Foreign Currency | 外币兑换

📚 Foreign Currency | 外币兑换

When you travel or buy goods from another country, you need to exchange your money. The rate at which one currency is swapped for another is called the exchange rate. In IGCSE Maths, you often need to convert amounts, compare rates, and solve practical problems involving commission and profit.

当旅行或购买外国商品时，你需要兑换货币。一种货币与另一种货币兑换的比率称为汇率。在 IGCSE 数学中，你常常需要换算金额、比较不同汇率，并解决涉及手续费和利润的实际问题。

1. Exchange Rate Basics | 汇率基础

An exchange rate tells you how much of one currency you get for one unit of another currency. For example, if the rate is £1 = $1.25, then every British pound can be exchanged for 1.25 US dollars.

汇率告诉你在兑换另一种货币的一个单位时，你能得到多少本国货币。例如，如果汇率是 £1 = $1.25，那么每 1 英镑可以兑换 1.25 美元。

Exchange rates are usually given in pairs, like £1 = €1.18 or $1 = ¥110. The currency on the left is the ‘base’ and the right is the ‘quoted’ currency.

汇率通常成对给出，例如 £1 = €1.18 或 $1 = ¥110。左侧货币是“基准货币”，右侧是“报价货币”。

2. Converting from Foreign to Home Currency | 外币兑换成本币

To find how many home currency units you receive for an amount of foreign money, multiply the foreign amount by the exchange rate (home per foreign).

要计算你用一定数量的外币能换回多少本币，需将外币金额乘以汇率（本币每外币）。

Home currency = Foreign amount × Exchange rate (home per foreign)

本币金额 = 外币金额 × 汇率（本币/外币）

Example: £1 = $1.25. Convert $80 into pounds. Since £1 = $1.25, divide $80 by 1.25: 80 ÷ 1.25 = £64.

例：£1 = $1.25。将 80 美元换算成英镑。因为 £1 = $1.25，用 80 ÷ 1.25 = 64 英镑。

3. Converting in the Reverse Direction | 反向兑换

If you know the rate home → foreign, you can find the reverse rate by using reciprocals. For example, if £1 = $1.25, then $1 = £(1 ÷ 1.25) = £0.80.

如果你知道本币 → 外币的汇率，可以通过倒数得到反向汇率。例如，若 £1 = $1.25，则 $1 = £(1 ÷ 1.25) = £0.80。

This is useful when the bank quotes rates differently or when you need to compare offers.

当银行报价方式不同或需要比较方案时，这种方法非常有用。

4. Using Exchange Rate Tables | 使用汇率表

Often rates are shown in a table. You must read the table carefully to know which factor to multiply or divide.

汇率常以表格形式呈现。必须仔细阅读表格，以确定是乘还是除。

Currency	Rate per £1
US Dollar ($)	1.25
Euro (€)	1.18
Japanese Yen (¥)	140

From the table, £1 = €1.18. To convert £50 to euros, multiply 50 × 1.18 = €59.

从上表可知 £1 = €1.18。将 50 英镑换成欧元，计算 50 × 1.18 = 59 欧元。

5. Commission and Fees | 手续费与佣金

Banks often charge a fee or commission on top of the exchange. You subtract this from the amount you receive.

银行通常会在兑换基础上收取手续费或佣金。你需要从兑换金额中减去这个费用。

Amount received = Converted amount − Commission

实际到账金额 = 兑换金额 − 手续费

Example: Convert £200 to US dollars at $1.25 per £1, with a commission of £4. First, 200 × 1.25 = $250. The commission is paid from your pounds, so you actually give £200 + £4? No – the commission is usually taken in the currency you hand over. You need 204 pounds or the bank deducts from the result. We will clarify: if a fee of 2% is charged on the foreign amount, subtract 2% of the converted amount.

例：以 £1 = $1.25 兑换 200 英镑，佣金为 4 英镑。先算 200 × 1.25 = 250 美元。如果手续费直接从英镑中扣除，则需要 204 英镑；若从外币中扣除，则到手金额为 250 − 4 = 246 美元。请看清楚题目要求。

6. Comparing Exchange Offers | 比较兑换方案

You may need to decide which provider gives the best deal. This requires converting the same amount using each rate and considering any fees.

你可能需要判断哪家兑换商最划算。这需要将相同金额按不同汇率换算，并考虑各项费用。

List the rates and fees.
Calculate the final amount received for the same starting amount.
Choose the largest final amount (or smallest cost).

列出汇率和费用。
用同一初始金额计算最终到手金额。
选择到手金额最大（或成本最低）的方案。

7. Multi-step Conversions | 多步兑换

Sometimes you have to exchange currency via a third currency, for example from pounds to dollars and then dollars to euros. Multiply all the rates together to find the overall effect.

有时需要通过第三种货币进行兑换，例如从英镑换成美元，再换成欧元。将所有汇率相乘，即可得到整体兑换率。

Final amount = Starting amount × Rate₁ × Rate₂ × …

最终金额 = 初始金额 × 汇率₁ × 汇率₂ × …

Example: £1 = $1.25 and $1 = €0.82. So £1 = 1.25 × 0.82 = €1.025.

例：£1 = $1.25，$1 = €0.82。所以 £1 = 1.25 × 0.82 = €1.025。

8. Ratio and Proportion | 比例与比值

Foreign currency problems can be solved using direct proportion. If you know the rate between two currencies, you can set up a ratio equation.

外币问题可以用正比例来解决。如果知道两种货币之间的汇率，就可以建立比例方程。

For example, if £5 = €6, then how many euros for £32? Set up: £5/€6 = £32/x. Cross-multiply: 5x = 6 × 32 → x = 38.4 euros.

例如，若 £5 = €6，则 32 英镑能换多少欧元？建立比例：£5/€6 = £32/x。交叉相乘：5x = 6 × 32 → x = 38.4 欧元。

9. Practical Problems | 实际问题

IGCSE questions often involve buying goods abroad, claiming tax refunds, or converting leftover cash. You must identify the correct operation and check units.

IGCSE 考题常涉及在国外购物、退税或兑换剩余现金。你需要确定正确的运算并检查单位。

Remember: always round appropriately. If an exchange rate is given to 3 decimal places, your answer may need rounding to two decimal places for money.

记住：要适当取近似值。如果汇率保留三位小数，金额答案通常保留两位小数。

10. Worked Example | 例题解析

Jane travels to the USA. The exchange rate is £1 = $1.25. She changes £400 and receives a 2% commission. How many dollars does she get?

Jane 去美国旅行。汇率为 £1 = $1.25。她兑换 400 英镑，银行收取 2% 佣金。她能拿到多少美元？

Step 1: Convert without commission: 400 × 1.25 = $500.

步骤 1：不计佣金兑换：400 × 1.25 = $500。

Step 2: Commission = 2% of £400 = £8. She only has £392 to exchange. 392 × 1.25 = $490.

步骤 2：佣金 = 400 × 2% = 8 英镑。实际用于兑换的金额为 392 英镑。392 × 1.25 = 490 美元。

So she receives $490.

因此她得到 490 美元。

Published by TutorHao | Mathematics Revision Series | aleveler.com

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Foreign Currency | 外币兑换