Problem 97 - Elementary Algebra Within Reach

Question

In Exercises 97-102, evaluate the expression. $$ 0-(-12) $$

Step-by-Step Solution

Answer

The result of the arithmetic operation \(0-(-12)\) is 12.

Step 1: Recognize the Expression

The given expression is \(0-(-12)\). In this case, we have a negative number being subtracted. It's important to recall and apply the arithmetic rule that subtracting a negative turns into addition.

Step 2: Apply Rule for Subtracting a Negative Number

Following the rule of subtracting a negative, the expression \(0-(-12)\) is equal to \(0+12\) which simplifies to 12. Subtracting a negative number is the same as adding the absolute value of that number.

Key Concepts

Negative Numbers

Negative numbers are numbers less than zero, and they are represented with a negative sign (-) in front of them. Examples include -1, -12, and -100. These numbers are opposite to positive numbers, which are greater than zero. When working with negative numbers, it is important to understand how they interact with other numbers in basic arithmetic operations like addition and subtraction.

• Negative numbers appear on the left side of zero on the number line.
• They represent values below zero or opposite in direction compared to positive numbers.
• When you add negative numbers, you move further left on the number line.

Being comfortable with negative numbers helps in evaluating expressions accurately, whether solving math problems in class or handling real-world calculations like temperatures below freezing or financial losses.

Subtracting Negative Numbers

When you subtract a negative number, it's helpful to think of it as adding the absolute value of that number. This might sound a bit tricky at first, but it's actually a consistent rule in mathematics. Understanding how it works can greatly simplify your calculations.

• The rule can be expressed as: \(a - (-b) = a + b\)
• Think of the two negatives "canceling" each other out, making the operation equivalent to addition.
• For example, if you have 5 - (-3), this is the same as 5 + 3, which equals 8.

This concept is important as it frequently shows up in algebra and number theory. Knowing that subtracting a negative number is the same as adding its positive counterpart can help you quickly simplify expressions and solve equations with confidence.

Expression Evaluation

Expression evaluation is the process where you simplify mathematical expressions down to a single number or value. It involves applying arithmetic operations and mathematical rules systematically. Let's go through how you might handle an expression like the given one: \(0 - (-12)\).
Start by identifying the operations involved. In this case, it's subtraction involving a negative number. Use the rule that subtracting a negative is the same as adding the positive number. Therefore, the expression \(0 - (-12)\) simplifies to \(0 + 12\), which equals 12.

• Always follow the order of operations (PEMDAS/BODMAS) when dealing with complex expressions: Parentheses/Brackets, Exponents/Orders, Multiplication & Division (from left to right), Addition & Subtraction (from left to right).
• Use known arithmetic rules, like subtracting negatives turns to addition, to simplify expressions step-by-step.

Properly evaluating expressions by applying rules and operations ensures accurate results. Practice is key to becoming proficient in simplifying and solving mathematical expressions.