Question

What number should be added to \[\dfrac{{ - 5}}{8}\] so as to get \[\dfrac{{ - 3}}{2}\]?

Answer 1

Hint: Assume the unknown value as any one variable. Later substitute the unknown variable in the given expression and solve the expression to get the required answer.

Complete step-by-step answer:
Now, consider the given question, we are asked to determine a number that should be added to \[\dfrac{{ - 5}}{8}\] so as to get \[\dfrac{{ - 3}}{2}\]. Let the number which has to be added be x, so it will be convenient to write this condition mathematically i.e. \[{\text{x}} + \left( {\dfrac{{ - 5}}{8}} \right) = \dfrac{{ - 3}}{2}\].
Substituting the unknown variable in the given expression.
\[\ {\text{x}} + \left( {\dfrac{{ - 5}}{8}} \right) = \dfrac{{ - 3}}{2} \\
  x - \dfrac{5}{8} = - \dfrac{3}{2} \\
  x = \dfrac{{ - 3}}{2} + \dfrac{5}{8}
 \]
Solving it further we obtain,
\[ {\text{x}} = \dfrac{{\left( { - 3 \times 4} \right) + 5}}{8} \\
  {\text{x}} = \dfrac{{ - 12 + 5}}{8} \\
  {\text{x}} = \dfrac{{ - 7}}{8}
\]

Hence, \[\dfrac{{ - 7}}{8}\] must be added to \[\dfrac{{ - 5}}{8}\] so as to get \[\dfrac{{ - 3}}{2}\].

Note: Any number which can be represented in the form of $\dfrac{p}{q}$ is termed as a rational number. Rational numbers can either be positive or negative.
We must also remember the BODMAS rule when different operations are given in a single expression.
BODMAS stands for,
BO: Bracket open
D: Division
M: Multiplication
A: Addition
S: Subtraction