Question

What is the lowest term in \[\dfrac{64}{32}?\]

Answer 1

Hint: To get the solution of this question firstly we have to take the prime factorization of numerator as well as denominator. After eliminating the common terms present in the numerator and denominator we are left with a relatively prime fraction which is the required answer.

Complete step by step answer:
In this question they are trying to ask the lowest term of the given fraction. To calculate the lowest term, first let us know what the meaning of lowest term for fractions is. When the numerator and denominator do not contain any factor in common except for \[1\].
So to solve this question firstly we have to find the prime factors of numerator and denominator individually after that the common factors will automatically get cancelled out and we are left with the final answer.
The prime factors mean the factors of any number and all the factors are prime numbers i.e. the number is either divisible by itself or by \[1\].
In the given question numerator is \[64\]and we can represent \[64\]as the multiple of \[2\] like \[2\times 2\times 2\times 2\times 2\times 2\]or we can say \[{{2}^{6}}\]. So the prime factors of numerator are \[2,2,2,2,2,2\] .And in the given question denominator is \[32\] so we can represent \[32\]as the multiple of prime numbers like \[2\times 2\times 2\times 2\times 2\] or we can say \[{{2}^{5}}\] so the prime factors of denominator are \[2,2,2,2,2\].
The given fraction can be represented as \[\dfrac{{{2}^{6}}}{{{2}^{5}}}\]. Now taking \[{{2}^{5}}\] common from the numerator, we get
\[\Rightarrow \dfrac{{{2}^{5}}\times 2}{{{2}^{5}}}\]
Cancelling out the term \[{{2}^{5}}\]from numerator as well as from denominator, we get
\[\Rightarrow \dfrac{2}{1}\]
Now further we cannot reduce the fraction because now the numerator and denominator are relatively prime. The fraction we get after reducing \[\dfrac{64}{32}\] is an improper fraction. It is that fraction in which the numerator value is greater than the denominator value.
There are two other major types of fraction, they are proper fraction and mixed fraction.

Note: Types of fraction are proper fraction, improper fraction and mixed fraction. The fraction whose numerator value is less than the denominator is known as the proper fraction. The fraction which contains the whole number part as well as the fraction part is known as mixed fraction.