Currency


Currency    Conversions

If we take a rough approximation for the purposes of example, we will say that a Euro is worth $\frac{2}{3}$ of a Pound. So if we had 30 Euros, they would equal

\[ 30 \times \frac{2}{3} \ \mbox{Pounds} = 20 \ \mbox{Pounds} \]

When you think of it, that means that to go from Pounds to Euros you multiply by $\frac{3}{2}$ (i.e. 1.5), because 1.5 Euros would equal 1 Pound.


Mathematically, what we have done is to take the conversion rate for Euros to Pounds and used the reciprocal of this conversion rate when we needed the conversion rate from Pounds to Euros.


By the reciprocal, I mean we have stated it as (c.r. means conversion rate)

\[ \mbox{c.r. from Pounds to Euros} = \frac{1}{\mbox{c.r. from Euros to Pounds}} \]

(Note : the reciprocal of 9 is $\frac{1}{9}$, and the reciprocal of 4 is $\frac{1}{4}$, ... etc.)


Inserting numbers

\[ \mbox{c.r. from Pounds to Euros} = \frac{1}{\frac{2}{3}}\]

This expression simplifies to $\frac{3}{2}$.

To convince yourself of this, carry out the division in full

\[ \frac{1}{ 2/3} \] \[ = 1 \div \frac{2}{3} \] \[ = 1 \times \frac{3}{2} \] \[ = \frac{3}{2} \]

(to go from the second line to the third line, we changed the division sign to a multiplication sign, and inverted the second term)


So all we are saying is, that given a conversion rate between two currencies A and B, the conversion rate from B to A will be the reciprocal of this original conversion rate.

If the conversion rate from A to B is 2.45, then the conversion rate from B to A is

\[ \frac{1}{2.45} \]



Using our Euro-Pound conversion rate, let's try a couple of examples

£ 310.94 = 310.94 x $\frac{3}{2}$ = 466.41 Euros
£ 92 pounds = 92 x $\frac{3}{2}$ = 138 Euros
214 Euros = 240 x $\frac{3}{2}$ = £ 142.67 (rounded)
91.4 Euros = 91.4 x $\frac{3}{2}$ = £ 60.93 (rounded)


Assuming that

£ 1 = $ 1.64

(which is probably very different from the current rate), then

£ 90 = 90 x 1.64 = $ 147.60
£ 213.40 pounds = 213.40 x 1.64 = $ 349.976
$ 45 = $\frac{45}{1.64}$ = £ 27.44 (rounded)
$ 493.40 = $\frac{493.40}{1.64}$ = £ 300.85 (rounded)

It helps considerably to have a 'feel' for which currency is lowest and/or highest in value. It makes it easier to decide whether a division or multiplication is appropriate in any particular conversion.


Currency Converter


Past Exam Questions



George and Pat are going on holiday to Greece.

1. Pat exchanged £200 for 104 000 drachmas. George exchanged £350 at the same exchange rate. How many drachmas did George get?

  • A    18 200
  • B    59 428
  • C    182 000
  • D    673 076

2. Pat has a choice of 4 suitcases and wants to take the one that will hold the most. Which case has the biggest volume?

  • A    60cm x 45cm x 25cm
  • B    60cm x 50cm x 20cm
  • C    70cm x 50cm x 15cm
  • D    80cm x 45cm x 15cm


1. In a competition to win a holiday you have to decide which of the following amounts of foreign money is worth the most:

  • A   10 800 Danish kroner
  • B   9 285 French francs
  • C   2 610 000 Italian lire
  • D   2 000 Swiss francs

The local newspaper gives the current exchange rates as:

£1 = 12 Danish kroner
£1 = 10 French francs
£1 = 3 000 Italian lire
£1 = 2.5 Swiss francs


1. If the exchange rate is £1 = 2.5 Marks, how much is 200 Marks worth in pounds ?

  • A   £ 70
  • B   £ 80
  • C   £ 100
  • D   £ 500

2. On a particular day, the exchange rate between pounds and dollars is £1 = $1.59$. Which of these calculations show the value in pounds of $200. ?

  • A   1.59 ÷ 200
  • B   1.59 × 200
  • C   200 ÷ 1.59
  • D   200 × 1.59