(ii) Simplify (2¹/₄ + 1⁵/₈) ÷ 3⁷/₁₆

$$2\frac{1}{4} = \frac{(2 \times 4) + 1}{4} = \frac{8 + 1}{4} = \frac{9}{4}$$ $$1\frac{5}{8} = \frac{(1 \times 8) + 5}{8} = \frac{8 + 5}{8} = \frac{13}{8}$$ $$3\frac{7}{16} = \frac{(3 \times 16) + 7}{16} = \frac{48 + 7}{16} = \frac{55}{16}$$

To add $\frac{9}{4}$ and $\frac{13}{8}$, find a common denominator, which is 8.

$$\frac{9}{4} + \frac{13}{8} = \frac{9 \times 2}{4 \times 2} + \frac{13}{8} = \frac{18}{8} + \frac{13}{8} = \frac{18 + 13}{8} = \frac{31}{8}$$

Now the expression is $\frac{31}{8} \div \frac{55}{16}$.
To divide by a fraction, multiply by its reciprocal.

$$\frac{31}{8} \div \frac{55}{16} = \frac{31}{8} \times \frac{16}{55}$$

$$\frac{31 \times 16}{8 \times 55}$$

Notice that 16 can be divided by 8.

$$\frac{31 \times (8 \times 2)}{8 \times 55} = \frac{31 \times 2}{55} = \frac{62}{55}$$

The simplified value is $\mathbf{\frac{62}{55}}$.