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In a nutshell​

Ratios are used to describe how something is divided between two or more categories. You need to know how to read, interpret and simplify ratios, as well as solve problems involving ratios.


A ratio is a piece of information that compares quantities.

Representing ratios

A ratio is written using colons (:) to separate and compare numbers. When reading ratios, read the colons as "to". For example, the ratio 2:32:3 is read as "two to three".

Interpreting ratios

Ratios are best understood through examples.

  • If a recipe says to mix flour and water in the ratio 3:13:1, it means for every 33​ cups of flour you add, you have to also add 11​ cup of water.
  • If money between three friends Adam, Becky and Claire is divided in the ratio 1:2:31:2:3, it means that for every 11​ pound that Adam gets, Becky gets 22​ pounds and Claire gets 33​ pounds.
  • If a class has boys and girls in the ratio 4:34:3​, it means that for every 44​ boys in the class, there are also 33​ girls.
  • If the ratio of chairs to tables in a room is 1:11:1, it means that for every chair, you also have a table. In other words, there is an equal amount of tables and chairs.

Simplifying ratios

It is possible to simplify ratios to their lowest form, much like fractions. However, it is first important to understand how two ratios can be equal.

Equal ratios

If all the numbers in a ratio are multiplied or divided by the same number, then the value of the ratio doesn't change.

  • 4:5=(4×2):(5×2)=8:104:5=(4\times2):(5\times2)=8:10
  • 9:30=(9÷3):(30÷3)=3:109:30=(9\div3):(30\div3)=3:10
  • 11:2:6=(11×4):(2×4):(6×4)=44:8:2411:2:6=(11\times4):(2\times4):(6\times4)=44:8:24
  • 4:5=(4÷4):(5÷4)=1:1.254:5=(4\div4):(5\div4)=1:1.25

Simplifying a ratio to its simplest form



Find a number that all numbers in the ratio can be divided by. This is called a common factor.


Divide all the numbers in the ratio by this common factor.


Keep doing this until the ratio cannot be simplified any further. This is called the simplest form of the ratio.

Example 1

Simplify the ratio 10:6:1610:6:16 to its simplest form.

1010​, 66​, and 1616​ are all even numbers. So, they are all divisible by 22​. Hence, 22​ is a common factor.

Divide all three numbers in the ratio by 22​:






The numbers 5533​ and 88​ have no common factors, so this ratio cannot be simplified further. Therefore:

10:6:16=5:3:8\underline{10:6:16=5:3:8} in its simplest form.

Ratio problems - scaling up

Ratios can be used to calculate how much of a certain quantity is needed in relation to another given quantity.

Example 2

The ratio of boys to girls in a classroom is 4:34:3. If there are 2020​ boys in this class, how many girls are there?

Call the number of girls in the class xx. The 2020​ boys and xx girls must be in the ratio 4:34:3. Therefore:


Find what number is multiplied by 44​ that gives 2020​:


Multiply 33​ by 55​ to get the number of girls in the class:



There are 15\underline{15} girls in the class.

Ratio problems - sharing

Another common type of ratio question is to divide and share a quantity into a given ratio. With these problems, it's easiest to think of "parts".

Example 3

£150£150 is split between two friends Carl and Daniel in the ratio 7:37:3. How much money does Carl get?

Calculate the total number of parts by adding the numbers in the ratio:

Carl gets 77​ "parts" of the money, and Daniel will get 33​ "parts".

77​ parts + 33​ parts = 1010​ parts in total.

Find the value of 11​ part:

If 1010​ parts =£150=£150​, then 11​ part = £150÷10=£15£150\div10=£15.

Find how much money Carl gets:

If 11​ part = £15£15, and Carl gets 77​ parts, then Carl gets £15×7=£105£15\times7=£105.

Carl gets £105.\underline{£105.}

Frequently Asked Questions (FAQ)


  • Question: How do you simplify ratios?

    Answer: First, find a common factor that divides all the numbers. Then, divide all the numbers in the ratio by this common factor. Repeat until you cannot simplify the ratio any further.

  • Question: How do you read and write ratios?

    Answer: Separate numbers with a colon, the colon is read as "to".

  • Question: What is a ratio?

    Answer: A ratio is a piece of information that compares quantities.



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