Practice · Grade 7 Percentages
Percentage Change — Practice
Practice problems of rising difficulty on percentage increase and decrease, plus a boss question. Hint and full working per problem. Grade 7, free.
Q1 of 6
0 correct
Find the percentage change:
50 → 75
Quick answer
How do I best practise percentage change?
Work several problems of rising difficulty. Always apply the same formula: (new − old) ÷ old · 100. Watch the sign — positive means an increase, negative a decrease — and remember the change is always relative to the old value. Practise problems with awkward results such as +37.5% too, and do a quick sanity check after each one: if the new value is larger, the result must be positive.
HowTo
A 4-step solving strategy
This order works for any percentage-change problem — increase or decrease alike.
- 1Step 1 of 4
Mark the old and new value
Read off which value is the starting (old) value and which is the end (new) value. In "from 50 to 75", 50 is old and 75 is new. The old value is always the reference (100%).
- 2Step 2 of 4
Take the difference: new − old
Subtract the old value from the new one. 75 − 50 = 25. If the result is negative (new smaller than old), it is a decrease and the final answer gets a minus sign.
- 3Step 3 of 4
Divide by the old value, then times 100
Divide the difference by the old value and multiply by 100: 25 ÷ 50 · 100 = +50%. For awkward values, just compute the fraction, e.g. 3 ÷ 8 · 100 = 37.5%.
- 4Step 4 of 4
Set the sign and sanity-check
Add the sign: + for an increase, − for a decrease. Check: if the new value is larger, the result must be positive — otherwise you slipped up.
Examples
Worked practice examples with full working
Four typical exam-style problems for Grade 7. Try each one yourself first, then compare with the working.
Easy
Find: 200 → 250
(250 − 200) ÷ 200 · 100
= 50 ÷ 200 · 100
= +25%
Sanity check: new larger than old → positive result ✓
A classic increase. Difference 50, the reference is the old value 200.
Easy
Find: 250 → 200
(200 − 250) ÷ 250 · 100
= −50 ÷ 250 · 100
= −20%
Sanity check: new smaller than old → negative result ✓
Same numbers as above but reversed — and the result is not −25%, because the reference is now 250.
Medium
Find: 80 → 120
(120 − 80) ÷ 80 · 100
= 40 ÷ 80 · 100
= +50%
Sanity check: 80 becomes 1.5 times itself → +50% ✓
Difference 40, divided by the old value 80 gives 0.5 — so +50%.
Hard
Find: 8 → 11
(11 − 8) ÷ 8 · 100
= 3 ÷ 8 · 100
= +37.5%
Sanity check: 3 ÷ 8 = 0.375 → +37.5% ✓
An awkward result. Don't fear decimals: 3 divided by 8 is 0.375.
Pitfalls
Common mistakes — and how to avoid them
These five traps show up again and again with percentage change.
Dividing by the new value
The change is relative to the old value. Divide by old, not new. From 200 to 250 is +25%, not +20%.
Forgetting the sign
A decrease needs a minus sign on the result. From 60 to 45 is −25%, not +25%. Always check: new smaller than old → negative.
Assuming increase and decrease cancel
+25% followed by −25% does not return to the start, because the second percent acts on a different value. 200 becomes 250, then only 187.5.
Mixing up percent and percentage points
A share rising from 20% to 25% is +5 percentage points, but +25% relative change. They are not the same thing.
Thinking awkward results are wrong
Not every percentage change is round. 8 → 11 gives +37.5% — perfectly correct. Just compute the fraction as a decimal.
Study
Practise with a plan — three quick tips
15 minutes at a time, not 90 at once
Three short sessions on three days stick better than one long session the night before the test. The keyword is "spaced repetition".
Solve first, then look at the answer
Write down your working before you reveal the hint. Active recall is three to four times more effective for learning than passive reading.
On every wrong answer, ask why
Was it a sign error? The wrong reference value? Note the cause — next time you will spot the same mistake straight away.
FAQ
Frequently asked questions about practising
Glossary
Terms in one sentence
- Percentage change
- The relative change of a value: (new − old) ÷ old · 100, in percent.
- Old value (starting value)
- The reference value before the change — equals 100%.
- New value (end value)
- The value after the change.
- Difference
- The result of new − old; positive for an increase, negative for a decrease.
- Increase
- A positive percentage change (new value larger).
- Decrease
- A negative percentage change (new value smaller).
- Percentage point
- The absolute difference between two percentages — not to be confused with percentage change.