Question

Find the value of \[38 - ( - 25) - 58 + ( - 15) - 23 - ( - 8)\]

Answer 1

Hint: In this question, we have to solve the given numerical expression. The numerical expression comprises the arithmetic operations like addition, subtraction and multiplication. We will start solving the question by writing $ - ( - 25)$ as $ - 1( - 25)$ , that is equal to the product of -1 and -25. 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 38 and the number obtained will be a plus sign, so we will add the number obtained with 38. The value obtained will be positive as two positive values are added to each other. Following a similar approach, we will simplify all the numbers in the given expression and thus get the correct answer by performing the given arithmetic operations.

Complete step-by-step solution:
We have to find the value of \[38 - ( - 25) - 58 + ( - 15) - 23 - ( - 8)\]
We know that $ - ( - a) = a$ so $ - ( - 25) = 25$ and $ - ( - 8) = 8$
We also know that $ + ( - a) = - a$ so $ + ( - 15) = - 15$
So, we get –
\[38 - ( - 25) - 58 + ( - 15) - 23 - ( - 8) = 38 + 25 - 58 - 15 - 23 + 8\]
38 and 25 are in addition, so we add them –
\[38 - ( - 25) - 58 + ( - 15) - 23 - ( - 8) = 63 - 58 - 15 - 23 + 8\]
63 and 58 are in subtraction, so we subtract 58 from 63 –
\[38 - ( - 25) - 58 + ( - 15) - 23 - ( - 8) = 5 - 15 - 23 + 8\]
Now, we subtract 15 from 5 –
\[38 - ( - 25) - 58 + ( - 15) - 23 - ( - 8) = - 10 - 23 + 8\]
Now, $ - a - b = - (a + b)$ so –
\[
  38 - ( - 25) - 58 + ( - 15) - 23 - ( - 8) = - 33 + 8 \\
   \Rightarrow 38 - ( - 25) - 58 + ( - 15) - 23 - ( - 8) = - 25 \\
 \]
Hence, the value of \[38 - ( - 25) - 58 + ( - 15) - 23 - ( - 8)\] is $-25$.

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 $a - ( - b) = a + b$.