Question

Solve the given expression.
\[\left( +42 \right)+\left( -64 \right)\]
A. -22
B. 28
C. +22
D. None of these

Answer 1

Hint: Take the 2 natural numbers, compare them and find the larger number. Subtract both numbers and put the sign of the larger number in the answer.

Complete step-by-step answer:
We have been given the expression \[\left( +42 \right)+\left( -64 \right).\] It consists of two numbers 42 and -64. From this we can say that both are integers. 42 is a positive integer and (-64) is a negative integer.
We know that integers consist of zero, the positive natural numbers and negative numbers.
Here comparing the numbers 42 and 64, we can say that 64 is larger compared to 42, i.e. \[64>42\].
Thus the sign of 64 is negative, i.e. (-64).
The sign of 42 is positive and it is smaller than 64. Now let us do the mathematical operation, i.e. subtraction.
Subtract 42 from 64 and put the negative sign in the answer.
Or you can directly subtract 42 from (-64), Both the answers will be correct.
i.e. \[\left( +42 \right)+\left( -64 \right)=42-64=-22\].
Or \[-\left( 64-42 \right)=-22\].
Thus we got the answer as -22, i.e. \[42+(-64)=-22\].
Option A is the correct answer.

Note: If the question was \[(-42)+64\], then the answer would’ve been +22.
Here comparing 42 and 64, 64 is larger, i.e. \[64>42\]. The sign of 64 is positive. Thus after subtraction put the sign of 22 as positive. Be careful with the sign of numbers. If you put (-22) as an answer, it is wrong.