Question

Solve the following:
\[\left( -8 \right)+\left( -9 \right)+\left( +17 \right)\]

Answer 1

Hint: Here first of all consider the expression given in the question as \[A=\left( -8 \right)+\left( -9 \right)+\left( +17 \right)\]. Now by using the BODMAS rule, first of all solve the brackets of the given expression, then use \[-a-b=-\left( a+b \right)\] and proceed.

Complete step-by-step answer:
Here we have to find the value of \[\left( -8 \right)+\left( -9 \right)+\left( +17 \right)\]. By proceeding with the question, we must know some of the important points related to numbers and signs (+, -) in mathematics.
First of all, we will see what the BODMAS rule is:
BODMAS rule basically tells us the order of operations to solve an expression. Here ‘B’ stands for Bracket, ‘O’ stands for Of, ‘D’ stands for division, ‘M’ stands for multiplication, ‘A’ stands for Addition and ‘S’ stands for Subtraction.
BODMAS rule states that, if an expression contains brackets (( ), { }, [ ]), we have to first solve or simplify the bracket followed by Of [Powers and roots etc.], then division, multiplication, addition, subtraction from left to right. Solving the problem in wrong order will result in a wrong answer.
We should also know the following points:
1. Negative number multiplied by a negative number gives a positive number.
That is, (-a) x (-b) = ab
where a and b are numbers such that a > 0, b > 0.
Also, ( -1) x (-a) = - (-a) = a
2. Negative number multiplied by a positive number gives a negative number.
That is, (-a) x (-b) = -(ab)
Or, (-b) x (a) = -(ab)
Also, (-1) x (+a) = - (+a) = -a
Or, (+1) x (-a) = + (-a) = -a
3. Positive number multiplied by a positive number gives a positive number.
That is, (a) x (b) = ab
Or, (b) x (a) = ba
Or, (1) x (+a) = + (+a) = +a
Now, let us consider the expression given in the question as
\[A=\left( -8 \right)+\left( -9 \right)+\left( +17 \right)\]
According to BODMAS, first we have to solve the bracket of above equation,
Also, we know that +(-a) = -a, +(+a) = +a and +(-a) = -a.
By applying these in above expression, we get
A = - 8 – 9 + 17
Since, we know that – a – b = - (a+b)
Therefore, we get – 8 – 9 = – (8+9) = – 17
By putting the value in the above expression, we get,
A = – 17 + 17
A = 0
Therefore, we get A = (-8) + (-9) + (+17) equal to 0.

Note: Here, students must note that they must follow the BODMAS rule to solve the questions instead of randomly solving the question and getting wrong results. Also, students must take special care of the signs of each term and convert them according to rules.