MathsRatio, proportion and rates of change28 min★★★ difficulty

Sharing in a ratio

Ratio compares parts; fractions compare a part with the whole. Confusing the two is the reason so many ratio questions go wrong, and the fix is to count parts first.

Part of your national curriculum

Ratio, proportion and rates of change: Divide a given quantity into two parts in a given part:part or part:whole ratio, and express the division of a quantity into two parts as a ratio

Lesson overview

What you'll learn in this lesson

Divide a given quantity into two parts in a given part:part or part:whole ratio, and express the division of a quantity into two parts as a ratio

Key learning points

• Count the parts
• Ratio and fraction together
• When one share is known
• Simplifying and comparing

This lesson at a glance

28 minutes
20 parts to scroll through
4 quick checks
Marked quiz at the end
Gentle pace: short sittings with pauses

Words to know

dividequantityexpressdivisionfraction

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Part 1 of 20 · Discover5%

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Part 1 of 20

Visual introduction

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Sharing in a ratio

Ratio compares parts; fractions compare a part with the whole. Confusing the two is the reason so many ratio questions go wrong, and the fix is to count parts first.

In a nutshell

Divide a given quantity into two parts in a given part:part or part:whole ratio, and express the division of a quantity into two parts as a ratio

Learning cycle

Part 2 of 20

Learning cycle 1 of 2

Part 1 · Count the parts

A short piece of teaching, then a check to make sure it has landed.

Explore the idea

Part 3 of 20

Learn

Count the parts

To share £450 in the ratio 4 : 5, there are 9 parts, so one part is £50 and the shares are £200 and £250. Always check that the shares add back to the original total, which catches arithmetic slips instantly.

Reset break

Part 4 of 20

Pause

That's sitting 1 of 5 done

Stretch, get a drink, look out of the window. There is no timer and nothing is counting down — your place is saved, so you can come back in five minutes or tomorrow.

Stop here for now

Explore the idea

Part 5 of 20

Learn

Ratio and fraction together

In the ratio 4 : 5, the first share is 4/9 of the total, not 4/5. Writing 'first share = 4/9 of £450' is often faster than finding one part, and it is the form that GCSE questions about fractions of amounts expect.

Quick check

Part 6 of 20

Quick check

£450 shared 4 : 5 gives the larger share as

Give me a hint

Quick check

Part 7 of 20

Quick check

In the ratio 3 : 7, the first share is

Give me a hint

Reset break

Part 8 of 20

Pause

That's sitting 2 of 5 done

Stretch, get a drink, look out of the window. There is no timer and nothing is counting down — your place is saved, so you can come back in five minutes or tomorrow.

Stop here for now

Learning cycle

Part 9 of 20

Learning cycle 2 of 2

Part 2 · When one share is known

A short piece of teaching, then a check to make sure it has landed.

Explore the idea

Part 10 of 20

Learn

When one share is known

If concrete mixes sand and cement 5 : 2 and you have 8 kg of cement, then 2 parts = 8 kg, so one part is 4 kg and the sand needed is 20 kg. The total mix is 28 kg. Starting from the known share, not the total, is the key move.

Explore the idea

Part 11 of 20

Learn

Simplifying and comparing

Ratios simplify like fractions by dividing all parts by a common factor: 45 : 30 becomes 3 : 2. To compare two ratios, write both in the form 1 : n, so 3 : 2 becomes 1 : 0.67 and 7 : 4 becomes 1 : 0.57.

Reset break

Part 12 of 20

Pause

That's sitting 3 of 5 done

Stretch, get a drink, look out of the window. There is no timer and nothing is counting down — your place is saved, so you can come back in five minutes or tomorrow.

Stop here for now

Quick check

Part 13 of 20

Quick check

Simplify 45 : 30.

Give me a hint

Quick check

Part 14 of 20

Quick check

Paint mixes 3 : 1 and you have 2 litres of the second colour. Total paint is

Give me a hint

Explore the idea

Part 15 of 20

Worked example

Worked answer: concrete mixes sand and cement 5 : 2. With 8 kg of cement, what mass of concrete can be made? (3 marks)

Cement is 2 parts, and 2 parts = 8 kg, so one part is 4 kg (1). Sand is 5 parts, which is 20 kg (1). The total mix is 20 + 8 = 28 kg (1). Treating 8 kg as one part, giving 40 kg of sand, is the standard error.

Reset break

Part 16 of 20

Pause

That's sitting 4 of 5 done

Stretch, get a drink, look out of the window. There is no timer and nothing is counting down — your place is saved, so you can come back in five minutes or tomorrow.

Stop here for now

Challenge round

Part 17 of 20

Game · Sort it

Which of these are true?

Drag each card into the right column. Tap a card first if dragging is fiddly.

True

Not true

Challenge round

Part 18 of 20

Game · Recall cards

Share 60 in the ratio 4 : 2.

Card 1 of 4

Mastery quiz

Part 19 of 20

Marked quiz

End of lesson quiz: Sharing in a ratio

4 questions, marked with the reasoning shown. No timer.

1. Share 60 in the ratio 4 : 2.
2. Simplify 24 : 36.
3. A sanctuary keeps otters and seals in the ratio 5 : 3. There are 32 animals. How many otters?
4. £450 shared 4 : 5 gives the larger share as

Lesson round-up

Part 20 of 20

Lesson round-up

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Part 1 of 20 · Watch & discover

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Divide a given quantity into two parts in a given part:part or part:whole ratio, and express the division of a quantity into two parts as a ratio