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Maths / Comparing Quantities / Ratio and Percentages
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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 large frac{a}{b}  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.

  • frac{a}{b}=frac{xa}{xb},; where ;(x neq 0) So,; a : b =; xa : xb
  • frac{a}{b}=frac{frac{a}{x}}{frac{x}{b}},; where ;(x neq 0) So,; a : b =; frac{a}{x} :frac{b}{x}
  • 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:     frac{15}{10}=frac{15div 5}{10div 5}= frac{3}{2}

    In this we cancelled the common factor 5.  Thus, we have expressed the ratio

    frac{15}{10}; in; the; simplest; form,; i.e.,frac{3}{2}

    and the terms 3 and 2 have common factor only 1.

    Percentages: The word percent means per hundred.

    Conversion of Ratio into Percent:  x:y=frac{x}{y}= left [ frac{x}{y};X ;100 right ] %

     

    Example: Convert 3:4 into percent

    Solution:  3:4=frac{3}{4}= left [ frac{3}{4};X ;100 right ] %=25%

     

    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.

      dpi{100} frac{2}{5}; X ;100 =; 40%

    The divide the second ratio i.e. 3 with 5 and multiply with 100

       frac{3}{5} ;X ;100 = ;60%

    Or The second ratio can also be found as 100% - 40% = 60%

    Hence, we can express each part of ratio x:y as percentage

    =frac{x}{x+y};X; 100,; frac{y}{x+y};X ;100


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