Question

How do you simplify $ \dfrac{{35}}{{100}} $ ?

Answer 1

Hint: In this question, the numerator of the given fraction is 35 and the denominator is equal to 100 and we have to simplify this fraction. When the numerator and the denominator are in the form of prime factors and don’t have any common factor, the fraction is said to be simplified. We can find whether the given fraction is simplified or not by writing both the numerator and the denominator as a product of their prime factors, and thus simplify the fraction if it is not in the simplified form

Complete step-by-step answer:
Given,
 $ \dfrac{{35}}{{100}} $
Prime factorization of 35 is –
 $ 35 = 5 \times 7 $
Prime factorization of 100 is –
 $ 100 = 2 \times 2 \times 5 \times 5 $
We see that 5 is present in both the numerator and the denominator, so we have 5 as a common factor, and thus we divide the numerator and the denominator by 5 –
 $ \dfrac{{35}}{{100}} = \dfrac{{\dfrac{{35}}{5}}}{{\dfrac{{100}}{5}}} = \dfrac{7}{{20}} $
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{{35}}{{100}} $ is $ \dfrac{7}{{20}} $ .
So, the correct answer is “ $ \dfrac{7}{{20}} $ ”.

Note: When a horizontal line divides a term into two parts such that there is one number above the horizontal line and one below it, the part above the horizontal line is called the numerator and the denominator is the lower part. The process of writing a number as a product of the prime factors is known as its prime factorization. The given fraction can be written in decimal form as 0.35. Following the information and the steps mentioned in the above solution, we can solve similar questions.