Ratio and Percentages
Ratio and Percentages
Ratio and Percentage:
Ratio: The ratio of two quantities 'a' and 'b' of the same kind and in the same units is a fraction which shows that how many times one quantity is of the other and is written as a : b and is read as 'a is to b' where b ≠ 0.
Terms of the ratio: In the ratio a : b, the quantities a and b are called terms of the ratio. Here, 'a' is called the first term or the antecedent and `b' is called the second term or consequent. In the ratio 5 : 9, 5 is called the antecedent and 9 is called the consequent.
Properties of ratio: If the first term and the second term of a ratio are multiplied / divided by the same non-zero number, the ratio does not change.
Ratio in the simplest form: A ratio a : b is said to be in the simplest form if a and b have no common factor other than 1.
Example: Express 15 : 10 in the simplest form.
Solution:
In this we cancelled the common factor 5. Thus, we have expressed the ratio
and the terms 3 and 2 have common factor only 1.
Percentages: The word percent means per hundred.
Conversion of Ratio into Percent:
Example: Convert 3:4 into percent
Solution:
Ratio and Percentage: To express a ratio as percentage we add both the ratios. Then we divide the ratio with the sum of ratios and multiply it with 100.
Example: Express 2:3 as percentage
Solution: First we find the sum of ratios: 2+3 = 5
The divide the first ratio i.e. 2 with 5 and multiply with 100.
The divide the second ratio i.e. 3 with 5 and multiply with 100
Or The second ratio can also be found as 100% - 40% = 60%
Hence, we can express each part of ratio x:y as percentage
72% of 50 students are good at Mathematics. How many are not good at it? | |||
| Right Option : D | |||
| View Explanation | |||
Express 18:36 in simplest form. | |||
| Right Option : C | |||
| View Explanation | |||
A ratio is a comparison by division of two quantities with the ________________ unit. | |||
| Right Option : A | |||
| View Explanation | |||
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