Question

Find $ - 12 + 17 - ( - 10)$ is equal to
A) -5
B) 5
C) 15
D) -15

Answer 1

Hint: In this question, we are given a numerical expression and we have to find the answer obtained by solving it. The numerical expression comprises the arithmetic operations like addition, subtraction and multiplication. We will start solving the question by writing $ - ( - 10)$ as $ - 1( - 10)$ , that is equal to the product of -1 and -10. We know that the product of two negative numbers is equal to a positive number, so the answer obtained will be a positive value. Now the sign between 17 and the number obtained will be a plus sign, so we will add the number obtained with 17. The value obtained will be positive as two positive values are added to each other. As the sign before 12 is a negative sign so we will subtract it from the obtained value and thus get the correct answer.

Complete step-by-step solution:
We have to solve $ - 12 + 17 - ( - 10)$
We know that $ - ( - a) = + a$ so $ - ( - 10) = 10$
$
   \Rightarrow - 12 + 17 - ( - 10) = - 12 + 17 + 10 \\
   \Rightarrow - 12 + 17 - ( - 10) = - 12 + 27 \\
 $
We also know that $ - a + b = b - a$ so $ - 12 + 27 = 27 - 12$
$
   \Rightarrow - 12 + 17 - ( - 10) = 27 - 12 \\
   \Rightarrow - 12 + 17 - ( - 10) = 15 \\
 $

Hence, option (C) is the correct answer.

Note: Numbers are of two types namely real numbers and imaginary numbers, real numbers are the numbers that can be shown on a number line. The numbers on the left side of the zero are negative and the numbers on the right side are positive. While multiplying two numbers, we multiply the signs of the numbers along with them. The signs are multiplied as (+)(+)=(+), (+)(-)=(-), (-)(+)=(-) and (-)(-)=(-) that’s why $a - ( - b) = a + b$ .