Question

How do you simplify \[\dfrac{5}{8}+\left( -\dfrac{7}{8} \right)\]?

Answer 1

Hint: This question is from the topic of algebra. In solving this question, we will first remove the bracket and take out the negative number and remove the positive sign. After that, we will take out the common term from the equation that we will solve. After that, we will subtract the terms easily. After that, we will multiply the common term with the subtracted term. After that, we will get the answer.

Complete step by step solution:
Let us solve the question.
In this question, we have asked to simplify the term \[\dfrac{5}{8}+\left( -\dfrac{7}{8} \right)\]. We are going to solve the given term and simplify it.
The term which we have to solve is
\[\dfrac{5}{8}+\left( -\dfrac{7}{8} \right)\]
The term \[\dfrac{7}{8}\] is in the bracket with negative sign. So after removing the bracket, the positive sign will be removed and negative sign will be there with the term \[\dfrac{7}{8}\].
So, the above term can also be written as
\[\dfrac{5}{8}+\left( -\dfrac{7}{8} \right)=\dfrac{5}{8}-\dfrac{7}{8}\]
The above equation can also be written as
\[\Rightarrow \dfrac{5}{8}+\left( -\dfrac{7}{8} \right)=5\times \dfrac{1}{8}-7\times \dfrac{1}{8}\]
Now, we can say that the term \[\dfrac{1}{8}\] is common in both the terms which are in the right side of the equation. So, we can write the above equation as
\[\Rightarrow \dfrac{5}{8}+\left( -\dfrac{7}{8} \right)=\dfrac{1}{8}\times \left( 5-7 \right)\]
As we know that if we subtract 7 from 5, then we get -2. So, we can write the above equation as
\[\Rightarrow \dfrac{5}{8}+\left( -\dfrac{7}{8} \right)=\dfrac{1}{8}\times \left( -2 \right)\]
The above equation can also be written as
\[\Rightarrow \dfrac{5}{8}+\left( -\dfrac{7}{8} \right)=\dfrac{-2}{8}\]
Now, we know that 8 is equal to multiplication of 4 and 2. So, we can write
\[\Rightarrow \dfrac{5}{8}+\left( -\dfrac{7}{8} \right)=\dfrac{-2}{2\times 4}\]
The above equation can also be written as
\[\Rightarrow \dfrac{5}{8}+\left( -\dfrac{7}{8} \right)=\dfrac{-1}{4}\]

Hence, we have simplified the term \[\dfrac{5}{8}+\left( -\dfrac{7}{8} \right)\]. The simplified value of the term \[\dfrac{5}{8}+\left( -\dfrac{7}{8} \right)\] is \[\dfrac{-1}{4}\].

Note: For solving this type of question, we should have a better knowledge in the topic of algebra. We can solve this question by an alternate method. The term which we have to solve is
\[\dfrac{5}{8}+\left( -\dfrac{7}{8} \right)\]
This can also be written as
\[\Rightarrow \dfrac{5}{8}+\left( -\dfrac{7}{8} \right)=\dfrac{5}{8}-\dfrac{7}{8}\]
Now, we can that both the terms are having same denominator, so, we can the above equation as
\[\Rightarrow \dfrac{5}{8}+\left( -\dfrac{7}{8} \right)=\dfrac{5-7}{8}\]
The above equation can also be written as
\[\Rightarrow \dfrac{5}{8}+\left( -\dfrac{7}{8} \right)=\dfrac{-2}{8}\]
The above equation can also be written as
\[\Rightarrow \dfrac{5}{8}+\left( -\dfrac{7}{8} \right)=\dfrac{-1}{4}\]
Here, we can see that we got the same answer.
Hence, we can use this method too for this type of question.