Question

Subtract – 134 from the sum of 38 and – 87.
A. – 85
B. 85
C. – 183
D. 183

Answer 1

Hint: To given question can be solved in two parts:
In part 1, you need to add 38 and (– 87) to get the sum.
In part 2, from the sum obtained above in part 1 subtract (– 134) and get the required answer.

Complete step by step answer:
We will start solving for part 1;
In part 1 of calculation, we need to add 38 to (– 87).
When we add a negative number to a positive number, the absolute value of the sum is the difference of the two numbers taking them without their sign.
For determining the sign of the sum, we will see for the sign of the greater of the two numbers and assign the sign of the greater number to the sum.
Therefore, 38 + (– 87).
Absolute value of sum = (87 – 38)
= (49)
Now, 87 is greater than 38 and sign of 87 is negative in the expression.
Hence, the sign of the sum is negative.
$\therefore 38+\left( -87 \right)=\left( -49 \right)$
Now, In part 2, we need to subtract (– 134) from the sum obtained above i.e. (– 49).
We need to calculate, (– 49) – (– 134).
Since, we know that – (– a) = +a i.e. negative of a negative number gives positive of that number.
Hence, the above expression becomes,
$\begin{align}
  & \Rightarrow \left( -49 \right)-\left( -134 \right) \\
 & \Rightarrow -49+134 \\
\end{align}$
As we have seen in part 1 for the addition of a positive number to a negative number, the absolute value of sum is the difference of the two numbers taken without sign and sign of the greater of the two numbers is assigned to the sum.
For the sum, – 49 + 134
Absolute value of sum = (134 – 49)
= 85
Now, since 134 is greater than 49 and sign of 134 is positive in the expression. Hence, sign of the sum here is positive.
Therefore, – 49 + 134 = (+ 85)
Hence, the required answer is 85 or (+ 85).

Note: Points to keep in mind while finding sum of two numbers:
1. For finding the sum of two numbers having the same sign, either positive or negative, just add the modulus of the two numbers and then assign a sign to the sum, similar to the sign of the two numbers.
2. For finding the sum of two numbers having opposite signs, the absolute value of the sum is the difference of the two numbers taken without their sign and a sign of greater than the two modulus values of the numbers is assigned to the sum.