Currency Conversion

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Converting an amount from one currency to another by multiplying by the exchange rate.

An exchange rate expresses how much of currency B you get per unit of currency A. To convert an amount X from currency A to currency B, multiply by the rate: X_B = X_A · rate(A→B). The reverse rate is 1 / rate(A→B). When converting between two currencies that aren't directly quoted, use a cross-rate through a base currency (often USD or EUR): rate(A→C) = rate(A→B) · rate(B→C).

X_B = X_A · rate(A→B); rate(B→A) = 1 / rate(A→B)

• Convert 100 USD to EUR at 1 USD = 0.85 EUR → 100 · 0.85 = 85 EUR
• Convert 500 EUR to USD at 1 USD = 0.85 EUR → 500 / 0.85 ≈ 588.24 USD
• USD → GBP via EUR: 1 USD = 0.85 EUR, 1 EUR = 0.86 GBP → 100 USD = 100 · 0.85 · 0.86 = 73 GBP

How to recognize it

• Problem mentions currencies, exchange rates, or conversions
• A rate like '1 USD = 0.85 EUR' is given
• Questions may require reversing a rate or chaining through a base currency

Common mistakes

• Reversing the direction of the rate (using rate(A→B) when B→A is needed)
• Multiplying when you should divide or vice versa
• Rounding too aggressively before the final answer

Practice guidance

Numerical Reasoning