Sharing in a given ratio
A ratio tells you how many parts each share gets. Once you know the total number of parts, every ratio question becomes a division followed by a multiplication.
Part of your national curriculum
- Ratio, proportion and rates of change: Use ratio notation, including reduction to simplest form
- 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 quantity in a given ratio
Key learning points
- • Counting the parts
- • Keeping ratios in simplest form
This lesson at a glance
- 20 minutes
- 12 parts to scroll through
- 3 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 12
Watch first
Sharing in a given ratio
An English teaching video on this topic from mathantics. Watch it, then scroll down for the lesson.
In a nutshell
Divide a quantity in a given ratio
Explore the idea
Part 2 of 12
Learn
Counting the parts
In the ratio 3 : 2 there are 5 parts altogether. Divide the total by 5 to find the value of one part, then multiply back up for each share.
Explore the idea
Part 3 of 12
Learn
Keeping ratios in simplest form
Divide both sides by their highest common factor. 12 : 18 becomes 2 : 3. The relationship is unchanged — only the numbers get friendlier.
Explore the idea
Part 4 of 12
Worked example
Worked example — a wildlife rescue centre
A rescue centre has 45 animals in the ratio 3 birds : 2 mammals. Parts = 5. One part = 45 ÷ 5 = 9. Birds = 3 × 9 = 27, mammals = 2 × 9 = 18. Check: 27 + 18 = 45.
Reset break
Part 5 of 12
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.
Quick check
Part 6 of 12
Quick check
Share 60 in the ratio 4 : 2.
Quick check
Part 7 of 12
Quick check
Simplify 24 : 36.
Quick check
Part 8 of 12
Quick check
A sanctuary keeps otters and seals in the ratio 5 : 3. There are 32 animals. How many otters?
Challenge round
Part 9 of 12
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 10 of 12
Game · Fill the gaps
Finish the sentences
Choose the word that belongs in each gap.
____ the total by 5 to find the value of one part, then multiply back up for each share.
Mastery quiz
Part 11 of 12
Marked quiz
End of lesson quiz: Sharing in a given ratio
4 questions, marked with the reasoning shown. No timer.
1. Share £84 in the ratio 5:2. What is the larger share?
2. Share 60 in the ratio 4 : 2.
3. Simplify 24 : 36.
4. A sanctuary keeps otters and seals in the ratio 5 : 3. There are 32 animals. How many otters?
Lesson round-up
Part 12 of 12
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 3 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 12 · Watch & discover
How this is going
- Not looked at yet
Use ratio notation, including reduction to simplest form
- 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