Question

Simplify.
(a) $ 28 + \left( { - 9} \right) - 4 - \left( { - 3} \right) $
(c) $ 402 + \left( { - 79} \right) + \left( { - 64} \right) - \left( { - 8} \right) + 26 $

Answer 1

Hint: In order to solve this question we need to know about PEMDAS . It is the acronym which helps in remembering the order of operations needed to be performed while simplifying a question . As we read PEDMAS , letter by letter from left to right we get to know that the preference or the priorities of the operators start getting lesser. We solve the operator of higher priority first , taking the operands from either of two sides of the operator and then calculating it terms by terms as per their precedence .

Complete step-by-step answer:
(a) $ 28 + \left( { - 9} \right) - 4 - \left( { - 3} \right) $
Rewriting the question, $ 28 + \left( { - 9} \right) - 4 - \left( { - 3} \right) $ , we can see here are four terms .
And we are supposed to simplify each term to get a single answer of each term and again simplify in the same manner until we get the single answer.
 $ 28 + \left( { - 9} \right) - 4 - \left( { - 3} \right) $
Using the PEMDAS , it suggests that P stands for Parentheses , E stands for Exponents , M stands for Multiplication , D stands for Division , A stands for Addition , S stands for Subtraction .
So as per our given question Parenthesis should be performed first and thereafter Addition and subtraction .
 $ 28 + \left( { - 9} \right) - 4 - \left( { - 3} \right) $ ,as we know when negative is multiplied with negative it becomes positive, similarly when negative multiplies with positive with positive it becomes negative.
 $ 28 - 9 - 4 + 3 $
And now according to the PEMDAS rule , addition operation has higher priority so it is solved first before the subtraction operator we get
 $
   = 28 - 9 - 1 \\
   = 18 \;
 $
So, the correct answer is “18”.

Now we will end simplifying here as no operator left to be performed also the answer to the original question has ended in a single answer $ 18 $ .
Therefore, the simplification of $ 28 + \left( { - 9} \right) - 4 - \left( { - 3} \right) = 18 $
(b) $ 402 + \left( { - 79} \right) + \left( { - 64} \right) - \left( { - 8} \right) + 26 $
As we have seen in the first simplification, all the steps are completely the same .
Parenthesis are first solved which give the simplification as
 $ = 402 - 79 - 64 + 8 + 26 $
Addition has higher priority, so all the addition operations are performed followed by all the subtraction operations
\[
   = 402 - 79 - 64 + 8 + 26 \\
   = 402 - 79 - 30 \\
   = 293 \;
 \]
Now we will end simplifying here as no operator left to be performed also the answer to the original question has ended in a single answer $ 293 $ .
Therefore, the simplification of $ 402 + \left( { - 79} \right) + \left( { - 64} \right) - \left( { - 8} \right) + 26 = 293 $
So, the correct answer is “293”.

Note: 1.While performing the simplification using PEMDAS also accepts to solve by the rule of PEDMSA .
2.Parentheses are not operations but can be considered as a container for operations.
3.Its Easier but needs to be simplified carefully as the variations in the priorities can result in obtaining wrong answers .
4.Multiplication and Division have the same equal powers in computing .
5.Also Addition and subtraction have equal powers in computing .