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
- 16 parts to scroll through
- 4 quick checks
- Marked quiz at the end
- Gentle pace: short sittings with pauses
Words to know
Scroll down — the lesson carries on below
Watch & discover
Part 1 of 16
Watch first
Sharing in a ratio
An English teaching video on this topic from The Organic Chemistry Tutor. Watch it, then scroll down for the lesson.
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 16
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 16
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.
Explore the idea
Part 4 of 16
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 5 of 16
Quick check
£450 shared 4 : 5 gives the larger share as
Quick check
Part 6 of 16
Quick check
In the ratio 3 : 7, the first share is
Reset break
Part 7 of 16
Pause
That's sitting 1 of 2 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.
Learning cycle
Part 8 of 16
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 9 of 16
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 10 of 16
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.
Quick check
Part 11 of 16
Quick check
Simplify 45 : 30.
Quick check
Part 12 of 16
Quick check
Paint mixes 3 : 1 and you have 2 litres of the second colour. Total paint is
Explore the idea
Part 13 of 16
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.
Challenge round
Part 14 of 16
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
Mastery quiz
Part 15 of 16
Marked quiz
End of lesson quiz: Sharing in a ratio
4 questions, marked with the reasoning shown. No timer.
1. £450 shared 4 : 5 gives the larger share as
2. In the ratio 3 : 7, the first share is
3. Simplify 45 : 30.
4. Paint mixes 3 : 1 and you have 2 litres of the second colour. Total paint is
Lesson round-up
Part 16 of 16
Lesson round-up
Ready when you are
Quiz score
Not sat
Games
Not played
Points this lesson
0
Best run
0 in a row
Luna: 0 out of 4 on the practice checks. Only if you feel up to it — one more?
Ask LunaDo the work
Your written work for this lesson
This is the part you'd do in your book at school. Pick the pieces below, write here or on paper, and photograph anything you draw or work out.
The cost of a school trip
A school is planning a trip to a wildlife park. The coach costs £480 however many people go. Entry costs £9.50 for each pupil and each adult goes free. The school says every pupil must pay the same amount, and the trip must not lose money.
If 60 pupils go, the coach works out at £8 each, so the total for each pupil is £17.50. If only 40 pupils go, the coach works out at £12 each, so the price rises to £21.50. The teacher explains that the coach is a fixed cost and the entry is a cost per person — which is why the price per pupil changes when the number changes.
The school decides to charge £20 and to use anything left over for a second trip later in the year.
Written for Good Learning Co.
Reading questions
- Work out the total cost of the trip if 50 pupils go.
- Show why the price per pupil falls when more pupils go, using numbers.
- At £20 each, how many pupils must go before the trip makes money? Show your working.
Working out
Working outDo the practice questions on paper, showing every step — not just the answer. Mark them yourself and circle anything you got wrong.
10–15 questions
Worked example, explained
WritingCopy one question out and write underneath, in words, why each step works.
1 question, 4–5 sentences
Problem in words
Working outWrite your own real-life problem that uses today's method, then solve it.
1 problem + solution
Saved as you type.
Part 1 of 16 · Watch & discover
How this is going
- Not looked at yet
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