Question

Solve \[50-(-40)-(-2)\].

Answer 1

Hint: The given numerical expression involves the operations of subtraction and multiplication. Using the BODMAS rule, multiplication operations are performed first, with the help of the rules for the multiplication of two integers. After that, the expression becomes simpler with only addition operation, which is then performed to get the required solution.

Complete step by step answer:
The number system which we are familiar with, is the real number system. This system consists of many numbers namely natural numbers (\[1,2,3\]etc.), whole numbers (\[0,1,2,3\]etc.), integers (\[0,\pm 1,\pm 2,\pm 3\]etc.), rational numbers (numbers of the form\[\frac{p}{q}\]where\[p,q\]are integers and\[q\ne 0\]) and irrational numbers (numbers that cannot be expressed in the above\[\frac{p}{q}\]form).
Of these numbers, let us concentrate on the rules that are used for multiplying two integers, as our problem involves them. Suppose\[x\]and\[y\]are integers, positive or negative, then their multiplication has the following rules:
Rule\[1\]:\[(-x)(+y)=-xy\]
Rule\[2\]:\[(-x)(-y)=+xy\]
Rule\[3\]:\[(+x)(+y)=+xy\]
Next, we should become familiar with the BODMAS rule. In an arithmetic or numerical expression, when we have different operators, we feel confused as to which operation we have to do first. In such situations, the BODMAS rule comes handy. It represents B for Brackets, O for Order of powers, D for Division, M for Multiplication and S for Subtraction. So, in an arithmetic expression, the sequence of operations is given by this rule. The terms inside brackets take precedence over order of powers, the order of powers take precedence over division and so on.
Consider the expression which is given:
\[50-(-40)-(-2)\]…… (\[1\])
The above expression (\[1\]) can be rewritten as,
\[50+(-1)(-40)+(-1)(-2)\] …… (\[2\]) according to Rule\[1\].
When we go from left to right of the expression (\[2\]), we first encounter addition operation and then multiplication operation. As per BODMAS rule, multiplication operations have to be dealt with first.
Also, using Rule\[2\], we have that,
\[(-1)(-40)=+40\] and
\[(-1)(-2)=+2\]
Substituting these values in (\[1\]),
\[\Rightarrow 50+(+40)+(+2)\]
\[=50+40+2\]using Rule\[3\]
\[=92\]
Thus \[50-(-40)-(-2)\]\[=92\]which is the required solution.

Note:
Negative and positive numbers are used in the representation of many real-life scenarios. For example, in banking sector credits and debits, in business sector loss and profit, in share markets downward trend and upward trend are represented by these numbers. Our world is not complete without these numbers. Hence it is really necessary to learn to deal with these numbers.