Question

Let the value of A = 5 and B = 9. Then the value of (– A) + (– B) is
(a) – 14
(b) 14
(c) 45
(d) – 45

Answer 1

Hint: We will apply the formula A + (– B) = A – B to solve the question. Here A and B are positive numbers but – B will be considered as a negative number. The following are the basic operations of the addition and subtraction that we will consider to solve the question further. These are given by
+ . + = +
+ . – = –
– . + = –
– . – = +
Here, . represents that we are multiplying the signs.

Complete step-by-step answer:
We will consider the expression (– A) + (– B)….(i)
First, we need to open +(– B). By applying the operation as used in the expression + . – = –. So, we get a new expression as
– A – B
Now we will use substitution here. Substitution is a step in which a value is replaced by a variable. For example, if we consider p + q, then p and q are called variables here. If the values of p and q are given as p = 1 and q = 2. Then 1 and 2 are called constants. Now, to do the substitution of p and q in p + q, we will replace p by 1 and q by 2. Therefore, we have,
p + q = 1 + 2
p + q = 3
Now, similarly, we will find the values of
(– A) + (– B) = – A – B
Now, we are given the value of A = 5 and B = 9. At this step, we will perform substitution as explained above. We will substitute the value of A = 5 and B = 9.
– A – B = – 5 – 9
Now, as we know that – a – a = – (a + a). Therefore, we have,
– A – B = – (A + B)
– (A + B) = – (5 + 9)
Now, we will perform the addition here. We will add the numbers 5 and 9 which results in 14.
– (A + B) = – 14
Hence, the value of (– A) + (– B) is – 14 which is option (a).

Note: Alternately, we could have also applied the substitution before using the formula A + (– B) as – 5 + (– 9). And then use the operation + . – = – which results into – 5 – 9 = – 14. Remember the use of the brackets in the expression (– A) + (– B) represents the separation between + and – by multiplication.