Read the first worked example with the solution open so the structure is clear.
Try the practice problems before revealing each solution.
Use the related concepts and background knowledge badges if you feel stuck.
What to Focus On
Core idea:A percent rewrites any comparison as a count out of 100 so different things can be compared on one scale.
Common stuck point:The procedure for percentages is the easy part; the trap is using the percent number directly without dividing by 100. Asking "Is the quantity being measured against a scale of 100?" first is what keeps a correct-looking calculation from being attached to the wrong concept.
Sense of Study hint:Ask: Is the quantity being measured against a scale of 100?
Worked Examples
Example 1
easy
What is 25% of $80?25% = 1 out of 4 equal parts — what is 1 part of $80?
Answer
$20
First step
1
Recall that "percent" means per hundred, so 25%=10025=0.25 as a decimal.
Full solution
2
Multiply the decimal by the whole amount: 0.25×80.
3
Calculate: 0.25×80=20
Finding a percentage of a number means multiplying the number by the percentage expressed as a decimal (or fraction). 25% is the same as 41.
Example 2
medium
A student scored 42 out of 60 on a test. What is the percentage score?42 out of 60 = 7 out of 10 = 70%
Example 3
easy
Convert 107 to a percent.7 out of 10 parts shaded — convert 7/10 to a percent
Example 4
medium
A store discounts a $120 item by 35%. Find the sale price.
Example 5
medium
A poll shows 45% favor candidate A and 40% favor candidate B. The rest are undecided. What percent are undecided?45% + 40% = 85% decided; remaining 3/20 = ? percent undecided
Example 6
hard
A college's enrollment rose from 2,400 to 3,000. By what percent did it rise?
Example 7
challenge
60% of the students in a school are girls; 30% of the girls play sports, and 40% of the boys play sports. What percent of the school plays sports?
Practice Problems
Try these problems on your own first, then open the solution to compare your method.
Example 1
easy
What is 15% of 200?15% = 3 out of 20 parts — shaded region = 30
Example 2
medium
If 18 is 30% of a number, what is the number?
Example 3
easy
Write 25% as a fraction in simplest form.25% shaded out of 100% whole = 1/4
Example 4
easy
Write 40% as a decimal.
Example 5
easy
Compute 20% of 80.
Example 6
easy
Compute 50% of 60.50% = 1/2 of 60 — shaded half = 30
Example 7
easy
What is 10% of 250?
Example 8
easy
Write 43 as a percent.3 out of 4 parts shaded — what percent is 3/4?
Example 9
easy
What percent of 200 is 50?50 out of 200 = 1/4 — what percent is shaded?
Example 10
easy
Compute 5% of 400.
Example 11
medium
15% of 80.
Example 12
medium
A shirt costs $40. With 25% off, what's the sale price?25% discount leaves 75% — 3 out of 4 parts remain at $30
Example 13
medium
30% of a number is 24. What is the number?
Example 14
medium
What percent increase from 50 to 60?
Example 15
medium
A bag holds 80 marbles, of which 30% are red. How many are NOT red?3 out of 10 parts = 30% red; unshaded 7/10 = 70% = 56 marbles not red
Example 16
medium
A price increases from $40 to $50. What is the percent increase?
Example 17
medium
Tax is 8%. A meal costs $50 before tax. Total cost?
Example 18
medium
A stock fell 20%, then rose 25%. Net change?
Example 19
medium
45 is what percent of 60?
Example 20
challenge
An item is marked up 50% above cost. Then a 20% discount is applied to the marked-up price. What is the final price as a percent of cost?
Example 21
challenge
A test has 80% pass rate. If 60 students passed, how many took the test?
Example 22
challenge
Simple interest at 4%/year on $2000 for 3 years. What's the total?
Example 23
easy
Write 60% as a fraction in simplest form.60% shaded = 3 out of 5 parts — write as a simplified fraction
Example 24
easy
Write 0.7 as a percent.
Example 25
easy
Compute 40% of 90.40% = 2 out of 5 parts of 90 — shaded region = 36
Example 26
easy
What percent of 60 is 15?15 out of 60 = 1/4 — what percent is 1 part out of 4?
Example 27
medium
A book has 320 pages. You've read 40%. How many pages have you read?40% of 320 pages = 2 out of 5 parts = 128 pages
Example 28
medium
The population of a town increased from 4,500 to 5,400. What is the percent increase?
Example 29
medium
A test had 25 questions. You got 20 right. Find your percent score.20 right out of 25 = 4 out of 5 parts — what percent score is this?
Example 30
medium
A meal costs $30 plus 7% tax and an 18% tip on the pre-tax amount. What is the total?
Example 31
medium
A class has 45 students; 92 are in band. What percent are in band?
Example 32
medium
A price drops from $60 to $45. What is the percent decrease?
Example 33
medium
15% of x is 36. Find x.
Example 34
medium
A $50 ticket goes up 12%. What is the new price?
Example 35
hard
A stock rises 10% Monday, then falls 10% Tuesday. What is the percent change over the two days?
Example 36
hard
A car's value depreciates by 20% in the first year and another 15% in the second. If it originally cost $30{,}000, what is its value after two years?
Example 37
hard
Simple interest at 5% per year on a $1{,}600 deposit. How much interest is earned in 3 years?
Example 38
hard
After a 25% discount, a coat costs $90. What was the original price?
Example 39
challenge
An item is marked up 40% above cost, then put on sale at 25% off the marked price. What is the final price as a percent of cost?