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Example : Compare: 3 : 5 and 4 : 7.

First, let us write the ratios 3 : 5 and 4 : 7 as fractions. The above two fractions do not have the same denominators. Let us make them to be same.

For that, we have to find L. M of the denominators 5,7.

We have to make each denominator as Now compare the numerators 21 and Hence the first ratio 3 : 5 is greater than 4 : 7. First find the common tern in the given two ratios P : Q and Q : R.

That is Q.

After having done the above step, take the values corresponding to P, Q, R in the above ratios and form the ratio P : Q : R. The value corresponding to Q in the first ratio is 3 and in the second ratio is 4. Example : The ratio of speeds of two vehicles is 2 : 3.

Example — Here last two digits 48 are divisible by 4, so is also divisible by 4. Example — , Here last 3 digits are divided by 8, hence the number is divisible by 8. Divisible by 10 — If a number ends with 0, then it is divisible by Example — , , Divisible by 12 — If a number is divisible by 3 and 4 both, then it will also be divisible by 12 as well.

Example — is divisible by 3 and 4 both, so it will be divisible by 12 also. Divisible by 14 — If a number is divisible by 2 and 7 both, then it will also be divisible by 14 as well.

Example — is divisible by 2 and 7 both, so it will be divisible by 14 also.

Divisible by 15 — If a number is divisible by 3 and 5 both, then it will also be divisible by 15 as well. Example — is divisible by 3 and 5 both, so it will be divisible by 15 also.