Question

How do you simplify the fraction 10/20?

Answer 1

Simplifying a fraction `\frac{p}{q}` means to rewrite it as an equivalent function `frac{m}{n}` such that `\frac{p}{q}=\frac{m}{n}`, but `m` and `n` have no common divisors.

In your case, the fraction `\frac{10}{20}` is not simplified, because both numbers are divided by 2 and 5.

Considering the generale case, if you want to simplify a fraction, you can write both numerator and denominator as the product of their prime factors, and then simplify all common primes.

In your case, one can write 10 as `2\cdot 5` and 20 as `2\cdot 2\cdot 5`.

Thus, the fraction `\frac{10}{20}` can be written as `\frac{2\cdot 5}{2\cdot 2\cdot 5}`. We can simplify one 2 and one 5 from both numerator and denominator, and so we conclude that `\frac{10}{20}` is simplified into `\frac{1}{2}`.