To divide \( 4 \frac{1}{3} \) by \( 2 \frac{1}{4} \), we first convert the mixed numbers into improper fractions.
-
Convert \( 4 \frac{1}{3} \): \[ 4 \frac{1}{3} = 4 \times 3 + 1 = 12 + 1 = 13 \quad \Rightarrow \quad \frac{13}{3} \]
-
Convert \( 2 \frac{1}{4} \): \[ 2 \frac{1}{4} = 2 \times 4 + 1 = 8 + 1 = 9 \quad \Rightarrow \quad \frac{9}{4} \]
Now, we divide \( \frac{13}{3} \) by \( \frac{9}{4} \): \[ \frac{13}{3} \div \frac{9}{4} = \frac{13}{3} \times \frac{4}{9} \]
Next, multiply the fractions: \[ = \frac{13 \times 4}{3 \times 9} = \frac{52}{27} \]
To convert \( \frac{52}{27} \) back to a mixed number, we divide 52 by 27:
- \( 52 \div 27 = 1 \) (whole number) with a remainder of \( 52 - 27 = 25 \).
Thus, we can write: \[ \frac{52}{27} = 1 \frac{25}{27} \]
So, the final answer is: \[ 4 \frac{1}{3} \div 2 \frac{1}{4} = 1 \frac{25}{27} \]