Problem 85 - Elementary Algebra

Question

For exercises 15-100, evaluate. $$ -16-18 \div(-2) $$

Step-by-Step Solution

Answer

-25

Step 1: Evaluate the Division

First, perform the division operation. Divide \(-18\) by \(-2\): \(-18\ \div (-2) = 9\)

Step 2: Perform the Subtraction

Next, subtract the result from the first number: \(-16 - 9 = -25\)

Key Concepts

Order of Operations

Understanding the order of operations is crucial in arithmetic and algebra. It tells you the correct sequence to solve parts of an expression. The usual order (remembered by the acronym PEMDAS) is: Parentheses, Exponents, Multiplication and Division (from left to right), and Addition and Subtraction (from left to right).
Without this, we can get different results for the same expression! Let's break down the order of operations for the problem \( -16-18 \div (-2) \).
According to PEMDAS, we need to perform the division before subtraction because division comes before subtraction when they are at the same level in an expression. So, we first divide \( -18 \div (-2) \).

Division

Now, let's handle the division operation involved in our expression. Division means taking one number and splitting it into equal parts. For this problem, we divide -18 by -2.
Here’s how we do it:
When you divide a negative number by another negative number, the result is a positive number because their signs cancel each other out.
So, \( -18 \div (-2) = 9\). Once this division is done, we move on to the next step in the original expression.

Subtraction

Finally, we need to perform the subtraction from the original expression. After solving the division, our expression now looks like this: \( -16-9 \).
Subtraction in algebra is taking one number away from another. When both numbers are negative or involve transactions resulting in a more negative number, you simply add the absolute values, but the result takes the sign of the larger absolute value.
Thus, \( -16 - 9 \) equals \( -25 \).
To summarize, by following the order of operations, performing the division correctly, and then the subtraction, we find that \( -16 - 18 \div (-2) = -25 \).