Proportional Reasoning with Percents — Drills
Proportional Reasoning with Percents has 6 drill skills. Each one generates fresh questions every time, with a hint and full worked steps, so you can keep practising a single skill until it settles.
What these drills 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.
Basicpct
Unlimited questions of this kind are generated in the app. Two examples:
Problem 1
What is 25% of 120?
Worked answer
30
0.25 × 120 = 30
Problem 2
What is 40% of 80?
Worked answer
32
0.4 × 80 = 32
Multiplier
Unlimited questions of this kind are generated in the app. Two examples:
Problem 1
A $120 item has 40% tax added. Find the total.
Worked answer
168
100% + 40% = 140%
120 × 1.40 = 168
Problem 2
A $80 item is 10% off. Find the sale price.
Worked answer
72
100% - 10% = 90%
80 × 0.90 = 72
Pctchange
Unlimited questions of this kind are generated in the app. Two examples:
Problem 1
A value changes from 25 to 18.75. Find the percent decrease.
Worked answer
25
Change = |18.75 - 25| = 6.25
6.2525 = 0.25
= 25%
Problem 2
A value changes from 50 to 60. Find the percent increase.
Worked answer
20
Change = |60 - 50| = 10
1050 = 0.2
= 20%
Findoriginal
Unlimited questions of this kind are generated in the app. Two examples:
Problem 1
After adding a 10% tip, the amount is $88.00. What was the original?
Worked answer
80
original × 1.1 = 88.00
88.00 ÷ 1.1 = 80
Check: 80 × 1.1 = 88.00 ✓
Problem 2
After a 20% discount, the amount is $48.00. What was the original?
Worked answer
60
original × 0.8 = 48.00
48.00 ÷ 0.8 = 60
Check: 60 × 0.8 = 48.00 ✓
Successive
Unlimited questions of this kind are generated in the app. Two examples:
Problem 1
A price rises 30%, then falls 20%. The final price is what percent of the original?
Worked answer
104
Up: × 1.3
Down: × 0.80
1.3 × 0.80 = 1.04
= 104%
Problem 2
A price rises 10%, then falls 20%. The final price is what percent of the original?
Worked answer
88
Up: × 1.1
Down: × 0.80
1.1 × 0.80 = 0.88
= 88%
Converting units
Unlimited questions of this kind are generated in the app. Two examples:
Problem 1
Write 35 as a percent. (Enter just the number.)
Worked answer
60
3 ÷ 5 = 0.6
= 60%
Problem 2
Write 12 as a percent. (Enter just the number.)
Worked answer
50
1 ÷ 2 = 0.5
= 50%