Question

How do you simplify: $\dfrac{1}{4} - \dfrac{2}{3}$ ?

Answer 1

Hint: Here in this question, we have a $ - $ symbol which represents the subtraction and we have to find the difference of the two numbers. The numbers are in the form of a 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 subtract them up.

Complete step by step answer:
Here in this question, we have to subtract the numbers. As we know the $ - $ sign indicates the subtraction. The numbers are in the form of a fraction. In fraction we have three types: proper fraction, improper fraction and mixed fraction.In the fraction the numerator is less than the denominator then it is the proper fraction. The numerator is greater than denominator then it is improper fraction. The fraction is a combination of whole number and fraction then it is a mixed fraction.Here in this question the both numbers are proper fraction.

Consider $\dfrac{1}{4} - \dfrac{2}{3}$. The values of the denominator are not the same so we take LCM for the denominator. Taking L.C.M. of denominators, we get,
$\dfrac{1}{4} - \dfrac{2}{3} = \dfrac{{\left( {1 \times 3} \right) - \left( {2 \times 4} \right)}}{{12}}$
Evaluating the product of numbers, we get,
$ \Rightarrow \dfrac{1}{4} - \dfrac{2}{3} = \dfrac{{3 - 8}}{{12}}$
Now, we can find the difference of the two fractions by doing the operations in numerators.Computing the difference, we get,
$ \therefore \dfrac{1}{4} - \dfrac{2}{3} = \dfrac{{ - 5}}{{12}}$
This is also a proper fraction, where the numerator is less than the denominator.We can’t simplify further.

Therefore, we have $\dfrac{1}{4} - \dfrac{2}{3} = - \dfrac{5}{{12}}$.

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 the numerators. Suppose if the fractions have different denominators, we have to take LCM for the denominators and we simplify for further.