Question

How do you simplify $\dfrac{1}{4} + (\dfrac{{ - 3}}{4})$ ?

Answer 1

A fraction is divided into two parts by a horizontal line, the numerator is defined as the number on the upper side of the horizontal line “p” and the denominator is defined as the number below the denominator.

In the fraction $\dfrac{p}{q}$ , “p” is the numerator and “q” is the denominator. We first take the least common factor of the denominators of the two fractions ( LCM is the smallest number divisible by both the numbers) for adding or subtracting two fractions.

After finding the common denominator for the two fractions, the numerators are multiplied with the quotients obtained on dividing the LCM by their denominator and then we have to perform the given arithmetic operation like addition, subtraction, multiplication and division in the numerator.

Complete step by step answer:
We have to simplify $\dfrac{1}{4} + ( - \dfrac{3}{4})$

In the given question, the denominator of the two fractions is same so the procedure is simpler as
follows –
$\Rightarrow \dfrac{1}{4} - \dfrac{3}{4} = \dfrac{{1 - 3}}{4} = \dfrac{{ - 2}}{4} \\\ \Rightarrow \dfrac{1}{4} + ( - \dfrac{3}{4}) = - \dfrac{1}{2} \\\$

Hence, the simplified form of $\dfrac{1}{4} + (\dfrac{{ - 3}}{4})$ is $- \dfrac{1}{2}$ .

Note: Real numbers and imaginary numbers are the two types of numbers, real numbers are the numbers can be shown on a number line. The numbers on the left side of the zero are negative and the numbers on the right side are positive. Fractions are a part of real numbers as they are shown on the number line. While multiplying two numbers, we multiply the signs of the numbers along with them. The signs are multiplied as (+)(+)=(+), (+)(-)=(-), (-)(+)=(-) and (-)(-)=(-) that’s why $a - ( - b) = a + b$ .