MathsRatios and Proportion11+

Ratio Notation

Ratio notation is a way to show how quantities relate to each other, often used in 11+ maths to compare parts of a whole or different amounts.

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Understanding ratio notation is a fundamental mathematical skill that expresses the relationship between two or more numbers or quantities. It tells you how much of one thing there is compared to another. For example, if a fruit bowl has 3 apples and 2 oranges, the ratio of apples to oranges is 3 to 2.

In ratio notation, we use a colon (:) to separate the numbers. So, "3 to 2" is written as 3:2. The order is crucial: 3:2 is different from 2:3. Ratios can also be simplified, much like fractions, by dividing all parts by their highest common factor. For instance, a ratio of 6:4 can be simplified to 3:2.

Learning how to write ratios is essential for 11+ exams, as questions frequently involve sharing amounts in a given ratio, finding missing parts, or scaling recipes. It's a key concept for mastering proportion and problem-solving.

Check Understanding

IdentificationEasy

What does the colon (:) represent in **ratio notation**?

Answer

It means "to" or "in comparison with," showing the relationship between quantities.

Why it works

For example, a ratio of 2:1 means "2 to 1," indicating there are two parts of the first item for every one part of the second.

Worked ExampleMedium

In a bag of sweets, there are 18 red sweets and 12 blue sweets. Write the ratio of red to blue sweets in its simplest form.

Answer

The ratio is 3:2.

Why it works

The initial ratio is 18:12. To simplify, find the highest common factor (HCF) of 18 and 12, which is 6. Divide both numbers by 6: 18 ÷ 6 = 3, and 12 ÷ 6 = 2.

MisconceptionEasy

Is a ratio of 4:5 the same as 5:4?

Answer

No, they are different. The order of numbers in a ratio is crucial.

Why it works

4:5 means four parts of the first item to five parts of the second. 5:4 means five parts of the first item to four parts of the second. For example, the ratio of apples to oranges as 4:5 is different from 5:4.

ApplicationMedium

A fruit punch recipe uses orange juice and pineapple juice in a ratio of 3:1. If you use 600ml of orange juice, how much pineapple juice do you need?

Answer

You need 200ml of pineapple juice.

Why it works

The ratio 3:1 means for every 3 parts of orange juice, there is 1 part of pineapple juice. If 3 parts = 600ml, then 1 part = 600ml ÷ 3 = 200ml.

Examples

A recipe uses 2 parts flour to 1 part sugar. How would you write this ratio?

The ratio of flour to sugar is 2:1. This means for every 2 scoops of flour, you use 1 scoop of sugar.

In a class of 20 pupils, there are 12 boys and 8 girls. What is the ratio of boys to girls in its simplest form?

The initial ratio is 12:8. Both numbers can be divided by 4, so the simplified ratio is 3:2.

If a fruit salad has 5 strawberries, 10 blueberries, and 3 bananas, what is the ratio of strawberries to blueberries to bananas?

The ratio is 5:10:3. This ratio cannot be simplified further as there is no common factor for all three numbers.

Quick Answers

What does the colon (:) mean in ratio notation?

The colon (:) means "to" or "in comparison with". So, 3:2 means "3 to 2".

Can ratios have more than two numbers?

Yes, ratios can compare three or more quantities, like 2:3:5, showing the relationship between three different things.

Is 1:2 the same as 2:1?

No, they are different. 1:2 means one part of the first item to two parts of the second, while 2:1 means two parts of the first item to one part of the second. The order matters.