📚 Percentage Increase and Decrease | 百分数的增加与减少
Percentage increase and decrease are core skills in the Cambridge KS3 mathematics curriculum. They appear in real-life contexts such as discounts, sales tax, interest, population growth, and profit calculations. This revision guide explains how to calculate percentage changes, use decimal multipliers, reverse a change to find an original amount, and handle repeated increases and decreases. Every method is shown with a worked example and a paired Chinese explanation to support independent study.
百分数的增加和减少是剑桥 KS3 数学课程中的核心技能。它们出现在现实生活场景中，例如折扣、销售税、利息、人口增长和利润计算。本复习指南将讲解如何计算百分数变化、使用小数乘数、逆推变化以求出原值，以及处理连续增减。每个方法都配有例题和对应的中文解释，以支持自主学习。
1. What is a percentage change? | 什么是百分数变化？
A percentage change compares the size of an increase or decrease to the original amount. The word ‘percent’ means ‘out of 100’, so writing a change as a percentage gives a standard way to compare different changes. For example, an increase of £10 on a £40 item is much larger than an increase of £10 on a £400 item.
百分数变化将增加量或减少量与原始数量进行比较。’百分’ 的意思是 ‘每一百份’，因此把变化写成百分数可以标准化地比较不同的变化。例如，在 40 英镑的商品上增加 10 英镑，比在 400 英镑的商品上增加 10 英镑幅度大得多。
The key formula is:
Percentage change = (change ÷ original) × 100
关键公式为：百分数变化 =（变化量 ÷ 原值）× 100。
If the new value is larger than the original, the change is an increase. If it is smaller, the change is a decrease. The original value is always the starting amount before the change.
如果新值大于原值，变化为增加；如果新值小于原值，变化为减少。原值始终是变化开始前的数量。
2. Percentage increase | 百分数增加
To increase an amount by a percentage, find the increase and add it to the original amount. The quickest method is to use a decimal multiplier.
要把一个数量增加某个百分数，先求出增加量，再加到原值上。最快的方法是使用小数乘数。
Example: Increase £80 by 15%.
例题：把 80 英镑增加 15%。
Step 1: 15% of £80 = 0.15 × 80 = £12.
步骤 1：80 英镑的 15% = 0.15 × 80 = 12 英镑。
Step 2: New amount = £80 + £12 = £92.
步骤 2：新金额 = 80 英镑 + 12 英镑 = 92 英镑。
A quicker method uses the multiplier 1 + p/100. For a 15% increase the multiplier is 1.15, so £80 × 1.15 = £92. This is because 100% + 15% = 115% = 1.15 as a decimal.
更快的方法是使用乘数 1 + p/100。增加 15% 的乘数是 1.15，所以 80 英镑 × 1.15 = 92 英镑。这是因为 100% + 15% = 115%，写成小数是 1.15。
New amount = original × (1 + p/100) for an increase
增加时：新金额 = 原值 ×（1 + p/100）。
3. Percentage decrease | 百分数减少
To decrease an amount by a percentage, subtract the decrease from the original amount. The multiplier method is also used here.
要把一个数量减少某个百分数，从原值中减去减少量。这里也使用乘数法。
Example: Decrease £80 by 15%.
例题：把 80 英镑减少 15%。
Step 1: 15% of £80 = 0.15 × 80 = £12.
步骤 1：80 英镑的 15% = 0.15 × 80 = 12 英镑。
Step 2: New amount = £80 − £12 = £68.
步骤 2：新金额 = 80 英镑 − 12 英镑 = 68 英镑。
The quick multiplier is 1 − p/100. For a 15% decrease, the multiplier is 0.85, so £80 × 0.85 = £68. This is because 100% − 15% = 85% = 0.85 as a decimal.
快速乘数是 1 − p/100。减少 15% 的乘数是 0.85，所以 80 英镑 × 0.85 = 68 英镑。这是因为 100% − 15% = 85%，写成小数是 0.85。
New amount = original × (1 − p/100) for a decrease
减少时：新金额 = 原值 ×（1 − p/100）。
Always check that a decrease gives a smaller answer, and an increase gives a larger answer. If your result goes in the wrong direction, you probably used the wrong multiplier.
始终检查：减少应得到较小的结果，增加应得到较大的结果。如果结果方向相反，你可能用错了乘数。
4. Using decimal multipliers | 使用小数乘数
Decimal multipliers turn a two-step percentage calculation into a single multiplication. They are especially useful for multi-step problems and for using a calculator.
小数乘数把两步百分数计算合并为一步乘法。它们对于多步问题和计算器使用尤其有用。
| Change | Meaning | Multiplier |
|---|---|---|
| Increase by 5% | 100% + 5% = 105% | 更多咨询请联系16621398022（同微信）
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