Ratio

The ratio is the method to show the relationship between two numbers or two quantities which indicate the number of times the first number contains the second. The ratio between two quantities is obtained by dividing the first quantity by the second. For example: the ratio between Rs 15 and Rs 30 = \(\frac{15}{30}\) = \(\frac{1}{2}\) = 1:2

There are three ways to write a ratio:

• As fraction = \(\frac{1}{2}\) ( 1 upon 2 )
• With a colon ( : ), 2 : 5 ( 2 is to 5)
• With the word " to", ( 2 to 5)

Things to remember

• A ratio doesn't contain any unit as it is pure number.
• While finding the ratio between two quantities, both quantities should be of the same unit. For example, the ratio between 20 cm and 3 m = ratio between 20 cm and 300 cm = \(\frac{20}{300}\) = \(\frac{1}{15}\) = 1:15.
• A ratio remains unchanged if both of its terms be multiplied or divided by the same number.
  For example:
  \(\frac{1}{3}\) = \(\frac{1}{3}\) x \(\frac{4}{4}\) = \(\frac{4}{12}\) = \(\frac{1}{3}\)
• A ratio should always be expressed in its lowest terms.
  For example;
  \(\frac{20}{32}\) = \(\frac{20}{32}\) ÷ \(\frac{4}{4}\) = \(\frac{5}{8}\)
  
  

To divide a given quantity in a given ratio

Let's divide Rs 450 among three persons in the ratio 2 : 3: 4

Since 2 + 3 + 4 =9

• Renu's share = \(\frac{2}{9}\) x Rs 450 = Rs 100
• Barsha's share = \(\frac{3}{9}\) x Rs 450 =Rs 150
• Sabina's share = \(\frac{4}{9}\) x Rs 450 =Rs 200