GRADE 10 MATHS PROJECT About this question: evaluate 4 1/2 ÷ 1 1/3 + 2 1/3 - 3/4

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

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 is now:

$$\frac{27}{8} + \frac{7}{3} - \frac{3}{4}$$

The denominators are 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:

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

The expression becomes:

$$\frac{81}{24} + \frac{56}{24} - \frac{18}{24}$$

$$\frac{81}{24} + \frac{56}{24} = \frac{81 + 56}{24} = \frac{137}{24}$$

The expression is now:

$$\frac{137}{24} - \frac{18}{24}$$

Divide 119 by 24:

$$119 \div 24 = 4 \text{ with a remainder of } 23$$

So, $\frac{119}{24} = 4 \frac{23}{24}$.

The final answer is $4 \frac{23}{24}$.