Practice · Grade 7 Percentages
Percentage Increase — Practice
Percentage increase practice problems in rising difficulty plus a boss question. A hint and full working for each. Grade 7, free.
Q1 of 7
0 correct
What is the percentage increase from 200 to 250?
200 → 250
Quick answer
How do I best practise percentage increase?
Work several problems in rising difficulty and switch between the two directions: find the increase in percent from two values — (new − old) ÷ old · 100 — and raise a value by p% — value + value · p ÷ 100. Write the rise down separately for each problem, remember the increase is always relative to the old value, and sanity-check with the factor (1 + p ÷ 100).
HowTo
A 4-step solving strategy
This order works for every percentage-increase problem — whether you want the increase in percent or the new value.
- 1Step 1 of 4
Identify the problem type
Are two values given (old and new) and you want the increase in percent? Or are a starting value and a percentage given and you want the new value? This choice fixes the formula.
- 2Step 2 of 4
Find the rise
With two values: new − old, e.g. 250 − 200 = 50. When raising: value · p ÷ 100, e.g. 200 · 25 ÷ 100 = 50. In both cases 50 is the rise.
- 3Step 3 of 4
Relate or add
For the increase in percent, divide the rise by the old value and multiply by 100: 50 ÷ 200 · 100 = 25%. For the new value, add the rise: 200 + 50 = 250.
- 4Step 4 of 4
Check the result
Verify with the factor (1 + p ÷ 100): 200 · 1.25 = 250 confirms the new value. An increase above 100% means more than doubling — a quick way to catch gross errors.
Examples
Worked practice examples with full working
Four typical percentage problems. Try each one yourself first, then compare with the working.
Easy
Increase: 200 → 250
Rise: 250 − 200 = 50
50 ÷ 200 = 0.25
0.25 · 100 = 25%
Check: 200 · 1.25 = 250 ✓
Two values given, increase in percent wanted. The increase is relative to the old value 200.
Medium
Increase 120 by 15%
Added amount: 120 · 15 ÷ 100 = 18
120 + 18 = 138
Check: 120 · 1.15 = 138 ✓
Starting value and percentage given, new value wanted. The factor 1.15 gets there in one step.
Medium
Increase 50 by 200%
Added amount: 50 · 200 ÷ 100 = 100
50 + 100 = 150
Check: 50 · 3 = 150 ✓ (factor 1 + 2 = 3)
Increases can exceed 100%. +200% equals tripling.
Hard
Boss: Increase 250 → 375
Rise: 375 − 250 = 125
125 ÷ 250 = 0.5
0.5 · 100 = 50%
Check: 250 · 1.5 = 375 ✓
Even with larger numbers the reference stays the old value 250 — not the new one.
Pitfalls
Common mistakes — and how to avoid them
These five traps cost the most marks in tests.
Dividing by the new value
The increase is relative to the old value. For 200 → 250 you divide by 200, not 250. 50 ÷ 200 = 25%, not 50 ÷ 250 = 20%.
Adding two increases directly
Two +10% increases don't make +20%. The factors multiply: 1.1 · 1.1 = 1.21, so +21%.
Expecting an increase to offset a decrease
After −20% you need +25%, not +20%, to get back to the start — the reference value has changed.
Confusing percentage points with percent
From 4% to 6% is +2 percentage points, but a 50% increase (2 ÷ 4 · 100). Always ask what the figure refers to.
Reporting only the rise instead of the new value
When the new value is wanted, add the rise to the starting value: 120 · 15 ÷ 100 = 18, but the answer is 138, not 18.
Study
Practise with a plan — three short tips
Mix both directions
Alternate between "find the increase in percent" and "find the new value". That way you learn to recognise which formula you need, not just one of them.
Use the factor to check
Compute the new value a second time with the factor (1 + p ÷ 100). If both ways agree, the result is safe.
For every wrong answer: why?
Was it the wrong reference value? Percentage points instead of percent? Note the cause — next time you'll spot the mistake at once.
FAQ
Frequently asked practice questions
Glossary
Terms in one sentence
- Percentage increase
- The relative rise of a value over the old value, in percent: (new − old) ÷ old · 100.
- Base (whole)
- The reference value that equals 100% — for an increase, the old value.
- Rise
- The absolute difference new − old, the gain in the unit of the quantity.
- Rate
- The percentage, i.e. per hundred.
- Growth factor
- The number (1 + p ÷ 100) you multiply by — for +25% that is 1.25.
- Percentage point
- The absolute difference between two percentages, e.g. from 4% to 6% is +2 percentage points.
- Boss question
- The last and hardest problem of a practice set.