Introduction to ratios

Suma is 8 years old and her mother is 32 years old.

So the age of Suma's Mother is 24 years more than Suma.

We can also say that Suma's age is 24 years less than her mother.

Here, we have compared the ages by considering the difference between them.

Let us consider few more examples.

Comparing lengths of a safety pin and a ruler by difference might not make sense.

For better comparison, find how many safety pins can be placed one after the other.....

.... to match the length of the ruler.

We can see that 10 safety pins have the same length as the ruler.

So we can say that length of the ruler is 10 times the length of the safety pin.

Example 2: The population of town A is 50,000 and town B is 3,00,000

Comparing by difference, population of town B is 2,50,000 more than that of A.

Comparing by division, population of town B is 6 times the population of town A.

This comparison by division is called ratio.

Ratio is denoted by the symbol shown above.

Let us solve few problems on ratio.

Problem 1: In a class, there are 16 girls and 8 boys. Find the ratio of girls to boys.

Given data is as above.

The ratio of girls to boys is as shown above.

The ratio of boys to girls is as shown.

Note that the ratios 16:8 and 8:16 are not equal.

In general a:b is not equal to b:a

Problem 2: The length of a ribbon is 15 cm and the length of a table is 15 m. Find the ratio of their lengths.

Finding the ratio of their lengths, we get 1:1

According to this the lengths should be the same which is not true.

Here, the units of the two quantities are different.

While finding the ratio, the units of the quantities should be the same.

Converting the units and finding the ratio, we get the ratio as above.

Revision

Comparison of division is known as ratio.

While finding the ratio between two quantities, the units should be the same.

The end