Practice · Grade 7 basics
Percentage Practice — Problems with Steps
Training problems on the part, the rate, the whole and percent change, in rising difficulty. A hint and full working for every question. Free.
Q1 of 6
0 correct
Find the percentage value: 19% of 250.
19% of 250
Quick answer
What's the best way to practise percentages?
Work problems for all four core types: the part (part = whole · P ÷ 100), the rate (P = part ÷ whole · 100), the whole (whole = part ÷ P · 100) and percent change ((new − old) ÷ old · 100). For each problem, first ask which two quantities are given and which is unknown. Write out the working, do a quick sanity check, and always take a percent change relative to the old value.
HowTo
A 4-step solving strategy
This order works for any percentage problem — whether the part, the rate, the whole or a change is unknown.
- 1Step 1 of 4
Identify the three quantities
Every problem involves the whole W (the base = 100%), the rate P (the percentage) and the part (the value). Read the problem to see which two are given and which is unknown. Change problems give you an old and a new value.
- 2Step 2 of 4
Pick the right formula
Part: part = whole · P ÷ 100. Rate: P = part ÷ whole · 100. Whole: whole = part ÷ P · 100. Percent change: (new − old) ÷ old · 100. All three core formulas follow from the single equation part ÷ whole = P ÷ 100.
- 3Step 3 of 4
Substitute and compute
Plug in the numbers and go in order: multiply first, then divide by 100 — or write the rate as a decimal (19% = 0.19). Example: 250 · 19 ÷ 100 = 4750 ÷ 100 = 47.5.
- 4Step 4 of 4
Check the result and mind the sign
Sanity check: 19% is just under a fifth of 250, so around 50 — 47.5 fits. For a change, the sign gives the direction: + for a rise, − for a fall.
Examples
Worked examples with full working
Four typical problem types from grade 6–8 tests. Try each one yourself first, then compare with the steps.
Easy
Part: 19% of 250
part = whole · P ÷ 100
part = 250 · 19 ÷ 100
part = 4750 ÷ 100 = 47.5
Check: 47.5 ÷ 250 · 100 = 19% ✓
The core 'P% of W' type: multiply first, then divide by 100.
Medium
Rate: 30 of 120 = ?%
P = part ÷ whole · 100
P = 30 ÷ 120 · 100
P = 0.25 · 100 = 25%
Check: 25% of 120 = 120 · 25 ÷ 100 = 30 ✓
The unknown is the rate. Part over whole, then times 100.
Medium
Whole: 36 is 24% → whole
whole = part ÷ P · 100
whole = 36 ÷ 24 · 100
whole = 1.5 · 100 = 150
Check: 24% of 150 = 150 · 24 ÷ 100 = 36 ✓
The unknown is the whole. Part over rate, then times 100.
Hard
Boss: change from 250 to 200
(new − old) ÷ old · 100
(200 − 250) ÷ 250 · 100
−50 ÷ 250 · 100 = −20%
Check: 250 − 20% of 250 = 250 − 50 = 200 ✓
A fall → negative sign. Always divide by the old value (250), never the new one.
Pitfalls
Common mistakes — and how to avoid them
These five traps show up in almost every percentage problem.
Confusing the part with the rate
The rate is the percentage (e.g. 19%); the part is the amount you compute from it (e.g. 47.5). Always ask: is the unknown a percentage or a concrete amount?
Forgetting to divide by 100
19% means 19 ÷ 100 = 0.19 — not 19. Multiplying the whole by 19 gives a hundred times too much. Either divide by 100 or write the rate as a decimal.
Wrong base for a change
A percent change is always relative to the old value. From 200 to 250 is +25%, but from 250 to 200 is −20% — the values are not mirror images.
Forgetting the sign on a decrease
When a value falls, the percent change is negative. Be sure to include the minus sign — otherwise the answer is wrong.
Confusing percentage points with percent
If a share rises from 20% to 25%, that is 5 percentage points in absolute terms — but a +25% relative increase. They are not the same.
Study
Practise with a plan — three quick tips
15 minutes at a time, not 90 in one go
Three short sessions across three days stick better than one long session the night before a test. The magic word is 'spaced repetition'.
Solve first, then look at the answer
Write out your working before revealing the hint. Active recall is three to four times more effective for learning than passive reading.
For every wrong answer: why?
Was it the missing division by 100? The wrong base? A sign? Note the cause — and next time you'll spot the mistake straight away.
FAQ
Frequently asked questions about practising
Glossary
Terms in one sentence
- Percent (%)
- One hundredth. 1% = 1 ÷ 100 = 0.01. The symbol % stands for 'per hundred'.
- Whole (base)
- The whole that equals 100% — e.g. the original price before a discount.
- Rate (P)
- The percentage, e.g. 19%. Tells you what share of the whole is meant.
- Part (value)
- The concrete amount belonging to the rate — 19% of 250 is 47.5.
- Percent change
- The relative change of a value: (new − old) ÷ old · 100, relative to the old value.
- Unitary method
- Solving via the intermediate step of 1%, which works for any percentage problem.
- Boss question
- The last and hardest problem in a practice set, combining several traps.