(i)

a = bc

Make c the subject by dividing both sides by b.

c = $\frac{\mathrm{a}}{\mathrm{b}}$

n = $\frac{\mathrm{mk}}{\mathrm{ec}}$

n = mk ÷ ec ----- eqn 1

Substitute c = $\frac{\mathrm{a}}{\mathrm{b}}$ into ---- eqn 1

n = mk ÷ (e x $\frac{\mathrm{a}}{\mathrm{b}}$)

n = mk ÷ $\frac{\mathrm{ae}}{\mathrm{b}}$

Reciprocate the fraction at the right of the ÷ and change ÷ to multiplication (x)

Note: reciprocate means the numerator becomes the denominator and the denominator becomes the numerator.

n = mk x $\frac{\mathrm{b}}{\mathrm{ae}}$

Get rid of the fraction by multiplying both sides by the denominator ae.

n x ae = mk x b

aen = bmk

Divide both sides by bm

k = $\frac{\mathrm{aen}}{\mathrm{bm}}$

(ii)

When a = $\frac{1}{2}$, b = -4, e = 3, m = 7 and n = -5.

k = $\frac{\frac{1}{2}x\mathrm{3\; x\; -5}}{\mathrm{-4\; x\; 7}}$

k = $\frac{\frac{-15}{2}}{-28}$

k = $\frac{-15}{2}$ ÷ -28

The negatives cancel each other.

k = $\frac{15}{2}$ ÷ 28

Every number is being divided by 1.

28 = $\frac{28}{1}$

k = $\frac{15}{2}$ ÷ $\frac{28}{1}$

Reciprocate the fraction at the right of the ÷ and change ÷ to multiplication (x)

Note: reciprocate means the numerator becomes the denominator and the denominator becomes the numerator.

k = $\frac{15}{2}$ x $\frac{1}{28}$

k = $\frac{\mathrm{15\; x\; 1}}{\mathrm{2\; x\; 28}}$ = $\frac{15}{56}$

k = 0.26786 ≈ 0.268 (three significant figures)