KS3 · Maths
Dividing a quantity into a given ratio
Andeep worked 2 hours and Sam worked 3. They're paid £15 between them. Splitting it equally gives each £7.50, so Sam earns nothing extra for his extra hour. Fair?
Maths · Ratio and proportion
Every time Andeep takes 11 sweets, Sofia takes 9. That's one lot of 20 sweets. Drag the handle along the bar to hand out more lots, and keep going until all 120 are gone. Watch what happens to both shares each time.
Worked example · the bar-model method
Problem
Andeep worked 2 hours and Sam worked 3 hours. They are paid £15 altogether. Share the £15 fairly, in the ratio 2 : 3.
WHAT YOU'VE LEARNED
A quick recap of today's lesson.
Split any amount fairly into parts, then check that nothing is left over.
What you need to know
- A ratio such as 2 : 3 compares parts: 2 parts of one thing for every 3 parts of the other.
- To share a total in a ratio, add the ratio numbers to count the equal parts, divide the total by that to find one part, then multiply by each number in the ratio.
- A ratio table does the same job another way: find the multiplier that takes the ratio total up to the amount, then multiply every part by it.
The big picture
Sharing in a ratio means cutting the amount into equal parts, finding what one part is worth, and giving each share its own number of parts. Underneath it all, every part is multiplied by the same number, which is why the shares keep the ratio and always add back to the total.
Key points
Worked example
Problem
Imani and Josh share 63 football stickers in the ratio 5 : 2, with Imani getting the bigger share.
⚠ Watch out
Adding the same amount to each part. For 3 : 5 shared into 20 litres, adding 12 to each part gives 15 and 17, which make 32 litres, not 20. Multiply both parts by the same number instead (20 ÷ 8 = 2.5), then add the shares back to check.
Memory hook
One part is like one hour's pay. Add up the hours, divide the money to get the pay for one hour, then pay each person for their hours. In short: add the parts, divide for one part, multiply for each share, then add back to check.
Check yourself
Without looking, what are the three moves for sharing an amount in a ratio, and what quick check tells you that the whole amount has been shared out?
Flashcards
(12)What does the ratio 2 : 3 tell you?
What are the three moves for sharing a total in a ratio?
Why is sharing equally often not fair?
What must be true of the parts in a bar model?
What is the ratio total, and what is it for the ratio 4 : 7?
How do you check shares in a ratio?
In a ratio table, what is the multiplier?
Share 120 sweets in the ratio 11 : 9 using a ratio table.
Can the multiplier be a fraction? Share a 4 litre drink as orange juice : lemonade = 3 : 7.
Share 450 g of cookie mix as flour : butter : sugar = 3 : 2 : 1.
Can a ratio compare more than two things?
To make 3 : 5 up to 20 litres, why doesn't adding 12 to each part work?
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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- Algebraic notation and conventions
- Angle sum in a triangle
- Angles on parallel lines (corresponding, alternate, co-interior)
- Area of a circle
- Area of a trapezium
- Area of a triangle
- Area of composite rectilinear shapes
- Arithmetic sequences and finding the nth term
- Associative, commutative and distributive laws
- Bisecting an angle
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