Calculating a percentage of an amount is useful when working with discounts, test results, budgets, statistics and many other everyday quantities.
In this lesson you will practise several ways to find a percentage of an amount and learn how to choose a method that fits the numbers.
Goal: calculate percentages of quantities using benchmark percentages, decomposition and decimal multiplication.
Before you start
Review Percentages and Where We Use Them.
You should already understand that percent means per hundred and that a percentage always refers to some quantity.
Paper or a private note may help with the practice activities.
What does finding a percentage of an amount mean?
Suppose you want to find:
25% of 80
This asks you to find the quantity represented by 25 parts out of every 100 parts of 80.
Because 25% is equivalent to one quarter:
25% of 80 = 20
Always identify the whole amount
Before calculating, ask:
What quantity represents 100%?
For example, if an item originally costs 500 units of money, then the original 500 represents 100% of that price.
A 20% discount is calculated from that original amount.
Strategy 1: Find 50% by halving
Fifty percent means one half.
To find:
50% of 84
divide 84 by 2:
84 divided by 2 = 42
Therefore:
50% of 84 = 42
Practice 1
Find:
50% of 150
Answer
75
Strategy 2: Find 25% by finding one quarter
Twenty five percent is equivalent to one quarter.
Find:
25% of 120
Divide by 4:
120 divided by 4 = 30
Therefore:
25% of 120 = 30
Practice 2
Find:
25% of 200
Answer
50
Strategy 3: Find 10% by dividing by ten
Ten percent is one tenth of a quantity.
Find:
10% of 360
Divide by 10:
360 divided by 10 = 36
Therefore:
10% of 360 = 36
Why 10% is especially useful
Many other percentages can be built from 10%.
For example:
- 20% is twice 10%
- 30% is three times 10%
- 5% is half of 10%
- 15% is 10% plus 5%
Strategy 4: Build 20% from 10%
Find:
20% of 450
First find 10%:
10% of 450 = 45
Twenty percent is twice that amount:
20% of 450 = 90
Practice 3
Find:
30% of 240
Suggested solution
Ten percent of 240 is:
24
Three groups of 24 give:
72
Therefore:
30% of 240 = 72
Strategy 5: Find 5% by halving 10%
Find:
5% of 180
First find 10%:
10% of 180 = 18
Five percent is half of 18:
5% of 180 = 9
Practice 4
Find:
5% of 500
Answer
Ten percent is 50.
Half of 50 is:
25
Strategy 6: Build 15% from 10% and 5%
Find:
15% of 300
Ten percent is:
30
Five percent is:
15
Add them:
30 + 15 = 45
Therefore:
15% of 300 = 45
Strategy 7: Find 1%
One percent means one hundredth.
Find:
1% of 700
Divide by 100:
700 divided by 100 = 7
Therefore:
1% of 700 = 7
Build another percentage from 1%
Suppose you need:
7% of 700
If 1% is 7, then seven groups of 7 give:
49
Therefore:
7% of 700 = 49
Strategy 8: Use several benchmark percentages
Find:
35% of 200
You can split 35% into:
25% + 10%
Twenty five percent of 200 is:
50
Ten percent is:
20
So:
35% of 200 = 70
There can be several good decompositions
For 35%, you could also use:
30% + 5%
If both methods are performed correctly, they produce the same result.
Choose the decomposition that makes the numbers easiest for you to work with.
Strategy 9: Convert the percentage to a decimal
A percentage can be converted to decimal form by dividing by 100.
For example:
32% = 0.32
To find:
32% of 250
calculate:
0.32 × 250 = 80
Therefore:
32% of 250 = 80
Why decimal multiplication works
Thirty two percent means:
32/100
which is:
0.32
Multiplying by 0.32 finds that proportion of the original quantity.
Choose the most useful method
For:
25% of 160
recognizing 25% as one quarter is probably very efficient.
For:
37% of 240
decimal multiplication may be more convenient.
There is no requirement to use the same method for every percentage.
Everyday example: calculate a discount
An item costs 600 units of money and has a 20% discount.
First find 10%:
10% of 600 = 60
Then double it:
20% of 600 = 120
The discount amount is 120 units of money.
Find the sale price
The original price was:
600
The discount was:
120
Subtract:
600 less 120 = 480
The sale price is 480 units of money.
Discount amount and sale price are different
If an item has a 20% discount, 20% of the original price is the amount removed.
The sale price is the amount remaining after that discount is subtracted.
Do not report the discount amount as the final price.
Another way to find the sale price
If 20% is removed, then 80% remains.
You could therefore calculate:
80% of 600 = 480
This reaches the same sale price directly.
Everyday example: a test score
A test contains 50 marks.
A learner earns 80% of the available marks.
Ten percent of 50 is 5.
Eight groups of 5 give:
40
So 80% of 50 marks is 40 marks.
Everyday example: a budget category
A simple example budget contains 2,000 units of money.
Suppose 30% is planned for one category.
Ten percent is:
200
Thirty percent is:
600
The planned amount for that category is 600 units of money.
