What is 405/1000 simplified as a fraction?
405/1000 in simplest form is 81/200.
Learn how to find what is 405/1000 simplified as a fraction just in a few minutes. We have covered why the GCF or factorization is important to simplify 405/1000 in simplest form.
To reduce 405/1000 in its lowest terms, you must be familiar with either how to find the greatest common factor or prime factors. Both of these methods are used to recognize if 405/1000 can be reduced in simplest form. In this case, the (greatest common factor) GDF of 405 and 1000 is 5. Dividing both the numerator and denominator by GCF, the fraction 405/1000 becomes 81/200 which is the simplest form.
405/1000 Simplified as a Fraction
Using Factorization:
405/1000 = (?)
405/1000 = (3 x 3 x 3 x 3 x 5)/(2 x 2 x 2 x 5 x 5 x 5) write 405/1000 in terms of factors
= 81/200
405/1000 = 81/200
405/1000 simplified is 81/200
Using GCF
405/1000 = (?)
GCF of 405 and 1000 is 5.
405/1000 = (405/5)/(1000/5)
= 81/200
405/1000 = 81/200
405/1000 simplified is 81/200 in fraction form
where,
405/1000 is the given fraction to be simplified,
81/200 is the lowest term of 405/1000.
Notes: 405/1000 simplified in lowest terms
1. 405/1000 can be simplified only if the GCF of numerator and denominator is greater than 1. In this case, the GCF of 405 and 1000 is 5 which is the greatest factor that evenly divides both numerator and denominator, so this fraction 405/1000 can be represented in its reduced form.
2. On the other hand, you can also reduce 405/1000 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 405/1000 becomes (3 x 3 x 3 x 3 x 5)/(2 x 2 x 2 x 5 x 5 x 5). Now you can check and cancel the factors if any factors of numerator and denominator cancel each other to simplify 405/1000 in its lowest terms.
step 1 Observe the input parameters and what to be found:
Input values:
Fraction = 405/1000
what to be found:
405/1000 = ?
Reduce 405/1000 in lowest terms.
step 2 Find the prime factors of the numerator of given fraction 405/1000.
Prime factors of 405 = 3 x 3 x 3 x 3 x 5
step 3 Find the prime factors of the denominator of given fraction 405/1000.
Prime factors of 1000 = 2 x 2 x 2 x 5 x 5 x 5
step 4 Rewrite the fraction 405/1000 in the form of prime factors as like the below:
405/1000= (3 x 3 x 3 x 3 x 5) / (2 x 2 x 2 x 5 x 5 x 5)
step 5 Check and reduce the factors of 405 and 1000 if any factors in the numerator and denominator cancel each other:
= (3 x 3 x 3 x 3 x 5) / (2 x 2 x 2 x 5 x 5 x 5)
= (3 x 3 x 3 x 3 )/(2 x 2 x 2 x 5 x 5)
405/1000 = 81/200
Hence,
405/1000 in simplest form is 81/200.
405/1000 simplified is 81/200, representing fraction in lowest terms is a better way than its original form, to easily recognize the fraction or use in mathematical operations. Simplifying 405/1000 to its simplest form involves the greatest common factor or factorization. Recognizing the GCF or prime factors of numerator and denominator of a fraction is key when you start reducing fractions like 405/1000 in its lowest terms.