Question

Simplify: $\dfrac{5}{4} - \dfrac{7}{6} - \left( {\dfrac{{ - 2}}{3}} \right)$

Answer 1

Hint: Here in this question, we have $ - $ symbol which represents the subtraction and we have to subtract one number from another. The numbers are in the form of fraction. We are going to simplify the difference of two fractions by taking the LCM of the denominators of the fractions such that the value of both the fractions remains unchanged and then add them up.

Complete step-by-step answer:
Here in this question, we have to subtract the fractions and simplify the value of the given expression. In fraction we have 3 types: proper fraction, improper fraction and mixed fraction.
If in the fraction the numerator is less than the denominator, then it is a proper fraction. If the numerator is greater than denominator, then it is improper fraction. If the fraction is combination of whole number and fraction then it is mixed fraction.
Here in this question, we have to simplify the expression: $\dfrac{5}{4} - \dfrac{7}{6} - \left( {\dfrac{{ - 2}}{3}} \right)$
The values of denominators are not the same, so we take LCM for the denominators.
The denominators of the fractions are: $4$, $6$ and $3$.
Now, we know that the LCM of $4$, $6$ and $3$ is $12$.
Now, multiplying the numerators and denominators of the fractions in order to have the same denominator for all the fractions, we get,
$ \Rightarrow \dfrac{5}{4} \times \left( {\dfrac{3}{3}} \right) - \dfrac{7}{6} \times \left( {\dfrac{2}{2}} \right) - \left( {\dfrac{{ - 2}}{3}} \right) \times \left( {\dfrac{4}{4}} \right)$
Simplifying the expression, we get,
$ \Rightarrow \dfrac{{15}}{{12}} - \dfrac{{14}}{{12}} - \left( {\dfrac{{ - 8}}{{12}}} \right)$
Now, we open the brackets and simplify the expression further.
$ \Rightarrow \dfrac{{15}}{{12}} - \dfrac{{14}}{{12}} + \dfrac{8}{{12}}$
$ \Rightarrow \dfrac{{15 - 14 + 8}}{{12}}$
$ \Rightarrow \dfrac{9}{{12}}$
Cancelling the common factors in numerator and denominator, we get,
$ \Rightarrow \dfrac{3}{4}$
Now, this is a proper fraction, where the numerator is less than the denominator.
We can’t simplify further. Therefore, we have $\dfrac{5}{4} - \dfrac{7}{6} - \left( {\dfrac{{ - 2}}{3}} \right) = \dfrac{3}{4}$.
So, the correct answer is “$\dfrac{3}{4}$”.

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