Comparing amounts, sharing fairly, and scaling up and down.
5 lessons · 35 questions (A–G) · 20 calculation + 15 word problems · no time pressure
A ratio compares two or more amounts, like 3 : 2, and proportion keeps that comparison fixed as the amounts grow or shrink — the same idea behind sharing money, scaling recipes and reading maps. Pupils most often slip by forgetting to add the ratio parts before dividing the total, sharing the parts in the wrong order, or not simplifying the answer.
At Improve Tuition, a qualified teacher makes the ‘parts’ idea concrete and gives one dependable method for sharing and scaling, in small worked steps — with read-aloud, comfort spacing and a reading tint for pupils who take in maths more easily that way.
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Lesson 1
What a ratio is
Aim: Read and write a ratio, knowing that it compares parts and that order matters.
A ratio compares amounts. 2 : 3 (say “2 to 3”) means that for every 2 of the first thing there are 3 of the second.
Order matters. The ratio of red to blue is not the same as blue to red — write the parts in the order the question gives them.
Two parts to three — for every 2 of the first there are 3 of the second.
Worked example
A team has 2 coaches and 22 players. Write the ratio of coaches to players.
Coaches first, players second: 2 : 22.
Both divide by 2: 1 : 11.
Check: there are still 11 times as many players as coaches. ✓
Watch out
A ratio is not a fraction on its own. 2 : 3 does not mean 2/3 — it means 2 out of every 5. Lesson 4 sorts this out.
Try one
A bag has 3 red and 7 green beads. Write the ratio red : green.
31.Two quantities are in the ratio 3 : 4. The larger part is 28. What is the smaller part?
Answer:
Show working
The larger part (4 parts) = 28, so 1 part = 7.
Smaller = 3 × 7 = 21.
32.Two numbers are in the ratio 5 : 8 and add up to 91. What is the larger number?
Answer:
Show working
Total = 5 + 8 = 13 parts = 91, so 1 part = 7.
Larger = 8 × 7 = 56.
33.In a shelter the ratio of cats to dogs is 4 : 3. There are 12 more cats than dogs. How many dogs are there?
Answer:
Show working
The difference is 4 − 3 = 1 part = 12.
Dogs = 3 × 12 = 36.
34.5 machines fill 200 bottles in an hour. At the same rate, how many bottles would 8 machines fill in an hour?
Answer:
Show working
1 machine = 200 ÷ 5 = 40 bottles.
8 machines = 8 × 40 = 320.
35.A recipe serves 6 and uses 450 g of flour. Jamie has 750 g of flour. What is the largest number of whole servings he can make?
Answer:
Show working
1 serving = 450 g ÷ 6 = 75 g.
750 ÷ 75 = 10 servings.
0 of 35 answered
Guide
What is the difference between ratio and proportion?
A ratio compares quantities, written with a colon, such as 3 : 2. Proportion is what stays the same when those quantities are scaled together — if a recipe uses flour and sugar in the ratio 3 : 2, doubling both keeps the proportion the same.
To share in a ratio, add the parts to find the total number of shares, divide the amount by that number to find one share, then multiply for each side. To simplify a ratio, divide every part by the same number, just like a fraction.
Common mistakes. Dividing by one part instead of the total number of parts, matching the shares to the wrong items, or leaving a ratio unsimplified.
Common questionsHow do you simplify a ratio?
Divide every part of the ratio by the same number until they share no common factor. For example, 10 : 15 simplifies to 2 : 3.
How do you share an amount in a ratio?
Add the parts to get the total number of shares, divide the amount by that total to find one share, then multiply by each part. To share £40 in 3 : 1, one share is £10, giving £30 and £10.
What is direct proportion?
Two quantities are in direct proportion when they increase or decrease at the same rate — double one and the other doubles too. The amount per unit stays constant.
What does a ratio like 3 : 2 mean?
For every 3 of the first thing there are 2 of the second. The actual amounts can be any matching multiple, such as 6 and 4, or 30 and 20.
How is ratio linked to fractions?
In the ratio 3 : 2 there are 5 parts altogether, so the first amount is 3/5 of the total and the second is 2/5.
Stuck on this topic?
A teacher can find the exact gap
Practising ratio and proportion on your own is a strong start. If the same marks keep slipping, a qualified teacher can pinpoint the precise gap and fix it. Improve Tuition offers one-to-one maths tuition with our maths tutors in Batley and online — the first assessment is free.