Question

Reduce the following fraction to the simplest form: \[\dfrac{7}{{28}}\].

Answer 1

Hint: Here, we need to express the given decimal as a fraction in the simplest form. We will divide the numerator and denominator by the same number until they become co-prime. A fraction \[\dfrac{a}{b}\] is in the simplest form if \[a\] and \[b\] are co-prime.

Complete step-by-step answer:
A fraction is a number which represents a part of a group. It is written as \[\dfrac{a}{b}\], where \[a\] is called the numerator and \[b\] is called the denominator. The group is divided into \[b\] equal parts.
We have to reduce \[\dfrac{7}{{28}}\] in the simplest form.
We know that a fraction \[\dfrac{a}{b}\] is in the simplest form if \[a\] and \[b\] are co-prime. We will divide the numerator and denominator by the same number till they become co-prime.
We know that 7 is the product of 7 and 1, and 28 is the product of 7 and 4.
Therefore, both the numerator 7 and the denominator 28 are divisible by 7.
Dividing the numerator and denominator by 7, we get
\[\begin{array}{l} \Rightarrow \dfrac{7}{{28}} = \dfrac{{\dfrac{7}{7}}}{{\dfrac{{28}}{7}}}\\ \Rightarrow \dfrac{7}{{28}} = \dfrac{1}{4}\end{array}\]
The factor of 1 is 1.
The factors of 4 are 1, 2, and 4.
Since the numbers 1 and 4 do not have a common factor other than 1, the numbers 1 and 4 are co-prime numbers.
Thus, we cannot simplify the fraction further.
Therefore, we have expressed \[\dfrac{7}{{28}}\] as a fraction in simplest form as \[\dfrac{1}{4}\].

Note: We used the term co-prime numbers in the solution. Two numbers are called co-prime numbers if they do not share any common factor other than 1. For example: The factors of 73 are 1 and 73. The factors of 200 are 1, 2, 4, 5, 8, 10, 20, 25, 40, 50, 100, 200. Since they have no common factor other than 1, the numbers 73 and 200 are co-prime numbers.