Question

How do you simplify $\dfrac{15}{13}+ -\dfrac{-11.75}{13}$

Answer 1

Hint: To solve the following given expression, first we will discuss the steps to simplifying the fractional addition or subtraction and then simplify the given expression on the basis of the followed steps.

Complete step-by-step solution:
Firstly, we are going to discuss the steps for simplifying the fractional addition or subtraction:-
Step-1: Make sure the bottom numbers (the denominators) are the same.
Step-2: Add the top numbers (the numerators), put that answer over the denominator.
Step-3: Simplify the fraction (if needed).
Now, we will simplify the given expression:
First, rewrite the expression. The rule is: when minus multiplied with plus, then it becomes always minus:
\[
  \Rightarrow \dfrac{{15}}{{13}} + \,\, - \dfrac{{11.75}}{{13}} \\
    \Rightarrow \dfrac{{15}}{{13}} - \dfrac{{11.75}}{{13}} \\
]
Because both fractions have common denominators, we can subtract the numerators over the common denominators:
$ = \dfrac{{15 - 11.75}}{{13}} \Rightarrow \dfrac{{3.25}}{{13}}$
If necessary we can multiply by the appropriate form of 1 to eliminate the decimal in the numerator:
\[\dfrac{4}{4} \times \dfrac{{3.25}}{{13}} = \dfrac{{4 \times 3.25}}{{4 \times 13}} = \dfrac{{13}}{{52}}\]
Now, we can reduce the fraction as:
\[\therefore \dfrac{{13}}{{52}} = \dfrac{{13 \times 1}}{{13 \times 4}} = \dfrac{1}{4}\]

Hence, the simplified form of the given expression is $\dfrac{1}{4}$.

Note: If necessary, simplify the numerator and denominator into single fractions. Complex fractions aren't necessarily difficult to solve. In fact, complex fractions in which the numerator and denominator both contain a single fraction are usually fairly easy to solve.