On this page
You stopped at:
ContinueRevision Mode is on. Questions and activities are hidden.
The linked question or activity is hidden by Revision Mode.
Work from a known percentage to the whole
Task reminder
30% is 24 cards. How many cards is 10%?
30% of a collection is 24 cards. The number of cards in the whole collection is unknown. The full strip is 100%, divided into ten equal parts. Use % in percentage answers; enter an ordinary number for a count, area, price or volume.
Three equal parts contain 24 cards
Each full strip is one equal-sized whole.
Scroll across to read every label.
Figure data
This table is included in print while it is open.
| Whole | Parts in order |
|---|---|
| All cards: 100% | marked; marked; marked; empty; empty; empty; empty; empty; empty; empty |
Show workingHide answer
Three parts contain 24 cards, so one part contains 24÷3 = 8 cards. Ten parts contain 8 × 10 = 80 cards.
The forward relationship is 0.30 × whole = 24. Reverse that multiplication:
Check forwards: 0.30 × 80 = 24. Dividing by 30 alone gives the amount for 1%, not the whole.
Task reminder
Which percentage of the garden does the known area cover?
A garden to restore
Vegetables occupy 45% of a garden, covering 54 m². Find the area of the whole garden. Enter the number of square metres.
Show workingHide answer
45% = 0.45, so the whole area is 54÷0.45 = 120 m². It is larger than 54 m² because the known area is less than the whole. Check: 0.45 × 120 = 54 m².
Task reminder
What percentage of the starting price do you still pay?
Work backwards from a sale price
A price after a 20% discount is 72 dollars. The discount is removed from the original price. Use the parts that remain to work backwards.
The remaining parts make the sale price
Each full strip is one equal-sized whole.
Scroll across to read every label.
Figure data
This table is included in print while it is open.
| Whole | Parts in order |
|---|---|
| Original price: 100% | removed; marked; marked; marked; marked |
Show workingHide answer
The final price represents 100%-20% = 80% of the original.
Check: 20% of 90 is 18, and 90-18 = 72. Adding 20% of 72 instead gives 86.40 dollars. That addition uses 72 as its whole, while the discount was a percentage of the original 90.
Task reminder
What percentage of the starting amount is the new amount?
Work back from an increased amount
After a 15% increase, a club has 92 members. The new membership includes all the original members and the increase.
Show workingHide answer
Check: 0.15 × 80 = 12 and 80 + 12 = 92. The original must be smaller than the final membership because a positive increase was added.
Task reminder
What percentage of the whole does the difference stand for?
Two shares of one whole
In a collection, 40% of the tiles are blue and 25% are yellow. There are 24 more blue tiles than yellow tiles. The 24 is a difference, not either colour’s count.
Scroll across to read every label.
Figure data
This table is included in print while it is open.
| Whole | Parts in order |
|---|---|
| Blue tiles | marked; marked; marked; marked; marked; marked; marked; marked; empty; empty; empty; empty; empty; empty; empty; empty; empty; empty; empty; empty |
| Yellow tiles | marked; marked; marked; marked; marked; empty; empty; empty; empty; empty; empty; empty; empty; empty; empty; empty; empty; empty; empty; empty |
Show workingHide answer
The difference represents 40%-25% = 15% of the same collection. The whole is 24÷0.15 = 160 tiles. Check: 40% of 160 is 64 blue tiles and 25% is 40 yellow tiles; 64-40 = 24.
Task reminder
Which amount did you start with before this change?
Calculate the change as a percentage of the original
A quantity rises from 50 to 65. Find the change, then compare it with the amount before the rise.
Return to the starting point
Now reverse the journey: the quantity falls from 65 back to 50. Give the percentage decrease to 1 decimal place, including %.
Show workingHide answer
The numerical change is the same in both directions, but the original whole changes.
On the return journey, 65 is the original:
Round only the final percentage. The rise and fall have different percentage sizes because they use different reference wholes.
Task reminder
Do the rise and fall start from the same whole?
Check your understanding 1
Which amount is 100%?
Check your understanding 1
Which amount is 100%?
A school club grows from 40 to 50 members. Another club shrinks from 50 to 40. Find the percentage change for each, naming the original whole. State whether each change is an increase or decrease.
Show answerHide answer
The first club gains 10 out of its original 40: 10/40 × 100% = 25% increase. The second loses 10 out of its original 50: 10/50 × 100% = 20% decrease. Both changes involve ten members, but each percentage compares with its own starting membership. Dividing by the final membership reverses the reference whole.
Task reminder
Can the change be zero or bigger than the starting amount?
Check zero change and large changes
A club has 40 members before and after a registration check. What is its percentage change? Include %.
A collection grows from 12 to 36 books. What is the percentage increase? Include %.
Show workingHide answer
For the unchanged club, (40-40)/40 × 100% = 0%. For the books, (36-12)/12 × 100% = 200%. The increase is 200% of the original; the final collection is 300% of the original.
To find a percentage change, the starting whole cannot be zero. You cannot divide by zero.
Task reminder
Which amount is the whole for the second change?
Check your understanding 2
Two successive changes
Check your understanding 2
Two successive changes
A 100-dollar price rises by 10%, then the new price falls by 10%. Find the final price and explain whether it returns to 100 dollars.
Show answerHide answer
The rise gives 110 dollars. Ten percent of 110 is 11, so the final price is 99 dollars. The second percentage uses 110 as its whole, so the changes do not cancel.
Each change starts from its own price
Count the values shown on the cards.
Scroll across to read every label.
Figure data
This table is included in print while it is open.
| Set | Values |
|---|---|
| Original price | $100 dollars |
| After the rise | $110 dollars |
| After the fall | $99 dollars |
Task reminder
What happened last, and how can you undo it?
Undo the last change first
A book collection grows by 20%. Then 12 books are donated, leaving 84 books. Find the number of books before the growth.
Show workingHide answer
Undo the last change first: 84 + 12 = 96 books. That is 120% of the original, so the original was 96÷1.20 = 80 books. Check forwards: 80 + 16 = 96, then 96-12 = 84.
Task reminder
What percentage of the starting water remains?
Check your understanding 3
Find the starting amount and check the original volume
Check your understanding 3
Find the starting amount and check the original volume
After a 25% decrease, a tank contains 18 ℓ. What was in it before the decrease?
Show answerHide answer
18 ℓ is 75% of the original, so 18÷0.75 = 24 ℓ. Check that one quarter of 24 is 6 and 24-6 = 18.
For a grown-up
Pip’s synthetic voice uses the University of Edinburgh’s Alba speech dataset, via Piper’s Alba voice, under CC BY 4.0. Audio is optional.
Loading reading progress…
Lesson done
- Monday
- Tuesday
- Wednesday
- Thursday
- Friday
- Saturday
- Sunday
Checking learning on this device…
Change goal
Progress options
Loading questions…
Syllabus and review details
- Primary 6 Mathematics 2026 · 2021-updated-2025-10
- G1 Mathematics 2027 · 2027
- Normal (Technical) Secondary 1 Mathematics 2020 · 2020-reprinted-2023
- G2 Mathematics 2027 · 2027
- Normal (Academic) Secondary 1 Mathematics 2020 · 2020-reprinted-2023
- G3 Mathematics 2027 · 2027
- Express Secondary 1 Mathematics 2020 · 2020-reprinted-2023
Last reviewed: