Question

How do you simplify 16/80?

Answer 1

Hint: The above problem will be solved by factoring both the numerator and denominator and then we will cancel the common multiples.
By factorization we mean that numbers are divided evenly into another number. Factors are the numbers which we multiply together to get the desired number.
Using the above concept of factorisation we will solve the problem.

Complete step-by-step solution:
Let us discuss the method of factorization in more detail.
 Factorisation is the process of writing a number or another mathematical object as a product of several factors, usually simpler or smaller objects of the same kind. In simple words we will break down the numbers written in smallest numbers which on multiplication gives the same number.
For example: 20 is the number for which we have to find the factors;
20 can be factorized as:
$ \Rightarrow 20 = 2 \times 2 \times 5$ (2 and 5 are the factors of 20)
Now, we will find the factors of both numerator and denominator of the fraction $\dfrac{16}{80}$.
$ \Rightarrow 16 = 2 \times 2 \times 2 \times 2$ (Factors of 16 are four times 2)
$ \Rightarrow 80 = 2 \times 2 \times 2 \times 2 \times 5$ (Factors of 80 are 2 and 5)
We can observe that 16 and 80 has four times 2 common in both;
$ \Rightarrow \dfrac{{2 \times 2 \times 2 \times 2}}{{2 \times 2 \times 2 \times 2 \times 5}}$ (We will cancel the common terms of 2 from both numerator and denominator respectively)
$ \Rightarrow \dfrac{1}{5}$

$\dfrac{1}{5}$ is the required answer.

Note: The method of factorisation is used in several mathematical concepts such as LCM (Lowest common multiple uses the method of factorisation for finding the Lowest common multiple), similarly HCF (Highest common factor also breaks the number into smallest factors for determining the HCF). Not only have the constant numbers used the method of factorization but polynomials containing variable terms having the degree 2, 3, 4, 5 etc.