Question

Add and express the sum as a mixed fraction: \[\dfrac{24}{7}\]and \[\dfrac{-11}{4}\]

Answer 1

Hint: To solve this question, we need to add both the fractions with each other. The fraction given above are positive proper fraction and negative proper definition respectively. The denominator of both the fractions are different. After adding, we need to convert the resultant fraction into mixed fraction. This will be our final answer.

Complete step-by-step answer:
Now, we will solve the complete question. First of all, we must understand that the above two fractions are proper fraction with opposite nature means one is positive proper fraction and the other is negative proper fraction.
Proper fraction is defined as a type of fraction in which the numerator is smaller than the denominator.
We can also see in the question that the denominators of both the fractions are different. So, for adding then we must know the Least Common Multiple (L.C.M.) of the denominators.
As we know that the L.C.M. of 7 and 4 is 28.
So, we can write,
\[\begin{align}
  & =\left( \dfrac{24}{7} \right)+\left( \dfrac{-11}{4} \right) \\
 & =\dfrac{24}{7}-\dfrac{11}{4} \\
 & =\dfrac{(24\times 4)-(11\times 7)}{28} \\
 & =\dfrac{96-77}{28} \\
 & =\dfrac{19}{28} \\
\end{align}\]
The answer which we got here is in proper fraction. Now we have to convert this proper fraction into mixed fraction.
Mixed fraction is defined as a type of fraction which consists of a whole number as well as a fraction together.
As we know that the answer we got now is in the proper fraction, and we have to convert it into mixed fraction.
We know that, to convert a proper fraction into a mixed fraction, we just have to put 0 at the whole number’s place, and the fraction’s place will be the same as the proper fraction.
So, the mixed fraction form of \[\dfrac{19}{28}\] is \[0\dfrac{19}{28}\].
Therefore, the mixed fraction is \[0\dfrac{19}{28}\].

Note: We must remember the types of fraction, otherwise a student solving this question without the knowledge of types of fraction may confuse and the solution can be wrong. Also remember the way of adding two fractions when their denominators are different. Sometimes students may think about the conversion of proper fraction into mixed fraction, and may just write the proper fraction as an answer because of the 0 at the whole number’s place.