Practice · Grade 7 percentages
Percent Off — Practice
Practice problems on “X% off” in rising difficulty, plus a boss problem. Find the saving, amount due, and reverse to the original price. Grade 7, free.
Q1 of 7
0 correct
How much do you save at 30% off?
30% of $120
Quick answer
What's the best way to practice percent off?
Work several problems in rising difficulty: first the saving with price · X ÷ 100, then the amount due as price · (1 − X ÷ 100), and finally the reverse — the original price with paid ÷ (1 − X ÷ 100). Do a quick check after each problem and finish with a boss problem on reversing a discount — going backward you divide, you do not add the discount back on.
HowTo
A 4-step solving strategy
This order works for any discount — whether you need the saving, the amount due, or the original price.
- 1Step 1 of 4
Identify the problem type
Forward (price and discount rate given → find saving or amount due) or backward (price paid and discount rate given → find original price)? This diagnosis decides whether you multiply or divide.
- 2Step 2 of 4
Build the remaining factor
The remaining factor is 1 − X ÷ 100. At 30% off it is 0.7, at 40% off 0.6. It tells you which share of the price you still pay.
- 3Step 3 of 4
Compute forward
Saving = price · X ÷ 100. Amount due = price − saving = price · remaining factor. Example: 120 · 0.7 = $84.
- 4Step 4 of 4
Reverse and check
Original price = paid ÷ remaining factor (84 ÷ 0.7 = 120). Check: 120 · 0.7 = 84 ✓. Only then is the problem done.
Examples
Worked practice examples with full working
Four typical problem types. Try each one yourself first, then compare with the solution.
Easy
30% off $120 — what do you save, what do you pay?
Saving: 120 · 30 ÷ 100 = $36
Amount due: 120 − 36 = $84
Check: 120 · 0.7 = 84 ✓
Classic forward problem. Don't mix up the saving and the amount due.
Medium
40% off $250 — what do you pay?
Saving: 250 · 40 ÷ 100 = $100
Amount due: 250 − 100 = $150
short: 250 · 0.6 = $150
Check: 150 + 100 = 250 ✓
The remaining factor 0.6 saves a step: multiply by 0.6 directly.
Medium
Original price: $84 paid after 30% off
Remaining factor: 1 − 30 ÷ 100 = 0.7
84 ÷ 0.7 = $120
Check: 120 · 0.7 = 84 ✓
Going backward you divide. 84 · 1.3 = 109.20 would be the typical mistake.
Hard
Boss: $180 paid after 40% off — original price?
Remaining factor: 1 − 40 ÷ 100 = 0.6
180 ÷ 0.6 = $300
Check: 300 · 0.6 = 180 ✓
Bigger discount, smaller remaining factor — the original price is well above what you paid.
Pitfalls
Common mistakes — and how to avoid them
These five traps show up in almost every test.
Reversing with · instead of ÷
You don't recover the original by adding the discount back: 84 · 1.3 = 109.20 ≠ 120. Divide by the remaining factor: 84 ÷ 0.7 = $120.
Reading the saving as the amount due
At 30% off $120 the saving is $36 and you pay $84. Read carefully whether the problem asks for the amount saved or the amount to pay.
Wrong remaining factor
At 30% off you pay 70%, so the factor is 0.7 — not 0.3. The remaining factor is always 1 minus the discount share.
Assuming percentage points
“30% off” means 30% of the price, not 30 cents or 30 units. It is always a share of the original price.
Misplaced decimal
120 · 30 ÷ 100 = 36, not 360 or 3.6. Divide by 100 at the end — a place-value slip throws off the whole result.
Study
Practice with a plan — three short tips
15 minutes at a time, not 90 in one go
Three short practice sessions on three days stick far better than one long session the night before the test (spaced repetition).
Solve first, then look at the solution
Write out your working before you reveal the hint. Active recall is three to four times more effective for learning than passive reading.
For every wrong answer, ask why
Multiplied backward instead of dividing? Mixed up saving and amount due? Misplaced a decimal? Note the cause — you'll spot the mistake instantly next time.
FAQ
Frequently asked questions about practising
Glossary
Terms in one sentence
- X% off
- A reduction of X percent on the price.
- Saving
- The amount saved: price · X ÷ 100.
- Amount due
- The price after the discount is taken off: price − saving.
- Remaining factor
- (1 − X ÷ 100) — the share of the price you still pay (0.7 at 30% off).
- Original price
- The list price before the discount, i.e. 100%.
- Reverse calculation
- Going from the price paid back to the original: paid ÷ remaining factor.
- Boss problem
- The last and hardest question of a practice set, combining several steps.