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What is ratio in Maths

In this article we are deeply going to explain the concept of Ratio.Ratio is something that we all use in our day to day life but most of the times we are not aware of it. we put the concept of ratio into practice whenever we have to make a division of quantities and then compare the divided quantities to make a decision . this article will first strengthen your conceptual understanding about Ratio next will help you apply your knowledge through solved and unsolved examples.

what is ratio in maths

what is ratio 

Ratio equals division Or Ratio is a comparison of two or more similar quantities .

below are given three examples related to the concept.Read them carefully 

Example 1: 15 kg rice is to be distributed between aman and raman in 3:2 then what will the amount of rice aman and raman get ?

Aaman get 3 parts while raman get 2 parts of 15 kg.it means 3 part and 2 parts make 15 kg.

(3+2) part  = 15 kg 
⇒ 5 parts = 15 kg
⇒ 1 part = 3 kg 

Amount of rice aman gets = 3 parts × 3 kg  = 9 kg
Amount of rice raman gets = 2 parts × 3 kg = 6 kg

Therefore 15 kg is divided into 9 kg and 6 kg  and the simplest  ratio/division = 9 kg / 6 kg = 3/2

Example 2 : 5 pens is to be given to two children in 3:2 then first child gets 3 pens and second one gets 2 pens. 

What if 12 pens is be given to 3 children in 1:2:3 then 
1 part + 2 part + 3 part = 12 pens
6 part =12 pens 
⇒1 part = 2 pens .

First child gets= 2 pens
Second child gets = 2 × 2 pens= 4 pens 
Third child gets= 3× 2 pens = 6 pens

Example 3 : A 0.5 foot rope is cut into 4:2 then what will be the length(in inches ) of the longer part ?

0.5 feet = 0.5 × 6 = 12 inches
4 parts +2 parts = 6 parts 
⇒ 6 parts = 12 inches
⇒ 1 part = 2 inches
length of the longer part =  4 part  × 2 inches
                                       = 8 inches

Conversion from Ratio to percentage 

The following formula is used if the percentage of the first value to be found for a given Ratio.

Percentage of first value = (First value    /Sum of all values) ×100

Percentage of second value= (second value/Sum of all values)×100

In a bottle the Ratio of milk and water is 2:3 find the percentage of milk in the bottle 

Total sum of quantities = 3+2 =5
Percentage of milk in the bottle =                                                                       =2/5×100
                                                        =40%

Similarly If we are asked to find the percentage the of water in the bottle 

Percentage of water = (3/5)×100
                                     = 60%

Ratio questions with Illustration 


Illustration 1 : What is the ratio of 8 to 4?




Illustration 2 : If a class has 10 boys and 15 girls, what is the ratio of boys to girls?




Illustration 3 : Simplify the ratio 12 : 18.



Illustration 4 : A bag has 5 red balls and 20 blue balls. What is the ratio of blue balls to red balls?





Illustration 5 : Write the ratio of 25 minutes to 1 hour.



Ratio FAQs

Q1: What is the unit of Ratio?

Ans : Since Ratio is a fraction, hence there is no unit of it.

Q2 : Are Ratio and Proportion the same?

Ans : No Both the terms refers to different things. Ratio compares two quantities whereas proportion compares two ratios.

Q3 : Can Ratio be Positive or Negative?
Ans : Yes ratio can be either positive or negative. But mostly in maths it is found postive.



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