Problem 71 - Elementary Algebra

Question

\(12+|-8| \div(-2)\)

Step-by-Step Solution

Answer

8

Step 1: Simplify the absolute value

First, we need to handle the absolute value in the expression 12 + |-8| First compute the absolute value of -8 which is 8. Now the expression becomes 12 + 8 ÷ (-2).

Step 2: Perform the division

Next, we perform the division part of the expression: 8 ÷ (-2) = -4. So the expression is now 12 + (-4).

Step 3: Perform Addition

Finally, perform the addition: 12 + (-4)which equals 8.

Key Concepts

Understanding Absolute Value

Absolute value is a concept that represents the distance of a number from zero on the number line. This means it is always a positive number, or zero.
For example, if we take the absolute value of -8, we get 8. This is because 8 units are the distance from -8 to 0.

To denote the absolute value of a number, we use vertical bars. For instance, the absolute value of -8 is written as \(|-8| = 8\).
This step is crucial in solving the expression because it simplifies the expression to only positive numbers, making further computations easier.

Performing Division

Division is one of the fundamental arithmetic operations. It involves splitting a number into equal parts. In mathematical terms, if we divide a number \(_a_\) by another number \(_b_\), we are finding out how many times \(_b_\) fits into \(_a_\).

For instance, to compute \(_8 \div (-2)_\), we ask how many times does -2 fit into 8. The answer is -4 because when you multiply -4 and -2, you get 8 (
\(-4 \times (-2) = 8\))

• Always remember that dividing by a negative number changes the sign of the quotient.


• Division is performed after handling operations inside parentheses and absolute values, according to the order of operations (PEMDAS/BODMAS).

Performing Addition

Addition is another foundational arithmetic operation where we combine quantities to find the total.
In the final step of our initial expression, we have \(_12 + (-4)_\). Here, we are adding 12 and -4. This is effectively the same as subtracting 4 from 12.

When working with addition involving negative numbers, think of moving in reverse on the number line.
For instance:

• Starting at 12, move 4 units to the left because we are adding a negative number (-4).
• The result is 8, meaning \(_12 + (-4) = 8_\).

Addition is typically the last operation performed in the hierarchy of operations, ensuring that all multiplicative, divisive, and absolute value operations preceding it have been correctly handled.