Everyday example: completed work
A project contains 120 equal tasks.
Seventy five percent are complete.
Since 75% is three quarters:
120 divided by 4 = 30
Three quarters is:
3 × 30 = 90
So 90 tasks are complete.
Everyday example: survey respondents
A survey has 400 responses.
Sixty percent choose one answer.
Ten percent of 400 is 40.
Six groups of 40 give:
240
So 240 respondents selected that answer.
Estimate before calculating
Suppose you need:
48% of 200
Forty eight percent is close to 50%.
Half of 200 is 100.
So you should expect the exact answer to be slightly less than 100.
The exact value is:
96
The estimate supports the result.
Use benchmarks to detect errors
Suppose someone says:
20% of 300 = 240
Twenty percent is less than one quarter.
One quarter of 300 is 75.
Therefore 240 cannot be a reasonable answer.
If the percentage is below 100%
For a positive quantity, a percentage below 100% should produce an amount smaller than the whole.
For example:
40% of 500
must be less than 500.
If your result is larger, check the calculation.
If the percentage is greater than 100%
A percentage above 100% can produce a result greater than the original quantity.
For example:
125% of 80
One hundred percent is 80.
Twenty five percent is 20.
So:
125% of 80 = 100
Practice 5: Find 10%
Find:
10% of 470
Answer
47
Practice 6: Find 20%
Find:
20% of 350
Answer
Ten percent is 35.
Double it:
70
Practice 7: Find 5%
Find:
5% of 260
Answer
Ten percent is 26.
Half of 26 is:
13
Practice 8: Find 15%
Find:
15% of 400
Answer
Ten percent is 40.
Five percent is 20.
So:
15% of 400 = 60
Practice 9: Find 75%
Find:
75% of 160
Answer
Seventy five percent is three quarters.
One quarter of 160 is 40.
Three quarters is:
120
Practice 10: Use decimal multiplication
Find:
36% of 250
Answer
Convert 36% to:
0.36
Then:
0.36 × 250 = 90
Practice 11: Calculate a discount
An item costs 900 units of money and has a 30% discount.
What is the discount amount?
Answer
Ten percent of 900 is 90.
Thirty percent is:
270
Practice 12: Find the sale price
Using the previous example, the original price is 900 and the discount is 270.
Calculate:
900 less 270 = 630
The sale price is 630 units of money.
Practice 13: Estimate first
Without calculating exactly, estimate:
51% of 600
Suggested estimate
Fifty one percent is close to 50%.
Half of 600 is 300.
So the exact answer should be slightly greater than 300.
The exact answer is:
306
Activity: Choose the easiest strategy
For each calculation, decide which method you would choose before calculating.
- 50% of 340
- 25% of 240
- 15% of 600
- 7% of 500
- 38% of 250
- 75% of 80
Possible strategies include:
- halving
- finding one quarter
- building from 10%
- building from 1%
- using several benchmark percentages
- decimal multiplication
Possible activity solutions
1.
50% of 340 = 170
2.
25% of 240 = 60
3.
15% of 600 = 90
4.
7% of 500 = 35
5.
38% of 250 = 95
6.
75% of 80 = 60
Common mistakes to avoid
- forgetting which quantity represents 100%
- using the percentage number as though it were already a decimal
- confusing the discount amount with the final sale price
- forgetting to adjust when building one percentage from another
- using an unnecessarily difficult method when a simple benchmark works
- accepting an answer that is unreasonable compared with the original quantity
Percentage calculation checklist
Before calculating, ask:
- What quantity represents 100%?
- What percentage do I need?
- Can I use 50%, 25%, 10%, 5% or 1%?
- Can I combine benchmark percentages?
- Would decimal multiplication be easier?
- Do I need the percentage amount or the remaining amount?
- What approximate answer should I expect?
- Does my final result make sense?
Self check
- Why is finding 10% useful for many other percentage calculations?
- How can you find 5% after finding 10%?
- How can a percentage be used as a decimal multiplier?
- Why is the discount amount different from the sale price?
- How can estimation help check a percentage calculation?
Suggested answers
- Many percentages can be built by multiplying, halving or combining 10% amounts.
- Five percent is half of 10%, so halve the 10% amount.
- Convert the percentage to decimal form by dividing by 100, then multiply by the original quantity.
- The discount is the amount removed, while the sale price is what remains after that amount is subtracted.
- An estimate gives an expected size for the answer and can reveal an unreasonable result.
Lesson summary
There are several reliable ways to calculate a percentage of an amount.
Benchmark percentages such as 50%, 25%, 10%, 5% and 1% make many calculations easy to perform mentally.
Other percentages can be built by combining those benchmarks or by converting the percentage to a decimal and multiplying.
Always identify the whole quantity, distinguish the percentage amount from any remaining amount and check that your answer is reasonable.
Continue learning
Review Percentages and Where We Use Them if you need to review fraction, decimal and percentage relationships.
Review Practical Number Sense for Everyday Mathematics for estimation and flexible mental calculation strategies.