Problem 83 - Elementary Algebra

Question

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

Step-by-Step Solution

Answer

-25

Step 1 - Evaluate the Division

First, evaluate the division part of the expression. Compute \(18 \div (-2)\).

Step 2 - Perform the Division

Calculate \(18 \div (-2)\). Dividing a positive number by a negative number results in a negative quotient. So, \(18 \div (-2) = -9\).

Step 3 - Simplify the Expression

Now replace \(18 \div (-2)\) with \(-9\) in the original expression: \(-16 + (-9)\).

Step 4 - Evaluate the Addition

Combine \(-16\) and \(-9\). Adding two negative numbers results in a more negative number: \(-16 + (-9) = -25\).

Key Concepts

negative numbers

Understanding negative numbers is crucial in algebra. Negative numbers are values less than zero, represented with a minus sign (-) before the number. Think of them as a thermometer: temperatures below zero are negative. When we work with negative numbers, certain rules apply:

• Adding a negative number is like subtracting a positive number.
• Subtracting a negative number is like adding a positive number.
• The product or quotient of two numbers with the same signs (both positive or both negative) is positive.
• The product or quotient of two numbers with different signs (one positive, one negative) is negative.

Understanding these rules helps make sense of operations involving negative values, like in our exercise: \(-16+18 \div(-2)\).

division in algebra

Division is one of the fundamental operations in algebra. When dividing numbers, it's essential to follow the rules for positive and negative values. In our example, we have \(18 \div (-2)\). When you divide a positive number (18) by a negative number (-2):

• You perform the division on the absolute values: \(18 \div 2 = 9\).
• Apply the rule that dividing numbers with different signs results in a negative answer, so \(18 \div (-2) = -9\).

This gives us the quotient of -9. Performing division correctly ensures you move through algebraic expressions accurately.

simplifying expressions

Simplifying expressions is about making them as straightforward as possible while keeping their value the same. It often involves several steps:
1. **Perform operations** in the correct sequence, according to the order of operations: parentheses, exponents, multiplication and division (left to right), addition and subtraction (left to right).
2. **Combine like terms** when possible.
In the given problem, we start by performing division first, \(18 \div (-2) = -9\). Next, replace this division in the original expression, transforming it into \(-16 + (-9)\). Finally, combine the two negative numbers: \( -16 + (-9) = -25\). This process of simplifying step-by-step leads us to the correct answer.