How do you decide to use fractions?

Answer 1

I use fractions whenever it makes the maths easier or to provide an exact result for a recurring decimal.

Examples:

* To square 15:

15 = 1.5 x 10 = 3/2 x 10

→ 15² = (3/2 x 10)² = 9/4 x 100 = 2 1/4 x 100 = 2.25 x 100 = 225

* To multiply by 5

5 = 10/2 so multiply by 10 and divide by 2.

*To divide by 5

dividing by 5 is the same as multiplying by 1/5

→ to divide by 5, multiply by 1/(10/2) = 2/10, ie double it and divide by 10.

If the result is a recurring decimal, eg what is 31 divided by 6: 31 ÷ 6 = 5 1/6 = 5.1666... (with the 6 recurring forever) only an approximate decimal can be given (5.2 or 5.17 or 5.167, etc) but the fraction gives an exact value: 5 1/6 - five and one sixth.