Practice · Grade 7 Percentages
Percentage Decrease — Practice
Percentage-decrease practice problems in rising difficulty, plus a boss question. Hint and worked solution per task. Grade 7, free.
Q1 of 7
0 correct
What is the decrease in percent?
250 → 200
Quick answer
How do I best practise percentage decrease?
Work several problems in rising difficulty: first the decrease in percent from two values with (old − new) ÷ old · 100, then the new value after a p% decrease with value · (1 − p ÷ 100). Always relate to the old value, do a quick check after each task, and finish with a boss question that chains two decreases — understanding beats guessing.
HowTo
A 4-step solving strategy
This order works for any decrease — whether you want the decrease in percent or the new value.
- 1Step 1 of 4
Identify the task type
Do you have two values (old and new) and want the decrease in percent? Or do you have a value and a percentage and want the new value? This diagnosis decides which formula you need.
- 2Step 2 of 4
Find the drop
With two values: old − new (e.g. 250 − 200 = 50). When applying a percentage: value · p ÷ 100 (e.g. 250 · 20 ÷ 100 = 50).
- 3Step 3 of 4
Relate or subtract
For the decrease in percent: drop ÷ old value · 100. For the new value: old value − drop. Shortcut: times factor (1 − p ÷ 100).
- 4Step 4 of 4
Check your answer
Plug the result back: a 20% decrease must give 250 · 0.8 = 200. Only then is the task truly solved.
Examples
Worked practice examples with full working
Four typical task types. Try each yourself first, then compare with the solution.
Easy
Find the decrease: 250 → 200
Drop: 250 − 200 = 50
50 ÷ 250 = 0.2
0.2 · 100 = 20%
Check: 250 · 0.8 = 200 ✓
Classic form: two values, find the decrease in percent. Always relate to the old value.
Easy
Find the decrease: 80 → 60
Drop: 80 − 60 = 20
20 ÷ 80 = 0.25
0.25 · 100 = 25%
Check: 80 · 0.75 = 60 ✓
Same as above. The reference is 80 — not the new value.
Medium
Reduce 120 by 15%
15% of 120: 120 · 15 ÷ 100 = 18
120 − 18 = 102
Check: 120 · 0.85 = 102 ✓
Here the percentage is given. First find the drop, then subtract — or just multiply by 0.85.
Hard
Boss: 500 drops by 10% twice
1st decrease: 500 · 0.9 = 450
2nd decrease: 450 · 0.9 = 405
short: 500 · 0.9 · 0.9 = 500 · 0.81 = 405
Check: 405 ÷ 500 = 0.81 → 19% total decrease ✓
Two 10% decreases do not make 20%, because the second acts on the already reduced value.
Pitfalls
Common mistakes — and how to avoid them
These five traps appear in almost every test.
Wrong reference value
The decrease is always relative to the old value. From 250 to 200 is 20% — divide by 200 instead and you wrongly get 25%.
Just adding two decreases
Two 10% decreases do not make 20% but 19% (0.9 · 0.9 = 0.81), because the second acts on the already reduced value.
Confusing decrease and increase
A 50% decrease halves the value; a following 50% increase does not undo it (0.5 · 1.5 = 0.75).
Confusing the drop with the new value
120 · 15 ÷ 100 = 18 is only the drop. The new value is 120 − 18 = 102, not 18.
Misplaced decimal point
15% is 0.15 as the factor for the drop, and the decrease factor is 0.85. Mixing the two shifts the result badly.
Study
Practise with a plan — three short tips
15 minutes at a time, not 90
Three short sessions over three days stick better than one long session the day before the test (spaced repetition).
Solve first, then check the solution
Write down your working before revealing the hint. Active recall is three to four times more effective for learning than passive reading.
On every wrong answer: why?
Wrong reference value? Misplaced decimal? Confused the drop with the new value? Note the cause — next time you will spot the mistake instantly.
FAQ
Common questions about practising
Glossary
Terms in one sentence
- Percentage decrease
- The drop in a value as a percentage, relative to the old value: (old − new) ÷ old · 100.
- Whole (base)
- The reference value that equals 100% — here the old value.
- Part (amount)
- The absolute amount belonging to a percentage (e.g. 18 as 15% of 120).
- Decrease factor
- The number you multiply by: for a p% decrease it is (1 − p ÷ 100), so 0.8 for 20%.
- Relative
- Expressed against a reference and dimensionless — like a percentage.
- Absolute
- Given in the unit of the quantity, without reference — like the raw drop.
- Boss question
- The last and hardest task of a practice set, combining several steps.