Question

Solve \[\dfrac{4}{3} - \dfrac{1}{2}\] ?

Answer 1

Hint: Here we have to find the difference of the given data. Here the data is in the form of fraction. Since in the given data are in fraction the value of denominator is different so we find the LCM for both the denominators and then we subtract the numbers. hence, we obtain the required solution for the given question.

Complete step-by-step answer:
Fractions are the numerical values that are a part of the whole. If a number or a thing is divided into equal parts, then each part will be the fraction of the whole. A fraction is denoted as \[\dfrac{a}{b}\], where a is the numerator and b is the denominator.
We apply the arithmetic operations on the fractions. Here in this question, we add and subtract the two fractions. The LCM is a least common multiple. The LCM will be common for both the numbers.
Now consider the given question, here the minuend value will be \[\dfrac{4}{3}\] and the subtrahend is value is \[\dfrac{1}{2}\]and we have to determine the value of difference .
So therefore, the given data is written as
\[ \Rightarrow \dfrac{4}{3} - \dfrac{1}{2}\]
The denominators are different so we have to take LCM for the numbers 3 and 2. The LCM for the numbers 3 and 2 is 6
Therefore the above inequality is written as
\[ \Rightarrow \dfrac{{\dfrac{4}{3} \times 6 - \dfrac{1}{2} \times 6}}{6}\]
On simplifying we have
\[ \Rightarrow \dfrac{{4 \times 2 - 1 \times 3}}{6}\]
On further simplifying we have
\[ \Rightarrow \dfrac{{8 - 3}}{6}\]
On subtracting the number 3 from 8 we get
\[ \Rightarrow \dfrac{5}{6}\]
Therefore \[\dfrac{4}{3} - \dfrac{1}{2} = \dfrac{5}{6}\]
So, the correct answer is “\[\dfrac{5}{6}\]”.

Note: While adding the two fractions we need to check the values of the denominator, if both denominators are having the same value then we can add the numerators. Suppose if the fractions have different denominators, we have to take LCM for the denominators and we simplify for further.