Percentages and Discounts

What you’ll learn

Find a percentage of an amount and a discounted total.

រកភាគរយនៃបរិមាណ និងតម្លៃក្រោយបញ្ចុះ។

Meaning and use

Percent means per hundred. A percentage calculation must identify the base amount. A discount reduces the original price by a percentage of that original price. The discount amount and the final price answer different questions, so label them separately.

ភាគរយមានន័យថាក្នុងមួយរយ។ ត្រូវកំណត់បរិមាណគោលឱ្យច្បាស់។ ប្រាក់បញ្ចុះ និងតម្លៃចុងក្រោយជាចម្លើយពីរខុសគ្នា។

Formulas

Percentage amount

\[A=\frac{p}{100}B\]

Price after a discount

\[F=B\left(1-\frac{p}{100}\right)\]

Symbols and units

Symbol	Meaning	Unit or restriction
p	Percentage number, such as 15 for 15%	Percent
B	Original or base amount	Currency or the contextual quantity
A	Percentage amount	Same unit as B
F	Final amount after discount	Same unit as B

Conditions and limits

• The base must be identified before multiplying.
• For an ordinary discount, use 0 ≤ p ≤ 100 and assume no extra charges.
• ភាគរយត្រូវបម្លែងជា p/100 មុនគុណ។

Worked examples

A percentage of a class

Find 25% of 40 learners.

1. Convert \(25\%=25/100=0.25\).
2. Multiply \(0.25\times40=10\).

10 learners

25% ជាមួយភាគបួន ដូច្នេះ 40 ចែក 4 បាន 10។

A discounted price

A $50 bag has a 20% discount, with no other charge.

1. Discount \(50\times0.20=10\) dollars.
2. Final price \(50-10=40\) dollars.

$40

ត្រូវដកប្រាក់បញ្ចុះពីតម្លៃដើម ដើម្បីបានតម្លៃចុងក្រោយ។

Common mistakes

Instead of	Use	Why
20% of 50 = 20 × 50	20% of 50 = 0.20 × 50 = 10	Convert percent to a fraction of 100.
A $10 discount on $50 means the final price is $10.	The final price is $40.	A discount amount is not the remaining price.

Practice

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

សាកល្បងដោះស្រាយមុនបើកមើលចម្លើយ។ សូមបង្ហាញជំហាន និងឯកតាដែលពាក់ព័ន្ធ។

1. Find 10% of 80.
2. Find the final price after a 25% discount on $40, with no extra fees.
3. What percentage of 20 is 5?

Answers and steps

Show solutions / បង្ហាញដំណោះស្រាយ

1. 8

   10/100 × 80 = 8.

2. $30

   The discount is $10; 40 − 10 = 30.

3. 25%

   5/20 × 100 = 25.

Quick recap

• Percent means per hundred.
• Always identify the base.
• Separate discount amount from final price.