Ratio
If we compare two quantities using division then it is called ratio. It compares quantities in terms of ‘How many times’. The symbol to represent ratio is “:”.
It reads as “4 is to 3”
It can also be written as 4/3.
Example
If there are 35 boys and 25 girls in a class, then what is the ratio of
- Number of boys to total students
- Number of girls to total students.
Solution
In the ratio, we want the total number of students.
Total number of students = Number of boys + Number of girls
35 + 25 = 60
- Ratio of number of boys to total number of students
- The ratio of the number of girls to the total number of students
The unit must be same to compare two quantities
If we have to compare two quantities with different units then we need to convert them in the same unit .then only they can be compared using ratio.
Example
What is the ratio of the height of Raman and Radha if the height of Raman is 175 cm and Radha is 1.35 m?
Solution
The unit of the height of Raman and Radha is not same so convert them in the same unit.
Height of Radha is 1.35 m = 1.35 × 100 cm = 135 cm
The ratio of the height of Raman and Radha
Equivalent Ratios
If we multiply or divide both the numerator and denominator by the same number then we get the equivalent ratio. There could be so many equivalent ratios of the same ratio.
In the case of equivalent ratios only their value changes but they represent the same portion of the quantity.
Example
Find two equivalent ratios of 2/4.
Solution
To get the equivalent ratio we multiply both the numerator and denominator with 2.
To get another equivalent ratio we divide both the numerator and denominator with 2.
From the above figure, we can see that in all the equivalent ratios only the number of equal parts is changing but all the ratios are representing the half part of the circle only.
The Lowest form of the Ratio
If there is no common factor of numerator and denominator except one then it is the lowest form of the ratio.
Example
Find the lowest form of the ratio 25: 100.
Solution
The common factor of 25 and 100 is 25, so divide both the numerator and denominator with 25.
Hence the lowest ratio of 25: 100 is 1: 4.
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