Converting currency - explanation of formula?

Question

If I want to convert between currencies, and I have the strength of other currencies, in (for example) relation to one pound, how do I convert between them?

Lets say £1 equals:
Canadian Dollars $0.45
US Dollars $0.6
Euro €1.74


First of all, how do I convert £300 into the other currencies?
Then, how do I convert 200 of the other currencies into pounds?
Then, how would I convert, between the other currencies, for example, €350 into US$?

I know there is a formula for this, but I cant find it and I keep getting confused with when to use division and when to use multiplication.

What I do not want is to be linked to a currency converter or to just give the answers to my theoretical questions - ideally, I am looking for the formulas to understand how this all works.

Como wrote:

€1.74 = £1
€350 = 350/01.74 x £1 = £201.15

£1 = $1.60
£201.15 = $321.84 ( and this is €350 (from above)

Thanks - that's excellent, but in the last part you put £1 = $1.60 - should that have been £1 = $0.6, which would give £120.69? Or have I missed something somewhere because I'm not sure where the 1.6 came from.?

Answer 1

£300 = 300 x 0.45 Canadian $ =135 Canadian $
£300 = 300 x 0.6 US $ = 180 US $
£300 = 300 x €1.74 = € 522

0.45 C$ = £1
200C$ = 200/0.45 x £1 = £444.44

$0.60 = £1
$200 = 200/0.60 x £1 = £333.33

€1.74 = £1
€200 = 200/1.74 x £1 = £114.94

€1.74 = £1
€350 = 350/01.74 x £1 = £201.15

£1 = $1.60
£201.15 = $321.84 ( and this is €350 (from above)

Answer 2

This is all kind of complicated, as bankers like to complicate things.There are two kinds of currency rates:

1) DIRECT quote which gives the amount of national currency payed for one unit of foregn currency.
Example:
Japanise banker may say that the rate of yen is Y210 per pound.
If that Japanise bank wants to buy 1000 pound,
the payment will be
"amount of foreign currency" * "DIRECT quote" =
1000 * 210 = 210,000 Yen.

2) INVERSE quote which gives the amount of foreign currency payed for one unit of foregn currency.
Example:
British banker may say that the rate of yen is Y210 per pound.
If that British bank wants to buy 1,000,000 Yen,
the payment will be
"amount of foreign currency" / "INVERSE quote" =
1,000,000 / 210 = 4762 pound.

Historically centuries ago the british pound was the primary
currency, thus traditionally all national currences were
quoted in DIRECT with respect to the pound,
i.e. how many say US dollars are paid for one pound.
This rate used to have a special ticker CBL
pronounced 'cable', after transatlantic cable which caried
this key finantial ingformation from London to New York.

Later the role of the primary currency was assumed by US
dollar, for this reason all other rates are quoted in DIRECT
with respect to the USD.

Answer 3

Multiply the initial number of pounds by the exchange rate to get the corresponding amoutn of other currency.

Answer 4

Set up ratio:

£1 : $0.45 :: £ 300 : x

Convert the ratio to equal fractions:
1/0.45 = 300/x

cross multiply
(1)(x) = (300)(.45)
x = $135

Answer 5

Check out www.yahoo.co.uk/finance