Question

Is the fraction $ \dfrac{4}{{10}} $ in its lowest terms? If not, how do you simplify it?

Answer 1

Hint: In this question, we are given a fraction whose numerator is 4 and denominator is 10 and we have to simplify the given fraction. A fraction is said to be simplified when the numerator and the denominator are in the form of prime factors and don’t have any common factor. By writing both the numerator and the denominator as a product of their prime factors, we can find whether the given fraction is simplified or not.

Complete step-by-step answer:
Given,
$ \dfrac{4}{{10}} $
Prime factorization of 4 is –
 $ 4 = 2 \times 2 $
Prime factorization of 10 is –
 $ 10 = 2 \times 5 $
We see that the numerator and the denominator have 2 as a common factor, so we divide the numerator and the denominator by 2 –
 $ \dfrac{4}{{10}} = \dfrac{{\dfrac{4}{2}}}{{\dfrac{{10}}{2}}} = \dfrac{2}{5} $
Now, the numerator and the denominator are both prime numbers and don’t have any common factor, so it cannot be simplified further.
Hence, the simplified form of $ \dfrac{4}{{10}} $ is $ \dfrac{2}{5} $ .
So, the correct answer is “ $ \dfrac{2}{5} $ ”.

Note: A fraction contains two parts namely the numerator and the denominator, the numerator is the part above the horizontal line that separates the two terms of a fraction and the denominator is the lower part. The prime factorization of a number is defined as the product of the prime factors (prime numbers are the numbers that are divisible by only 1 and themselves). The given fraction can be written in decimal form as 0.4. Following the information and the steps mentioned in the above solution, we can solve similar questions.