Practice · Grade 7 percentages
Discount Practice Problems
Training problems on final price, savings, and discount percent — in rising difficulty, with a hint and full working for every question. Free.
Q1 of 6
0 correct
Find the final price: 20% off $50.
$50 − 20%
Quick answer
How do I practice discount problems?
Drill the two basic problems separately: the final price given a discount rate (saving = price · discount rate ÷ 100, then subtract) and the discount percent from the original and sale price ((original − sale) ÷ original · 100). For each question, first decide what is given and what is asked, write down the working, and check with the factor trick — at p% off you pay (100 − p)%.
HowTo
A 4-step solving strategy
This order fits every discount problem — whether you need the final price, the saving, or the discount percent.
- 1Step 1 of 4
Clarify given vs. wanted
Is the discount rate in percent stated? Then you want the saving or final price. Are the original and sale price both given? Then you want the discount percent. This distinction fixes the formula.
- 2Step 2 of 4
Pick the right formula
Saving = price · discount rate ÷ 100. Final price = price − saving, or shorter price · (1 − discount rate ÷ 100). Discount percent = (original − sale) ÷ original · 100.
- 3Step 3 of 4
Plug in and compute
Substitute the numbers: first compute the saving (multiply, then divide by 100), then subtract. Example: 49 · 30 ÷ 100 = 14.70, so 49 − 14.70 = $34.30.
- 4Step 4 of 4
Check the result
Sanity-check with the factor: at 30% off you pay 70%, so 49 · 0.7 = $34.30 — it fits. Watch whether the problem wants the saving or the final price.
Examples
Worked practice examples
Four typical clearance-sale problems. Try each yourself first, then compare with the working.
Easy
Final price: 20% off $50
Saving = 50 · 20 ÷ 100
= 1000 ÷ 100 = $10
Final = 50 − 10 = $40
Check with the factor: 50 · 0.8 = $40 ✓
Basic type: find the saving first, then subtract from the price.
Medium
Final price: 30% off $49
Saving = 49 · 30 ÷ 100
= 1470 ÷ 100 = $14.70
Final = 49 − 14.70 = $34.30
Check: 49 · 0.7 = $34.30 ✓
Decimal result — round to cents.
Medium
Percent off: $120 → $90
(original − sale) ÷ original · 100
(120 − 90) ÷ 120 · 100
30 ÷ 120 · 100 = 25%
Check: 120 · 0.75 = $90 ✓
Here you want the discount rate. Difference over the original price, then times 100.
Hard
Boss: final price with 12.5% off $39.90
Saving = 39.90 · 12.5 ÷ 100
= 498.75 ÷ 100 = $4.9875
Final = 39.90 − 4.9875 = $34.9125
Check: 39.90 · 0.875 = $34.9125 ✓
Awkward price and awkward rate — the factor 0.875 is the fastest path.
Pitfalls
Common mistakes — and how to avoid them
These five traps show up in almost every discount problem.
Confusing saving with final price
At 25% off $80 the saving is $20 and the final price is $60. Read carefully whether the reduction or the amount to pay is wanted.
Adding discounts
20% then another 10% is not 30%. The second discount applies to the already reduced price: 0.8 · 0.9 = 0.72 → 28% total discount.
Wrong reference value
A discount is always relative to the original price. From $80 to $60 is 25% off — measured against $60 you would wrongly get 33%.
Forgetting the hundredth
25% means 25 ÷ 100 = 0.25, not 25. Computing 80 · 25 gives a hundred times the discount.
Rounding wrong
Round money to two places (cents), but only at the end. Rounding intermediate results too early introduces rounding errors.
Study
Practice with a plan — three short tips
15 minutes at a time, not 90
Three short sessions on three days stick better than one long session the night before a test. It is called spaced practice.
Solve first, then look at the answer
Write down your working before you reveal the hint. Active recall is far more effective for learning than passive reading.
Use the factor trick to verify
Solve each problem once via the saving and once via the factor (1 − p ÷ 100). If both routes agree, the result is reliably correct.
FAQ
Frequently asked questions about practicing
Glossary
Terms in one sentence
- Original price
- The price before any discount — the whole, equal to 100%.
- Discount rate
- The reduction in percent, e.g. 25%.
- Discount amount
- The saving in money: price · discount rate ÷ 100.
- Final price
- The price to pay after the discount is taken off.
- Remaining factor
- (1 − discount rate ÷ 100). At 25% it is 0.75 and leads straight to the final price.
- Cash discount
- A discount for fast payment, usually 2–3%.
- Boss question
- The last and hardest problem in a practice set, combining several traps.