例題 1 Example 1：百分變化 Percentage change
一個手袋的價錢由 $80 增至 $92，求百分增加。The price of a bag rises from $80 to $92. Find the percentage increase.
92 − 80 = 12- 除以原價：
12 / 80 = 0.15Divide by the original price:12 / 80 = 0.15
答案： Answer: 15%
【百分比公式：百分增減、逆向百分比及折扣】Percentage Formulas: Percentage Change, Reverse Percentage and Discount
SketchMath 數學團隊 SketchMath Maths Team ｜ 更新 Updated 2026-10-20
百分變化 = (新值 − 原值) / 原值 × 100%。增加 r% 就乘以 (1 + r%)，減少就乘以 (1 − r%)。要求原值（逆向百分比），便用新值除以該乘數。Percentage change = (new − old) / old × 100%. To increase by r% multiply by (1 + r%); to decrease multiply by (1 − r%). To find the original amount, divide the new amount by that multiplier.
百分比公式一覽 Percentage Formulas
部分佔整體的百分比Percentage of a whole
part / whole × 100%百分變化Percentage change
(new − old) / old × 100%增加／減少 r%Increase / decrease by r%
new = old × (1 + r%) / new = old × (1 − r%)逆向百分比（求原值）Reverse percentage (find the original)
old = new ÷ (1 ± r%)連續百分變化Successive changes把各個乘數相乘，不可把百分率相加Multiply the multipliers, never add the percentages
利潤及折扣Profit and discount
profit % = profit / cost × 100%, selling price = marked price × (1 − d%)百分比公式例題詳解 Worked Examples
例題 2 Example 2：逆向百分比 Reverse percentage
一件外套打八折後售 $360，求標價。After a 20% discount a jacket costs $360. Find its marked price.
- 售價是標價的
80%：標價 × 0.8 = 360The selling price is80%of the marked price:marked × 0.8 = 360 marked = 360 ÷ 0.8
答案： Answer: $450
例題 3 Example 3：連續百分變化 Successive percentage changes
某價錢先增加 10%，再減少 10%，求整體的百分變化。A price is increased by 10% and then decreased by 10%. Find the overall percentage change.
1.10 × 0.90 = 0.99- 最終價錢是原價的 99%。The final price is 99% of the original.
答案： Answer: 減少 1%（並非不變）。A decrease of 1% (not 0%).
💡 應試陷阱與秘訣 Exam Traps & Secrets
⚠️ 基數永遠是原值 The base is always the original由 $80 加到 $92 是增加 15%（除以 80）；由 $92 回到 $80 則是減少約 13.0%（除以 92），並非 15%。A price that goes from $80 to $92 is a 15% rise (÷80). Going back from $92 to $80 is a fall of about 13.0% (÷92), not 15%.
⚠️ 逆向百分比：要除，不要減 Reverse percentage: divide, do not subtract若 $360 是折扣 20% 後的價錢，原價是
360 ÷ 0.8 = 450。把 360 加上它的 20%（得 $432）是錯的。If $360 is the price after a 20% discount, the original is 360 ÷ 0.8 = 450. Adding 20% of 360 gives $432, which is wrong.✏️ 自我測試：互動練習 Self-Test: Interactive Practice
溫習方法：點擊以下任何題目，即時在坐標網格載入並核對計算步驟。How to study: click any question to load it on the coordinate grid and check your steps.
(逆向百分比 Reverse percentage)一件恤衫打七五折後售 $240，求原價。A shirt costs $240 after a 25% discount. Find the original price.
(百分變化 Percentage change)某鎮人口由 12 500 增至 13 750，求百分增加。The population of a town grows from 12 500 to 13 750. Find the percentage increase.
(連續變化 Successive changes)某價錢先加 20% 再減 20%，求整體變化。A price rises by 20% then falls by 20%. Find the overall change.
百分比公式練習題（DSE 模擬題） Exercises: DSE-Style Practice
SketchMath 題庫內的 DSE 風格練習，選擇題及長題目均附解答。 DSE-style practice from the SketchMath question bank, with solutions for every MC and long question.
百分法（一） · 中一
39 條選擇題 39 MC · 26 條長題目 26 long questions
百分法（二） · 中三
76 條選擇題 76 MC · 52 條長題目 52 long questions
DSE 溫習：百分法 · 中六
10 條選擇題 10 MC · 8 條長題目 8 long questions
常見問題 Frequently Asked Questions
用新值減原值，除以原值，再乘以 100%。答案為負數即是減少。
Subtract the old value from the new one, divide by the old value and multiply by 100%. A negative answer is a decrease.
第二次變化是以較大的新值計算。乘數 1.1 與 0.9 相乘得 0.99，所以結果低 1%。
The second change is taken on the new, larger amount. The multipliers 1.1 and 0.9 give 0.99, so the result is 1% lower.
用售價除以餘下百分比（小數）。打八折，便除以 0.8。
Divide the selling price by the remaining percentage as a decimal. After 20% off, divide by 0.8.