📚 Percentages, Ratio and Proportion | 百分比、比与比例
Percentages, ratios and proportion form one of the most important bridges between arithmetic and algebra in the IGCSE Mathematics curriculum. Mastering these tools allows you to solve problems in finance, measurement, maps and everyday decision-making with confidence.
在 IGCSE 数学课程中，百分比、比与比例是连接算术与代数最关键的桥梁之一。掌握这些工具，你可以自信地解决涉及理财、测量、地图以及日常决策中的各类问题。
1. The Meaning of Percentage | 百分比的意义
A percentage is a fraction with denominator 100. The word percent comes from Latin and means "by hundred". So 8% means 8 parts out of every 100 equal parts, which is equivalent to the fraction 8/100 and the decimal 0.08.
百分比是分母为100的分数。percent 一词源自拉丁语，意思是“每一百”。因此，8% 表示在每100个相等部分中取8份，在数值上等于分数 8/100，也等于小数 0.08。
One of the key ideas is that percentage gives us a common scale for comparison. If one school class has 25% girls and another has 40% girls, we can compare their results even when the total numbers of students are different.
百分比的关键思想是提供了一个统一的比较尺度。如果一个班有25%的女生，另一个班有40%的女生，即使两个班总人数不同，我们也能直接比较这两个百分比。
| Percentage | Fraction | Decimal |
|---|---|---|
| 50% | 1/2 | 0.5 |
| 25% | 1/4 | 0.25 |
| 75% | 3/4 | 0.75 |
| 10% | 1/10 | 0.1 |
2. Converting Percentages, Fractions and Decimals | 百分比、分数与小数互化
raction to a percentage, multiply the fraction by 100. For example, 7/20 = 7/20 × 100 = 35%. To convert a percentage to a decimal, divide it by 100. For example, 35% = 35 ÷ 100 = 0.35.
把分数化成百分数，需要将分数乘以100。例如，7/20 = 7/20 × 100 = 35%。把百分数化成小数，则需要除以100。例如，35% = 35 ÷ 100 = 0.35。
Percentage = Fraction × 100 and Decimal = Percentage ÷ 100
To convert a decimal to a percentage, simply multiply by 100. For example, 0.72 × 100 = 72% rt a percentage to a fraction, write the percentage over 100 and simplify. For example, 35% = 35/100 = 7/20.
把小数化成百分数，只需将小数乘以100。例如，0.72 × 100 = 72%。把百分数化成分数时，先把百分数写成以100为分母的分数，再化简。例如，35% = 35/100 = 7/20。
These conversions must become automatic. You will often need the same value in different forms during a multi-step exam question.
这些互化必须做到熟练。在解答多步骤考试题时，你常常需要把同一个数值在不同形式之间转换。
3. Finding a Percentage of a Quantity | 求一个量的百分比
The fastest method for finding a percentage of a quantity is to use the decimal multiplier. Convert the percentage to a decimal and multiply it by the amount.
求一个量的百分比，最快的方法是使用小数乘数：把百分数化成小数，再与这个量相乘。
Answer = Percentage (as a decimal) × Amount
For example, find 15% of 80. Write 15% as 0.15, then 0.15 × 80 = 12. So 15% of 80 is 12.
例如，求80的15%。先把15%写成0.15，再计算 0.15 × 80 = 12。所以80的15%是12。
You can also use the 10% method when performing mental arithmetic. Since 10% of 80 is 8, and 5% of 80 is half of 8, which is 4, we get 8 + 4 = 12.
在心算时，也可以使用10%法。80的10%是8，80的5%是8的一半即4，所以 8 + 4 = 12。
Finding 10% of a number is the same as dividing it by 10.
求一个数的10%就等于把这个数除以10。
Finding 1% of a number is the same as dividing it by 100.
求一个数的1%就等于把这个数除以100。
Finding 50% of a number is the same as dividing it by 2.
求一个数的50%就等于把这个数除以2。
4. Percentage Increase and Decrease | 百分比的增加与减少
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