Proportional Reasoning with Percents — Practice
A percent is a rate out of 100. Turn it into a multiplier and every percent problem becomes one multiplication.
What these questions cover
These questions use 6 ideas from the course. Follow any of them for a definition, where it is taught, and what it leads to.
- Percent — Parts per hundred. 37% = 37100 = 0.37.
- Multiplier — The single number you multiply by. A 20% increase has multiplier 1.20.
- Discount — An increase / a decrease applied to a starting price.
- Net — A 3-D shape unfolded flat.
- Base — The number being multiplied. In 53 the base is 5.
- Percent increase — How much something grew, as a percentage of what it was.
Problem 1
What is 25% of 80?
Worked answer
20
0.25 × 80 = 20
Problem 2
Write 0.36 as a percent. (Enter just the number.)
Worked answer
36
0.36 = 36%
Problem 3
Write 720 as a percent. (Enter just the number.)
Worked answer
35
720 = 35100 = 35%
Problem 4
A shirt costs $40. Sales tax is 6%. How much is the tax?
Worked answer
2.40
0.06 × 40 = 2.40
Problem 5
A $60 item is 20% off. What is the sale price?
Worked answer
48
100% - 20% = 80%
60 × 0.80 = 48
Problem 6
A $85 jacket has 8% tax added. What is the total cost?
Worked answer
91.80
85 × 1.08 = 91.80
Problem 7
A price rises from $40 to $52. What is the percent increase?
Worked answer
30
Change = 52 - 40 = 12
1240 = 0.30
= 30% increase
Problem 8
A town's population falls from 8,000 to 7,200. What is the percent decrease?
Worked answer
10
Change = 8000 - 7200 = 800
8008000 = 0.10 = 10%
Problem 9
After a 25% discount, a game costs $36. What was the original price?
Worked answer
48
Sale price is 75% of the original
original × 0.75 = 36
36 ÷ 0.75 = 48
Check: 48 × 0.75 = 36 ✓
Problem 10
A bill including 20% tip came to $54. What was the bill before the tip?
Worked answer
45
bill × 1.20 = 54
54 ÷ 1.20 = 45
Problem 11
18 is what percent of 72?
Worked answer
25
1872 = 0.25
= 25%
Problem 12
30% of a number is 21. What is the number?
Worked answer
70
0.30n = 21
n = 21 ÷ 0.30 = 70
Problem 13
A price goes up 20%, then down 20%. The final price is what percent of the original?
Worked answer
96
Up 20%: multiplier 1.20
Down 20%: multiplier 0.80
1.20 × 0.80 = 0.96 = 96%
A 4% net decrease — the two changes are measured from different starting points.
Problem 14
A coat is marked down 30%, then another 10% off the sale price. What single percent discount is this equal to?
Worked answer
37
0.70 × 0.90 = 0.63
You pay 63%, so the discount is 100% - 63% = 37%
Not 40% — the second cut applies to a smaller amount.
Problem 15
A stock drops 20%. By what percent must it rise to return to its original value?
Worked answer
25
Say it started at 100; after the drop it is 80
It needs to gain 20
2080 = 0.25 = 25%
The gain is measured from the smaller number, so the percent is larger.
Problem 16
A $1,200 laptop is 15% off, then 8% tax is added to the sale price. Find the final cost.
Worked answer
1101.60
Sale: 1200 × 0.85 = 1020
Tax: 1020 × 1.08 = 1101.60
Or in one line: 1200 × 0.85 × 1.08 = 1101.60