find the unit rate 3 1/3 divided by 1 1/4

1 answer

To find the unit rate of \( 3 \frac{1}{3} \) divided by \( 1 \frac{1}{4} \), we first need to convert these mixed numbers into improper fractions.

  1. Convert \( 3 \frac{1}{3} \): \[ 3 \frac{1}{3} = 3 \times 3 + 1 = 9 + 1 = \frac{10}{3} \]

  2. Convert \( 1 \frac{1}{4} \): \[ 1 \frac{1}{4} = 1 \times 4 + 1 = 4 + 1 = \frac{5}{4} \]

Now, we need to divide \( \frac{10}{3} \) by \( \frac{5}{4} \). Dividing fractions involves multiplying by the reciprocal:

\[ \frac{10}{3} \div \frac{5}{4} = \frac{10}{3} \times \frac{4}{5} \]

Now, we perform the multiplication:

\[ = \frac{10 \times 4}{3 \times 5} = \frac{40}{15} \]

Next, we simplify \( \frac{40}{15} \) by finding the greatest common divisor (GCD) of 40 and 15, which is 5:

\[ \frac{40 \div 5}{15 \div 5} = \frac{8}{3} \]

This fraction, \( \frac{8}{3} \), can also be converted back into a mixed number:

\[ \frac{8}{3} = 2 \frac{2}{3} \]

Thus, the unit rate of \( 3 \frac{1}{3} \) divided by \( 1 \frac{1}{4} \) is \( \frac{8}{3} \) or \( 2 \frac{2}{3} \).