Question

How do you write the fraction \[\dfrac{{20}}{{35}}\] in the simplest form?

Answer 1

Hint: When a term is divided into two parts by a horizontal line such that one number lies above the horizontal line and one below it, the numerator is defined as the part above the horizontal line and the denominator is the lower part. In this question, the numerator of the given fraction is 20 and the denominator is equal to 35 and we have to simplify this fraction. By writing both the numerator and the denominator as a product of their prime factors and then canceling out the common factors, we can simplify the given fraction. The process of writing a number as a product of the prime factors is known as its prime factorization. We can simplify the given fraction by using the above-mentioned information.

Complete step by step answer:
Prime factorization of 20 is –
$20 = 2 \times 2 \times 5$
Prime factorization of 35 is –
$35 = 5 \times 7$
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 –
$\dfrac{{20}}{{35}} = \dfrac{{\dfrac{{20}}{5}}}{{\dfrac{{35}}{5}}} = \dfrac{4}{7}$
Now, the numerator and the denominator don’t have any common factor, so it cannot be simplified further.

Hence, the simplified form of $\dfrac{{20}}{{35}}$ is $\dfrac{4}{7}$ .

Note: 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. This way we can check if the fraction is already simplified or not. The given fraction can be written in decimal form as 0.571428571. We can solve similar questions by following the information and the steps mentioned in the above solution.