Question

What numbers should be added to $\dfrac{{ - 5}}{8}$ so as to get $\dfrac{{ - 3}}{2}$?

Answer 1

Hint: First, we have to assume that the number which should be added is $x$ (variable). Take the sum as a rational number $\dfrac{{ - 5}}{8}$ with the variable x and then we will equate with $\dfrac{{ - 3}}{2}$ to form equation with x. thus solving the equation we get the required number that should be added to get $\dfrac{{ - 3}}{2}$.

Complete step by step solution:
Let us assume the number to be added as a variable $x$ and here we are asked to find the number that must be added to the given number is in the rational form as $\dfrac{{ - 5}}{8}$
Thus, add both the rational number and variable we get $\dfrac{{ - 5}}{8} + x$
Now we will equate the terms into the given value $\dfrac{{ - 3}}{2}$ so that we can able to find the required number by finding the unknown value x.
Hence comparing both we have $\dfrac{{ - 5}}{8} + x = \dfrac{{ - 3}}{2}$
Now place the variable in the left-hand side and all the numbers in the right-hand side we get $\dfrac{{ - 5}}{8} + x = \dfrac{{ - 3}}{2} \Rightarrow x = \dfrac{{ - 3}}{2} + \dfrac{5}{8}$
Further solving using the cross-multiplication method we get $x = \dfrac{{ - 3}}{2} + \dfrac{5}{8} \Rightarrow x = \dfrac{{ - 12 + 5}}{8}$ where multiple the first numbers with$4$ to get the same denominator.
Hence using the subtraction operation, we get $x = \dfrac{{ - 7}}{8}$
Therefore $x = \dfrac{{ - 7}}{8}$ is the number that needed to add with $\dfrac{{ - 5}}{8}$ so it gets the number $\dfrac{{ - 3}}{2}$.

Note:
The concept of the cross multiplication is the LCM, which is the least common multiple method. We need to take the least common number and then equate with the numerator to obtain the result as $x = \dfrac{{ - 3}}{2} + \dfrac{5}{8} \Rightarrow x = \dfrac{{ - 12 + 5}}{8}$
The two operations that we used to solve are addition and multiplication.
The addition is the sum or addition of the two given numbers or variables like $x + x = 2x$
Multiplication is the number that multiplies times of another number or variable $x \times x = {x^2}$.