Problem 84 - Elementary Algebra

Question

For exercises 15-100, evaluate. $$ -8+20 \div(-4) $$

Step-by-Step Solution

Answer

-13

Step 1: Identify the operations

Notice the operations within the expression: subtraction and division. According to the order of operations (PEMDAS/BODMAS), division comes before subtraction.

Step 2: Perform the division

First, compute the division: \(20 \div (-4) \). This results in \(20 \div (-4) = -5\).

Step 3: Perform the subtraction

Now, substitute \(20 \div (-4)\) with \(-5\) in the original expression. We have: \(-8 + (-5)\). Perform the addition: \(-8 - 5\).

Step 4: Simplify the expression

Lastly, add the numbers: \(-8 - 5 = -13\).

Key Concepts

Understanding PEMDAS in Algebra

PEMDAS is an acronym that helps remember the order of operations in math. PEMDAS stands for
Parentheses, Exponents, Multiplication and Division (from left to right), Addition and Subtraction (from left to right).
It is crucial to follow this order to correctly solve algebraic expressions. Ignoring it can lead to wrong answers.

For example, in the expression \( -8+20 \div(-4) \), division must happen before subtraction.
So we solve \( 20 \div(-4) \) first, then proceed with the remaining operations.

Some key points to remember:

• Always solve operations inside parentheses first.
• Handle exponents (powers and roots) next.
• Then do multiplication and division from left to right.
• Finally, perform addition and subtraction from left to right.

Division in Algebra

Division in algebra is similar to regular arithmetic division but can include variables and signs. In our example, we have:

\( 20 \div (-4) = -5 \).
Here, dividing a positive number by a negative number yields a negative result. This is because:

• A positive divided by a negative is negative.
• A negative divided by a positive is negative.
• A negative divided by a negative is positive.

It's important to handle signs accurately to get the correct answer in algebraic problems.
Also, always perform division before you handle addition or subtraction, according to PEMDAS.

Subtraction in Algebra

Subtraction in algebra can sometimes be tricky, especially when negative numbers are involved.
In the exercise \(-8 - 5\), we are essentially adding two negative numbers.

The process of subtraction in algebra follows these steps:
1. Identify if you're subtracting a positive or negative number.
2. If subtracting a positive number from a negative, the result becomes more negative.
3. Simplify by treating the subtraction as adding a negative number: \(-8 - 5\) is \(-8 + (-5)\).

This gives us:
\( -8 + (-5) = -13 \).
Remember that subtracting a number can be thought of as adding its negative counterpart.