KS3 · Maths
Finding a fraction of a quantity
3/8 of Alex's sweets is 15. How many sweets are there? One bar answers that AND 'what is 3/8 of 40?', because they're the same question run in opposite directions.
Drag the shading
The bar is two bags of 40 sweets side by side, and each bag is cut into 8 equal parts, so each cell is one eighth of a bag: 40 ÷ 8 = 5 sweets. Drag to 3/8 and read 15. Now run it backwards: if 3/8 is 15, one eighth is 15 ÷ 3 = 5, and all eight eighths are 8 × 5 = 40. Keep dragging past 8/8 and you are taking more than one whole bag, so you get more than 40.
The written method: 'of' means ×
Problem
Work out (a) 4/9 of 81, (b) 5/8 of £26.40, (c) 2/3 of 2 3/4 and (d) 11 5/8 × 32.
Choose your route
Divide first or multiply first?
You can divide by the denominator first or multiply by the numerator first: the answer is the same either way. Which route is easier for each one?
Still to sort
Divide by the denominator first (0)
The amount is a multiple of the denominator, so it shares out exactly.
Where the line is: Ask one question: does the denominator go into the amount exactly? If yes, divide first and the numbers stay small.
Multiply by the numerator first (0)
The amount is not a multiple of the denominator, so dividing first would leave an awkward remainder.
Where the line is: If the denominator doesn't go into the amount exactly, multiply first and divide once at the end.
WHAT YOU'VE LEARNED
A quick recap of today's lesson.
Share the amount into the denominator's equal parts, take the numerator's worth, and run the same picture backwards to find the whole.
What you need to know
- 'Of' means multiply: a fraction of an amount is the amount × the fraction.
- Bar model: share the amount into as many equal parts as the denominator, find one part, then multiply by the numerator.
- To find the original amount, divide the result by the fraction: find one part, then multiply by the number of parts in the whole.
The big picture
Finding a fraction of an amount means multiplying the amount by the fraction: 'of' means ×. With a bar, share the whole amount into as many equal parts as the denominator, find one part, then take the numerator's worth. The amount can be money or a mixed number, and a fraction bigger than 1 gives more than the amount. To find the original amount from a fraction and its result, divide by the fraction, which is the same as multiplying by its reciprocal.
Key points
Worked example
Problem
A coat is in a sale with 1/3 off. The sale price is £30. What was the original price?
⚠ Watch out
Swapping the jobs of the top and bottom numbers. For 3/8 of 40, doing 40 ÷ 3 × 8 gives about 107, more than the whole 40! The denominator cuts: 40 ÷ 8 = 5. The numerator takes: 3 × 5 = 15.
Memory hook
Bottom cuts, top takes. The denominator cuts the whole into equal parts; the numerator takes that many. Going backwards? Find one part, then rebuild the whole.
Check yourself
2/3 of the pupils on a trip are in Year 7, and 24 pupils are in Year 7. How many pupils are on the trip? First decide: more or less than 24?
Flashcards
(13)What does 'of' mean in '3/5 of 600'?
Bar model: how do you find 2/5 of 20?
How can you write 4/9 of 81 as a multiplication of two fractions?
What is 5/8 of £26.40?
What do you do first to find a fraction of a mixed number, like 2/3 of 2 3/4?
When is it easier to divide by the denominator first?
Does it matter whether you multiply or divide first?
Is 2 2/3 of 18 more or less than 18?
What's a quick way to work out 11 5/8 × 32?
3/8 of Alex's sweets is 15. How do you find how many sweets Alex has?
What is a reciprocal?
2/7 of the crayons in a box is 4 crayons. How many crayons are there?
A mass goes down by 2/7 and is now 4.5 kg. What fraction of the original is 4.5 kg?
Tap any card to flip it, or use Study as deck to go through them one at a time. In the full lesson these run as a spaced-repetition deck — you rate each card Hard, Good or Easy and the tricky ones keep coming back until they stick.
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Keep me postedMore KS3 Maths topics
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- Area of a triangle
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- Arithmetic sequences and finding the nth term
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