Percentage Change and Successive Changes

What you’ll learn

Compare a change with its original base.

ប្រៀបធៀបការផ្លាស់ប្ដូរទៅនឹងបរិមាណដើម។

Meaning and use

Percentage change divides the change by the original amount. Positive and negative results indicate increase and decrease under this convention. Successive percentage changes multiply factors because the second change uses a new base. Equal increases and decreases do not generally cancel.

អត្រាបម្រែបម្រួលភាគរយយកបម្រែបម្រួលចែកតម្លៃដើម។ ការប្ដូរជាប់គ្នាប្រើបរិមាណគោលថ្មី ដូច្នេះត្រូវគុណមេគុណ មិនបូកភាគរយតែម្ដងទេ។

Formulas

Percentage change

\[p=\frac{N-O}{O}\times100\%\]

Successive factors

\[F=O(1+r_1)(1+r_2)\]

Symbols and units

Symbol	Meaning	Unit or restriction
O	Original positive amount	Contextual unit
N, F	New or final amount	Same unit as O
p	Signed percentage change	Percent
r₁, r₂	Signed changes as decimals	Dimensionless

Conditions and limits

• Original amount O must be positive for the ordinary comparison here.
• Use decimal rates in factors: 10% becomes 0.10.
• ការប្រែប្រួលលើកទីពីរគិតលើតម្លៃក្រោយលើកទីមួយ។

Worked examples

An increase

A quantity rises from 80 to 100.

1. Change \(100-80=20\).
2. Percentage change \((20/80)\times100\%=25\%\).

25% increase

តម្លៃដើម 80 ជាភាគបែង។

Up and then down

Start with 100, increase by 10%, then decrease by 10%.

1. First amount \(100\times1.10=110\).
2. Then \(110\times0.90=99\).

99, a net 1% decrease

ការថយ 10% គិតលើ 110 មិនមែន 100។

Common mistakes

Instead of	Use	Why
Increase from 80 to 100 is 20%.	It is 25%.	Divide the change by the original 80, not the new 100.
+10% then −10% always returns the original value.	The combined factor is 1.10 × 0.90 = 0.99.	Successive changes use different bases.

Practice

Solve these before revealing the worked solutions. Include units where relevant.

សាកល្បងដោះស្រាយមុនបើកមើលចម្លើយ។ សូមបង្ហាញជំហាន និងឯកតាដែលពាក់ព័ន្ធ។

1. Find the percentage increase from 50 to 60.
2. Find the percentage decrease from 200 to 150.
3. Increase 80 by 25%, then reduce the result by 20%.

Answers and steps

Show solutions / បង្ហាញដំណោះស្រាយ

1. 20%

   (60 − 50)/50 × 100 = 20.

2. 25% decrease

   (200 − 150)/200 × 100 = 25.

3. 80

   80 × 1.25 = 100; 100 × 0.80 = 80. These particular factors are reciprocal.

Quick recap

• Use the original base.
• Multiply factors for successive changes.
• Equal opposite percentages need not cancel.