Sharing in a ratio
Ratio questions are nearly all the same question: how much is one part worth? Find that and the rest is multiplication.
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
- • The one-part method
- • Ratio as a fraction
- • When you are given one share
- • Difference questions
This lesson at a glance
- 30 minutes
- 18 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 18
Watch first
Sharing in a ratio
An English teaching video on this topic from mathantics. 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
What you already know
Part 2 of 18
Before we start
What you already know
You can simplify fractions and multiply and divide whole numbers.
Key words
Part 3 of 18
Key words
Words you'll need today
- ratio
- A comparison of two or more amounts, written with a colon.
- part
- One share of the total in a ratio.
- part:whole
- A ratio comparing one share to the total.
Learning cycle
Part 4 of 18
Learning cycle 1 of 2
Part 1 — Finding one part
A short piece of teaching, then a check to make sure it has landed.
Explore the idea
Part 5 of 18
Learn
The one-part method
Share £45 in the ratio 4:5. There are 4 + 5 = 9 parts, so one part is £45 ÷ 9 = £5. The shares are 4 × £5 = £20 and 5 × £5 = £25. Check by adding: £45. Write the total-parts line down every time — it is where most marks are lost.
Explore the idea
Part 6 of 18
Learn
Ratio as a fraction
In the ratio 4:5, the first share is 4/9 of the total and the second is 5/9. That makes 'part:whole' questions quick: if boys to girls is 3:7, then 3/10 of the class are boys. Simplify ratios like fractions: 12:18 = 2:3.
Quick check
Part 7 of 18
Quick check
Share £60 in the ratio 3:2. The larger share is...
Reset break
Part 8 of 18
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 9 of 18
Quick check
Boys:girls = 2:5. What fraction are girls?
Learning cycle
Part 10 of 18
Learning cycle 2 of 2
Part 2 — Harder ratio problems
A short piece of teaching, then a check to make sure it has landed.
Explore the idea
Part 11 of 18
Learn
When you are given one share
Paint is mixed white:blue in the ratio 5:2 and you have 8 litres of blue. Two parts are 8 litres, so one part is 4 litres and white is 5 × 4 = 20 litres. Notice the total was never mentioned — you still only needed the value of one part.
Explore the idea
Part 12 of 18
Learn
Difference questions
Two people share money 7:3 and one gets £60 more than the other. The difference is 7 − 3 = 4 parts, so one part is £15. The shares are £105 and £45, and the total is £150. Read carefully whether the number given is a share, a difference or a total.
Quick check
Part 13 of 18
Quick check
Simplify 18:24.
Quick check
Part 14 of 18
Quick check
Squash:water = 1:6 and you use 300 ml squash. Water needed?
Common mix-ups
Part 15 of 18
Common mix-ups
Things people often get wrong
- Dividing by the first number instead of the total number of parts.
- Treating the amount given as the total when it is one share.
- Writing the shares in the wrong order.
Challenge round
Part 16 of 18
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 17 of 18
Marked quiz
End of lesson quiz: Sharing in a ratio
6 questions, marked with the reasoning shown. No timer.
1. Share 84 in the ratio 5:2. The smaller share is...
2. A ratio 4:6 simplifies to...
3. Ratio 3:5, and the total is 400. First share?
4. Two share 9:4 and the difference is £75. One part is...
5. Cement:sand = 1:4. What fraction is cement?
6. Share 121 in the ratio 6:5. The larger share is...
Lesson round-up
Part 18 of 18
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 18 · Watch & discover