \[ \frac{2}{3} \times \frac{5}{4} = \frac{2 \times 5}{3 \times 4} = \frac{10}{12}. \]

3. Simplify \( \frac{10}{12} \):

   • The greatest common divisor (GCD) of 10 and 12 is 2.
   • Divide the numerator and the denominator by 2: \[ \frac{10 \div 2}{12 \div 2} = \frac{5}{6}. \]

Thus, the answer in simplest form is \( \frac{5}{6} \).