Question

What is $\dfrac{16}{64}$ simplified?

Answer 1

Hint: Assume the simplest form of the given fraction as ‘E’. Now, use the method of prime factorization to 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 $\dfrac{16}{64}$ 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 use the prime factorization method to write the numbers as a product of their primes.
Let us assume this fraction as E, so we have,
\[\Rightarrow E=\dfrac{16}{64}\]
Here the numerator 16 can be written as \[16=2\times 2\times 2\times 2\] as the product of its prime factors. Also, the denominator 64 can be written as \[64=2\times 2\times 2\times 2\times 2\times 2\] as the product of its primes. So we get,
\[\Rightarrow E=\dfrac{2\times 2\times 2\times 2}{2\times 2\times 2\times 2\times 2\times 2}\]
Clearly, we can see that four 2’s common in numerator and the denominator so cancelling them we get,
\[\begin{align}
  & \Rightarrow E=\dfrac{1}{2\times 2} \\
 & \therefore E=\dfrac{1}{4} \\
\end{align}\]

Hence \[\dfrac{1}{4}\] is the simplified form of the given expression.

Note: Note that here the numbers are small so we can directly cancel the common factors as we know that 4 times 16 equals 64. Sometimes the numbers will be large and in that case will need the help of prime factorization methods to simplify. Remember that this method is useful in finding the H.C.F and L.C.M of two or more numbers.