An exchange rate like $£1 = €1.17$ always states how much foreign currency one unit of the base currency buys. This gives a simple rule:

• Converting away from the "1" currency (£ → €): multiply by the rate.
• Converting towards the "1" currency (€ → £): divide by the rate.

Take the reciprocal: if $A = R \times B$, then $1$ unit of $B$ is worth $\frac{1}{R}$ units of $A$.

Example: If $€1 = 0.95$ CHF, then $1$ CHF $= \dfrac{1}{0.95} \approx 1.05$ €. To convert 100 CHF to euros, multiply: $100 \times 1.05 = €105$.

Chain the two conversions, applying the multiply/divide rule at each stage — and keep full calculator precision between steps, only rounding the final answer.

Example: Convert 40 USD to AUD, given $1$ USD $=155.62$ JPY and $1$ AUD $=102.09$ JPY.

1. USD → JPY (away from the "1"): $40 \times 155.62 = 6224.80$ JPY.
2. JPY → AUD (towards the "1"): $6224.80 \div 102.09 \approx 60.97$ AUD.

Convert every price into the same currency first, then compare directly.

Example: A watch costs 98 CAD abroad, or £60 in England, with $£1=1.75$ CAD. Convert 98 CAD to pounds (towards the "1"): $98 \div 1.75 = £56$. The difference is $£60 - £56 = £4$ — the foreign watch is cheaper.

A currency conversion graph plots one currency against another as a straight line through the origin — so you can read off conversions directly, and for values beyond the drawn axes, find the gradient from any clear point on the line and apply it as a multiplier.

Example: A graph shows $£20=€23.40$. The rate is $€23.40 \div 20 = €1.17$ per pound, matching the same multiply/divide rule used algebraically.

A holiday spending money calculator uses the rate £1 = \1.28. Yusuf changes £350 into dollars, spends \300, then changes the rest back into pounds. How many pounds does he get back (to 2 d.p.)?

1. Convert £350 to dollars: 350 \times 1.28 = \448$.
2. Dollars remaining: 448 - 300 = \148$.
3. Convert back to pounds (towards the "1"): $148 \div 1.28 = £115.625 \approx £115.63$.