975/100 Simplified

Learn how to find what is 975/100 simplified as a fraction just in a few minutes. We have covered why the greatest common divisor or factorization is important to simplify 975/100 in simplest form.

To simplify 975/100 in its lowest terms, you must be familiar with either how to find the greatest common divisor or prime factors. Both of these methods are used to recognize if 975/100 can be reduced in simplest form. In this case, the greatest common divisor of 975 and 100 is 25. Dividing both the numerator and denominator by GCD, the fraction 975/100 becomes 39/4 which is the simplest form.

Simplify 975/100 as a Fraction
Using Factorization:
975/100 = (?)
975/100 = (3 x 5 x 5 x 13)/(2 x 2 x 5 x 5)      //write 975/100 in terms of factors
= 39/4
975/100 = 39/4
975/100 simplified is 39/4

Using GCD:
975/100 = (?)
GCD of 975 and 100 is 25.
975/100 = (975/25)/(100/25)
= 39/4
975/100 = 39/4
975/100 simplified is 39/4 in fraction form
where,
975/100 is the given fraction to be simplified,
39/4 is the lowest term of 975/100.

Notes: Simplify 975/100 in lowest terms
1. 975/100 can be simplified only if the GCD of numerator and denominator is greater than 1. In this case, the GCD of 975 and 100 is 25 which is the greatest factor that evenly divides both numerator and denominator, so this fraction 975/100 can be represented in its reduced form.
2. On the other hand, you can also reduce 975/100 in simplest form by using the factorization method. In this case, the numerator and denominator of fraction should be written in the form of prime factors, so the fraction 975/100 becomes (3 x 5 x 5 x 13)/(2 x 2 x 5 x 5). Now you can check and cancel the factors if any factors of numerator and denominator cancel each other to simplify 975/100 in its lowest terms.

step 1 Observe the input parameters and what to be found:
Input values:
Fraction = 975/100

what to be found:
975/100 = ?
Simplify 975/100 in lowest terms.

step 2 Find the prime factors of the numerator of given fraction 975/100.
Prime factors of 975 = 3 x 5 x 5 x 13

step 3 Find the prime factors of the denominator of given fraction 975/100.
Prime factors of 100 = 2 x 2 x 5 x 5

step 4 Rewrite the fraction 975/100 in the form of prime factors as like the below:
975/100= (3 x 5 x 5 x 13) / (2 x 2 x 5 x 5)

step 5 Check and reduce the factors of 975 and 100 if any factors in the numerator and denominator cancel each other:
= (3 x 5 x 5 x 13) / (2 x 2 x 5 x 5)
= (3 x 13)/(2 x 2 )
975/100 = 39/4

Hence,
975/100 in simplest form is 39/4.

Representing fraction 975/100 in lowest terms is a better way than its original form to easily recognize the fraction or use in mathematical operations. Simplify fraction involves finding the greatest common factor or factorization. Recognizing the GCD or prime factors of numerator and denominator of a fraction is key when you start reducing fractions like 975/100 in its lowest terms.