An exchange quote relates two units of money. Before multiplying or dividing, write which currency one unit of the other buys. This article uses imaginary currencies and a fixed fictional quote solely to explain the arithmetic.
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Write the relationship with its units
Suppose 1 unit of currency A equals 1.25 units of currency B. Converting 80 A to B gives 80 A × 1.25 B/A = 100 B.
The units show the direction: A cancels, leaving B. A bare number such as 'the exchange rate is 1.25' is incomplete unless its quotation convention is also clear.
Reverse the conversion consistently
For the reverse direction, 1 B equals 1/1.25 A, or 0.80 A. Thus 80 B convert to 64 A, not 100 A.
Using the same multiplier in both directions would fail a round-trip check. Under this frictionless fictional model, converting 80 A to 100 B and then back by division returns the original 80 A.
Separate a quote change from an amount change
If the relationship changed to 1 A = 1.50 B in another hypothetical comparison, one unit of A would buy more B. That statement describes the quotation direction; it does not require guessing which number should be called 'stronger' without naming the currencies.
The amount received also depends on the amount being converted. A larger receipt can arise from converting more money even when the exchange relationship itself stays unchanged.
Keep the arithmetic model limited
Actual conversions may involve different buying and selling quotes, fees and timing. The round-trip identity here assumes none of those effects, and the numbers are not current rates or a prediction about any currency.
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