Introduction of ratio:   

In mathematics, a ratio expresses the consequence of quantities relative to every individual other.  In our daily life, a lot of a times we evaluate two quantities of the similar type. Ratio is the numerical relation of individual quantity to an additional of the similar type. This relationship is well-known as the Ratio. We refer to ratio by means of symbol ‘:’

Note:

        (i) The ratio be supposed to be expressed in simplify form.

        (ii) Ratio contains no units.

 

Definitions of Ratio fraction and Whole numbers:

 

Ratio fractions:

Set ratio up as Numerator: Denominator.

Whole numbers:

The natural numbers along with zero form the  group of whole numbers.

Same ratio in different situations:

Consider the following:

Length of a room is 30 m and its breadth is 20 m. So, the ratio of length of

the room to the breadth of the room = 30/20=3:/2=3:2

There are 24 girls and 16 boys going for a picnic. Ratio of the number of

girls to the number of boys =24/16=3/2==3:2

The ratio in both the examples is 3: 2.

 

Examples of ratio fraction to whole numbers:

 

Let us some examples of ratio fraction to whole numbers:

Example 1:

      Reduce 36:12 to the simplest form

Solution:

      Given: Ratio 24:36

      Prove: Simplest form of ratio

                   36:12 = `36/12`        (divide the 12 on both(numerator and denominator) sides)

                              = 3.  

       So simplest form of ratio is 3.

Example 2: (Writing ratio form)

Look at the following objects and put in writing the ratios of:

              

(1)   Red circles to green circles

(2)   Green circles to blue stars.

Solution:

Given: Red circles are 7

            Green circles are 4

            Blue stars are 4.

Therefore,

              (1)   7:4

              (2)   4:4.

 

Example 3:

      Find the missing values of following problems

              (1)   15:30::3:x

              (2)   x:21::3:7

Solution:

         (1)  Now convert the fraction

                         `15/30` = `3/x`

                Using the cross multiply, we get

                         15x=30*3=90

                             x = `90/15`     

                             x = 6.

               The missing value is 6.

         (2)  Now convert the fraction

                           ` x/21` = ` 3/7`

              Using the cross multiply, we get

                            7x = 21*3 = 63

                              x = `63/7`

                              x = 9.

         So, the missing the value is 9.

        These are the examples of ratio fraction to whole number.