Maths · Finding a Percentage of a Quantity
Quantity Split
Build 60% of 60 marbles on the board, then work out 60% of 40 without it.
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Why this works
Per cent means "out of a hundred", so 60% is . Both numbers divide by 20, which leaves - the same share, with far fewer groups to cut. The bottom number is how many equal groups the whole pile is cut into and the top number is how many of those groups you keep. , so one group holds 8 marbles, and 3 groups hold . The groups add straight back up to 40 with nothing left over.
Helping a child through Quantity Split
It runs in 3 steps
- 1. Cut it up. Cut 60 marbles into 5 equal groups.
- 2. Take your share. Now light up 3 of those 5 groups.
- 3. A new pile. The board is covered. What is 60% of 40 marbles?
Hints, least revealing first
- 60% cancels: both numbers divide by 20, leaving . Cut the pile into 5 groups, not 100.
- , so each group holds 8 marbles.
- Now take 3 of those groups: .
When they finish it: “Split and shared exactly!”
3 11+ skills this exercise practises
Each of these has its own page, with a worked example on it.
- Find a fraction of a quantityCalculate one unit or non-unit fraction of a quantity.
- Find a percentage of a quantityCalculate one familiar percentage of a quantity.
- Recognise equivalent fractionsRecognise two fractions representing the same value.
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