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Ratio and proportion are about comparing quantities and describing how they relate to each other. You use them when following a recipe, reading a map, or working out fair shares. This topic is introduced in Year 6.
A ratio compares two or more quantities of the same type.
If a bag contains 3 red sweets and 5 blue sweets, the ratio of red to blue is 3:5 (read as "3 to 5").
The order matters — 3:5 is not the same as 5:3.
Writing ratios:
This is a very common source of confusion. Make sure you know which type of comparison is being asked for.
Part-to-part ratio compares one part with another part.
Part-to-whole compares one part with the total.
Example: In a class of 30, the ratio of boys to girls is 2 : 3.
Always check: does the question ask for a ratio (part-to-part) or a fraction/percentage (part-to-whole)?
You simplify a ratio by dividing both sides by their highest common factor — exactly like simplifying fractions.
Example: Simplify 12:8
Example: Simplify 15:10:25
Like equivalent fractions, you can scale a ratio up or down by multiplying or dividing both sides by the same number.
Example: A recipe uses flour and butter in the ratio 3:1. If you use 12 cups of flour, how much butter do you need?
A bar model shows each "part" as a block of the same size. For the ratio 2:3 sharing £60, draw 5 equal blocks (2 + 3 = 5 total parts), each worth £12:
flowchart LR
subgraph Total[Total = 60 pounds, 5 parts]
direction LR
A[12] --- B[12]
B --- C[12]
C --- D[12]
D --- E[12]
end
F["Share 1: 2 parts<br/>= 24 pounds"] -.- A
F -.- B
G["Share 2: 3 parts<br/>= 36 pounds"] -.- C
G -.- D
G -.- E
To share a quantity in a given ratio:
Example: Share £60 in the ratio 2:3
Example: Share 90 sweets in the ratio 1:2:3
A scale factor multiplies all dimensions of a shape by the same amount.
Example: A rectangle is 4 cm wide and 6 cm tall. It is enlarged by scale factor 2.
Fractional scale factor (reduction):
A shape can also be made smaller using a fractional scale factor.
Example: A triangle has sides 12 cm, 9 cm and 6 cm. It is reduced by scale factor 1/3.
The new triangle is the same shape but every length is one-third of the original.
Maps: A scale of 1:50,000 means that 1 cm on the map represents 50,000 cm (500 m) in real life.
Proportion describes how one quantity relates to a whole, or to another quantity.
"4 out of every 10 students have a pet" means 4/10 = 2/5 = 40% of students have a pet.
Direct proportion: when two quantities increase (or decrease) at the same rate.
Unitary method: find the value of one unit first, then scale up.
The unitary method lets you compare prices to find the best value.
Example: Which is the better buy?
Find the price per pencil:
25p < 30p, so Pack B is better value.
Tip: Always compare the cost of one item (or one gram, one litre, etc.) to find the better deal.
Aisha is making fruit smoothies for a school party. The recipe for 8 servings uses strawberries and bananas in the ratio 3 : 2, and altogether the recipe uses 500 g of fruit. She needs to make smoothies for 30 servings. How much of each fruit should she buy, in grams?
Step 1 — Find the fruit per serving.
500 g / 8 servings = **62.5 g per serving**
Step 2 — Scale up to 30 servings.
62.5 g x 30 = **1,875 g** total fruit needed
Step 3 — Split using the ratio 3:2. Total parts = 3 + 2 = 5.
Value of one part = 1,875 / 5 = **375 g**
Strawberries = 3 x 375 = **1,125 g**
Bananas = 2 x 375 = **750 g**
Step 4 — Use a bar model to picture the split.
|---strawberries (3 parts)---|---bananas (2 parts)---|
| 375 | 375 | 375 | 375 | 375 |
| 1,125 g | 750 g |
Total bar = 1,875 g ✓
Step 5 — Check the proportions are still correct.
1,125 / 750 = 1.5 = 3/2 ✓
1,125 + 750 = 1,875 ✓
The ratio 3:2 is preserved.
Step 6 — Convert into shopping units. Strawberries are sold in 250 g punnets and bananas in bunches that average 600 g.
Strawberries: 1,125 / 250 = 4.5 punnets — Aisha must buy **5 punnets** (rounding up).
Bananas: 750 / 600 = 1.25 bunches — Aisha must buy **2 bunches** (rounding up).
This shows pupils that real-world ratio problems often need a practical rounding step at the end — buying a fraction of a punnet is not possible.
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