Question

Evaluate: \[ - 36 - 40 + 43 - \left( { - 29} \right) + 18 - \left( { - 74} \right)\]

Answer 1

Hint:
Here, we will evaluate the given arithmetic expression. We will use the properties of integers and the BODMAS rule to evaluate the given expression. An arithmetic expression is a sentence with a minimum of two numbers or more. These numbers are related by arithmetic operations like addition, subtraction, multiplication, or division.

Complete step by step solution:
We will evaluate the expression \[ - 36 - 40 + 43 - \left( { - 29} \right) + 18 - \left( { - 74} \right)\]
We will solve the bracket operation at first.
We know that the product of two negative integers is a positive integer. Therefore, we get
\[ \Rightarrow - 36 - 40 + 43 - \left( { - 29} \right) + 18 - \left( { - 74} \right) = - 36 - 40 + 43 + 29 + 18 + 74\]
We will add the integers from the left, we get
\[ \Rightarrow - 36 - 40 + 43 - \left( { - 29} \right) + 18 - \left( { - 74} \right) = - 36 - 40 + 43 + 29 + 92\]
Again adding the integers from the left, we get
\[ \Rightarrow - 36 - 40 + 43 - \left( { - 29} \right) + 18 - \left( { - 74} \right) = - 36 - 40 + 164\]
Whenever the integers are of opposite sign, then we will subtract the integers and mark them with the greater number sign. So, we will subtract the integers from the left, we get
\[ \Rightarrow - 36 - 40 + 43 - \left( { - 29} \right) + 18 - \left( { - 74} \right) = - 36 + 124\]
We will subtract the integers from the left, we get
\[ \Rightarrow - 36 - 40 + 43 - \left( { - 29} \right) + 18 - \left( { - 74} \right) = 88\]

Therefore, \[ - 36 - 40 + 43 - \left( { - 29} \right) + 18 - \left( { - 74} \right) = 88\].

Note:
We know that the BODMAS rule states that the first operation has to be done which is in the brackets, next the operation applies on the indices or order, then it moves on to the division and multiplication and then using addition and subtraction we will simplify the expression. If addition or subtraction and division or multiplication are in the same calculations, then it has to be done from left to right. We should know the properties of Integers such that the product of two positive integers and the product of two negative integers is a positive integer. The product of a positive and a negative integer is a negative integer.