Ratio

Mathematical numbers utilized in contrasting two things which are comparative with one another regarding units are ratios.

 A ratio can be written in three distinct manners viz, x to y, x: y and xy yet read as the ratio of x to y.

For example: The ratio of 4 to 5 is 4: 5.

Contrasting things comparable with one another is the idea of ratio. Furthermore, when two ratios are equivalent, they are supposed to be in proportion to one another. It is addressed by the symbol '::'or ' = '.

Golden ratio

Two quantities are in the golden ratio if their ratio is equivalent to the ratio of their sum to bigger of the two quantities.

Example- If a and b are in golden ratio, then \dfrac{{{\rm{a + b}}}}{{\rm{a}}} = \dfrac{{\rm{a}}}{{\rm{b}}}

Ratio

The ratio is the examination of a quantity concerning another quantity. It is signified by .

Two quantities can measure up just in the event that they are in a similar unit.

Example: Father’s age is 50 years and the daughter’s age is 20 years.

The ratio of father’s age to daughter’s age =\dfrac{{{\rm{Father's age}}}}{{{\rm{Daughter's age}}}} = \dfrac{{50}}{{20}} = \dfrac{5}{2} = 5:2Difference between fractions and ratios

  • A fraction depicts a part of a whole and its denominator addresses the total number of parts.
    Example: \dfrac{1}{3} means one part out of 3 parts.
  • A ratio is an examination of two distinct quantities.

Example: In a club, 10 people like driving, 20 people like swimming and the total number of people in the club is 30.

The ratio of the number of people liking driving to the total number of people  = \;10:30.

The ratio of the number of people liking swimming to the number of people liking driving is 20:10.

Comparing quantities using ratios

  • Quantities can be compared using ratios.

Example: Sam worked for 8 hours and Jones worked for 2 hours. How many times Jones working hours is of Sam’s working hours?
Working hours of Sam = 8 hours
Working hours of Jones = 2 hours
The ratio of working hours =\dfrac{8}{2} = 4

Therefore, Sam works four times more than Jones.

Equivalent Ratios

When the ratios given are equal, they are called as equivalent ratios.

Equivalent ratios are obtained by multiplying and dividing the numerator and denominator with the same number.

Example: Ratios 10:20\;\left( { = 1:2} \right)\;and 11:22\;\left( { = 1:2} \right)\;are equivalent ratios.

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