Question

The value of $\left( { - 46} \right) + \left( {15} \right)$ is:
A) $ + 31$
B) $31$
C) $ - 31$
D) None of these

Answer 1

Hint: For any two integers $a$ and $b$, we have following addition identities-
$\left( a \right) + \left( b \right) = \left( {a + b} \right)$
$\left( { - a} \right) + \left( { - b} \right) = - \left( {a + b} \right)$
$\left( { - a} \right) + \left( b \right) = \left( {b - a} \right)$
$\left( a \right) + \left( { - b} \right) = \left( {a - b} \right)$

Complete step-by-step answer:
Given, $\left( { - 46} \right) + \left( {15} \right)$
It is of the form of $\left( { - a} \right) + \left( b \right) = \left( {b - a} \right)$, so we get,
$\left( { - 46} \right) + \left( {15} \right) = 15 - 46 = - 31$
Hence, option (C) is the correct answer.

Collection of all positive $\left( {1,2,3,4,.....} \right)$ and negative numbers $\left( { - 1, - 2, - 3, - 4,.....} \right)$ including $0$ is called integers. $0$ is neither a positive nor a negative integer.
The numbers on the right hand side of the number line are always bigger than the number on the left hand side.

Note: Rules for operations on number line are:
To add a positive number, move right.
To add a negative number, move left.
To subtract a positive number, move left.
To subtract a negative number, move right.