# GRE Arithmetic | Ratio

The **Ratio** is the measure of the relative quantity of two or more than two entity. It is often expressed in terms of the fraction, i.e., one quantity in numerator another quantity in the denominator.

Let’s say a is proportional to b. It will be notated as ‘a is to b’ or ‘a : b’.

**For example:**

- The ratio of age of son to father is ‘1 is to 7’.

It can be written as 1 : 7.

or the ratio of age of son to father is 1 / 7. - In a class there are 39 boys and 13 girls. What is the ratio of boys to girls?

It can be written as ’39 is to 13′

or 39 : 13

or in terms of fraction 39 / 13

Like a fraction, it can be simplified:

i.e. the ratio of boys to girls is 39 / 13 = 3 / 1

or 3 : 1.

Since the ratio is not limited over only two quantities, it can be expressed for more than two entities.

**For example:**

- In furniture shop the ratio of ‘chairs is to tables is to sofas’ is 5 is to 7 is to 10

or 5 : 7 : 10 What is the ratio of chairs to sofas?

**Solution:**Te ratio of chairs to tables is 5 is to 7

or 5 : 7

or 5 / 7

The ratio of tables to sofas is 7 is to 10

or 7 : 10

or 7 / 10

i.e. there are 5 chairs for every 10 sofas

or 5 : 10

or 1 / 2 - There are 2 pens for every 3 pencils and 5 notebooks for every 2 pencils in a bag.
Pen to pencil ratio can be written as ‘2 is to 3’

or 2 : 3

or 2 / 3

Pencil to notebook ratio can be written as ‘2 is to 5’

or 2 : 5

or 2 / 5.To find the ratio of pen is to pencils is to notebooks:

Equate the denominator of 2 / 3 and numerator of 2 / 5

To complete the above task, take LCM of 2 and 3 which is 6.To convert 3 into 6, multiply 3 by 2 and to convert 2 into 6 multiply it by 3. While doing this both fraction will be disturbed. To balance this multiply the numerator and denominator of the first fraction by 2 and second fraction by 3.

New fraction will be:

- (2 * 2) / (3 * 2) = 4 / 6
- (2 * 3) / (5 * 3) = 6 / 15

The ratio of pen is to pencils is to notebooks = 4 is to 6 is to 15

or 4 : 6 : 15 - A : B : C : D = 1 : 3 : 5 : 4

For Each A there are 3 B, for each A there are 5 C and for each A there are 4 D

or for each 3 B there are 5 C and for each 3 B there are 4 D

or for each 5 C there are 4 D.

**Proportion:**

When two ratios are related by an equation it is called proportion. For example:

x / 2 = 3 /4 x = 3 / 2

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