Question

What is $\dfrac{13}{20}$ simplified?

Answer 1

Hint: Assume given fraction as ‘E’. Now, write the numbers present in the numerator and denominator as the product of their prime factors. Check if there are any common factors or not, if there are common factors then cancel them and take the product of remaining factors to get the answer. If there are no common factors then we will say that the given fraction is already in simplified form.

Complete step by step solution:
Here we have been provided with the fraction $\dfrac{13}{20}$ and we are asked to write it in its simplest form. That means we have to cancel the common factors of both the numerator and denominator if present. To find whether they have common factors or not we write the numbers as a product of their primes.
Let us assume this fraction as E, so we have,
\[\Rightarrow E=\dfrac{13}{20}\]
Now, the numerator 13 is already a prime so it can be further written as the product of prime numbers. However, the denominator 20 can be written as \[20=2\times 2\times 5\] as the product of its primes. So we get,
\[\Rightarrow E=\dfrac{13}{2\times 2\times 5}\]
Clearly we can see that there are no common factors to cancel that means we cannot simplify the fraction, it is already in simplified form.
\[\therefore E=\dfrac{13}{20}\]
Hence \[\dfrac{13}{20}\] is the simplified form of the given expression.

Note: If you want you may convert the given fraction into the decimal although it is not asked in the question. To change it in the decimal, multiply the denominator with 5 to get 100 there and to balance multiply the numerator also with 5. Now, take the decimal point two digits to the left to get the answer as 0.65. You must remember the prime factorization method as it helps in simplifying the fractions containing large numbers as the numerator and the denominator.