📚 KS3 Maths: Percentage Increase and Decrease | KS3 数学：百分数的增加与减少
Percentage increase and decrease are essential skills in the Cambridge KS3 Mathematics curriculum. They appear in word problems about prices, discounts, interest, profit, tax and data changes. This article explains the core methods, common formulas and exam strategies step by step.
百分数增加与减少是剑桥 KS3 数学课程中的基本技能。它们经常出现在关于价格、折扣、利息、利润、税收和数据变化的文字题中。本文将逐步讲解核心方法、常用公式和考试策略。
1. Understanding Percentages | 理解百分数
A percentage is a number expressed as a fraction of 100. The symbol % means ‘out of 100’, so 45% means 45 out of 100, or 45/100. In decimal form, 45% is 0.45.
百分数是以 100 为分母的分数。符号 % 表示“每一百份中”，所以 45% 表示 100 份中的 45 份，即 45/100。写成小数就是 0.45。
| Percentage | Decimal | Fraction | 中文含义 |
|---|---|---|---|
| 25% | 0.25 | 1/4 | 四分之一 |
| 50% | 0.5 | 1/2 | 二分之一 |
| 75% | 0.75 | 3/4 | 四分之三 |
| 10% | 0.1 | 1/10 | 十分之一 |
| 5% | 0.05 | 1/20 | 二十分之一 |
Being able to switch quickly between percentages, decimals and fractions makes all percentage calculations easier.
能够快速在百分数、小数和分数之间转换，会让所有百分数计算变得更加简单。
2. Finding a Percentage of a Quantity | 求一个数量的百分之几
To find p% of a quantity N, first write p% as a decimal by dividing by 100. Then multiply the decimal by N. For example, 15% of 240 is 0.15 × 240 = 36.
求某个量 N 的 p%，先把 p% 除以 100 写成小数。然后用这个小数乘以 N。例如，240 的 15% 是 0.15 × 240 = 36。
p% of N = (p ÷ 100) × N
Always check that your answer makes sense. A useful benchmark is 10%. For 240, 10% is 24, so 15% should be 24 + 12 = 36.
始终检查答案是否合理。10% 是一个有用的基准。对于 240，10% 是 24，因此 15% 应该是 24 + 12 = 36。
3. Percentage Increase | 百分数增加
Percentage increase describes how much a value grows compared with its original amount. The increase is always measured against the original value, not the new value.
百分数增加描述一个值相对于原始值增长了多少。增加量始终是相对于原始值来衡量的，而不是相对于新值。
Percentage increase = (increase ÷ original) × 100%
To find a new value directly, add the increase to the original. If a quantity increases by r%, its new value can also be written as original × (1 + r/100).
要直接求新值，将增加量加到原始值上。如果一个量增加了 r%，它的新值也可以写成 原始值 × (1 + r/100)。
Example: a school club had
Published by TutorHao | KS3 Mathematics Revision Series | aleveler.com
更多咨询请联系16621398022（同微信）
屏轩国际教育cambridge primary/secondary checkpoint, cat4, ukiset,ukcat,igcse,alevel,PAT,STEP,MAT, ibdp,ap,ssat,sat,sat2课程辅导，国外大学本科硕士研究生博士课程论文辅导