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.
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Convert \( 3 \frac{1}{3} \): \[ 3 \frac{1}{3} = 3 \times 3 + 1 = 9 + 1 = \frac{10}{3} \]
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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 \( 2 \frac{2}{3} \).