Sometimes, we have to deal with the quantities whose comparison is required. Suppose in a class of 45-students, 15 of the students are girls, 30 of the students are boys, and then we can compare the number of boys with number of girls in two different ways.

**1. **There are 15 more boys than girls in the class. In this case we are comparing the number of boys and number of girls by finding their difference.

**2. **The number of boys is twice the number of girls in the class. Here, we are comparing the number of boys and number of girls by finding a fraction consisting of the number of boys over the number of girls. i.e., fraction is

**“Ratio is fraction of two quantities of the same kind”**

In other words

**“Ratio is the comparison of two homogeneous quantities” or ” Ratio is the division of two quantities**

**and**

**having the same units”**

It is denoted by (read as “

**a**ratio

**b**”) or

The ratio has no unit. It is a numerical quantity which indicates how many times one quantity is greater than the other.

**For example:**The boy : girl, i.e. 30 : 15 or 2 : 1 indicates that the number of boys is twice the number of girls.

**For example:**The girl : boy, i.e. 1 : 2 or indicates that there are half girls than boys.

**Example:**

Find the ratio of (1) 50g to 200g (2) 700g to 1kg

**Solution:**

**(1)**The ratio of 50g to 200g can be found in two ways.

50 : 200 or 50 : 200

= or (divided by 50)

= or 1 : 4

=1 : 4

Hence, ratio of 50g to 200g is 1 to 4.

**(2)** 700g and 1kg have different units. First, we express them in the same units we know that

700g : 1kg

=700g : 1000g (since 1kg=1000g)

=700 : 1000 (divided by 100)

=7 : 10

Hence, ratio of 700g to 1kg is 7 to 10.

**Example:**

Suppose three men receive their profits as 4000, 3000 and 1000. Find the ratio between their profits.

**Solution:**

The ratio of their share (profit) is

4000 : 3000 : 1000

= 4 : 3 : 1 (divided by 1000)

**Example:**

Simplify the ratio of 3.5 : 2.5

**Solution:**

We are given that

3.5 : 2.5

=

= 35 : 25 (multiply by 10)

= 7 : 5 (Dividing by 5)

**Example:**

Express in the form of and fraction

(a) 25, 45 (b) 30min, 1hour

**Solution:**

- 25, 45

= 25 : 45

=5 : 9 (Divided by 5)

And in fraction form we have

- 30min, 1hour

30min : 1hour (since 60min=1hour)

= h : 1h (1min=hour)

= : 1 (30min=hour=h)

= 1 : 2 (Multiply by 2)

And in fraction form we have