Solve a different way: evaluate 4 1/2 ÷ 1 1/3 + 2 1/3 - 3/4

• $4 \frac{1}{2} = \frac{(4 \times 2) + 1}{2} = \frac{8 + 1}{2} = \frac{9}{2}$
• $1 \frac{1}{3} = \frac{(1 \times 3) + 1}{3} = \frac{3 + 1}{3} = \frac{4}{3}$
• $2 \frac{1}{3} = \frac{(2 \times 3) + 1}{3} = \frac{6 + 1}{3} = \frac{7}{3}$

The expression becomes:
$\frac{9}{2} \div \frac{4}{3} + \frac{7}{3} - \frac{3}{4}$

To divide by a fraction, multiply by its reciprocal.
$\frac{9}{2} \div \frac{4}{3} = \frac{9}{2} \times \frac{3}{4} = \frac{9 \times 3}{2 \times 4} = \frac{27}{8}$

The expression now is:
$\frac{27}{8} + \frac{7}{3} - \frac{3}{4}$

First, find a common denominator for 8, 3, and 4. The least common multiple (LCM) of 8, 3, and 4 is 24.

Convert each fraction to have a denominator of 24:

• $\frac{27}{8} = \frac{27 \times 3}{8 \times 3} = \frac{81}{24}$
• $\frac{7}{3} = \frac{7 \times 8}{3 \times 8} = \frac{56}{24}$
• $\frac{3}{4} = \frac{3 \times 6}{4 \times 6} = \frac{18}{24}$

Substitute these back into the expression:
$\frac{81}{24} + \frac{56}{24} - \frac{18}{24}$

Now, perform the addition:
$\frac{81}{24} + \frac{56}{24} = \frac{81 + 56}{24} = \frac{137}{24}$

Finally, perform the subtraction:
$\frac{137}{24} - \frac{18}{24} = \frac{137 - 18}{24} = \frac{119}{24}$

Divide 119 by 24:
$119 \div 24 = 4$ with a remainder of $119 - (4 \times 24) = 119 - 96 = 23$.
So, $\frac{119}{24} = 4 \frac{23}{24}$.