📚 Percentage Increase and Decrease | 百分比增减
Percentages are one of the most practical topics in KS3 mathematics. You will meet them in shopping, banking, statistics and science. This revision guide covers percentage increase and decrease, percentage change, multipliers and reverse percentages, with clear examples and exam tips.
百分比是 KS3 数学中最实用的主题之一。你会在购物、银行、统计和科学中遇到它们。本复习指南涵盖百分比增减、百分比变化、乘数法和逆向百分比，并提供清晰的例子和考试提示。
1. What is a Percentage? | 什么是百分比？
A percentage is a fraction with a denominator of 100. The symbol % means "out of 100". For example, 35% means 35 out of 100, which can be written as 35/100 or 0.35.
百分比是分母为 100 的分数。符号 % 表示 "每一百份中的多少"。例如，35% 表示 100 份中的 35 份，可以写作 35/100 或 0.35。
Percentages allow us to compare quantities fairly when the totals are different. If one class has 18 out of 24 students passing a test and another has 20 out of 30, converting both to percentages shows which class performed better.
百分比使我们能够在总数不同的情况下公平地比较数量。如果一个班 24 名学生中有 18 人通过考试，另一个班 30 名学生中有 20 人通过，将两者都转换为百分比就可以看出哪个班表现更好。
2. Converting Percentages to Fractions and Decimals | 百分比与分数、小数的互化
rt a percentage to a fraction, write it over 100 and simplify if possible. For example, 45% o a decimal, divide by 100, which means moving the decimal point two places to the left: 7% = 0.07 and 120% = 1.20.
要将百分比转换为分数，先写成 100 的分母再化简。例如，45% = 45/100 = 9/20。要将百分比转换为小数，除以 100，即将小数点向左移动两位：7% = 0.07，120% = 1.20。
raction or decimal to a percentage, multiply by 100. For example, 3/5 = (3 ÷ 5) × 100 = 60%. For a decimal, 0.625 × 100 = 62.5%.
要将分数或小数转换为百分比，乘以 100。例如，3/5 = (3 ÷ 5) × 100 = 60%。对于小数，0.625 × 100 = 62.5%。
3. Finding a Percentage of an Amount | 求一个数的百分之几
To find a percentage of an amount without a calculator, first find 10% by dividing by 10, then build up. For example, to find 35% of 80: 10% of 80 = 8, 5% of 80 = 4, so 35% = 3 × 8 + 4 = 28.
不使用计算器求一个数的百分比时，先除以 10 求出 10%，再逐步组合。例如，求 80 的 35%：80 的 10% = 8，80 的 5% = 4，所以 35% = 3 × 8 + 4 = 28。
or calculator questions, convert the percentage to a decimal and multiply. For example, 18% of 240 = 0.18 × 240 = 43.2.
在计算器题目中，将百分比转换为小数后相乘。例如，240 的 18% = 0.18 × 240 = 43.2。
4. Percentage Increase Without a Calculator | 不使用计算器计算百分比增加
method is to find the increase, then add it to the original amount. For example, increase £60 by 15%. First find 15% of 60: 10% = 6, 5% = 3, so 15% = 9
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