Question

What is the absolute value of $5+7-15$?

Answer 1

Hint: The absolute value of any number is easy to find. The absolute number simply means the magnitude of the quantity, i.e. the amount it contains without the involvement of sign. The absolute quantity of any value is basically given by a function, where if the number is negative we multiply by -1 to get the absolute quantity or if the given quantity is positive, we multiply it by 1 only. Here, we are given an expression, which we need to solve first. After that we will directly apply the function and obtain the absolute value of the given quantity.

Complete step by step solution:
We are first given a mathematical expression that we need to simplify. The expression is:
$5+7-15=12-15$
Subtracting 15 from 12 we get -3, so:
$5+7-15=-3$
We could also have done it by doing the right side first and then the left one i.e.:
$5+7-15=5+\left(-8\right)$
This again will result in the same solution:
$5+7-15=-3$
Now, we need to calculate the absolute value of the quantity $-3$.
We find the absolute quantity of any given number using the following function:
\[f\left(x\right)=\begin{cases}
      -x & x< 0 \\
      x & x>0\\
     0 & 0
   \end{cases}\]
After plugging the value of -3 in the above function we get,
$f\left(-3\right)=-1\times \left(-3\right)=3$

Hence, we can say that the absolute value of -3 is 3.

Note: Do not put a negative sign if the quantity is 0 because mathematically that would be wrong. Moreover, you can simply remove the negative sign from any quantity if you want to find the absolute value of it. It is a short trick that you could use to calculate the absolute value faster than usual.