Problem 24 - Beginning and Intermediate Algebra

Question

Subtract. See Examples 1 through 5 $$ -17-(-17) $$

Step-by-Step Solution

Answer

The result of -17 - (-17) is 0.

Step 1: Identify the Expression

The expression given is \(-17 - (-17)\). We need to subtract \(-17\) from \(-17\).

Step 2: Recognize the Subtraction of a Negative

Subtracting a negative number is the same as adding its positive equivalent. Therefore, \(-17 - (-17)\) can be rewritten as \(-17 + 17\).

Step 3: Perform the Addition

Now, simply add \(-17\) and \(+17\). When you add these two numbers, it becomes \(-17 + 17 = 0\).

Step 4: Conclude the Result

After the calculations, the result is \(0\).

Key Concepts

Subtracting Negative Numbers

Subtracting negative numbers might seem tricky at first, but it's actually quite simple once you understand the concept. When you see a problem like \(-17 - (-17)\), you are tasked with subtracting a negative number. Remember, subtracting a negative is the same as adding its positive counterpart.

• Think of it like removing debt or receiving a refund for something you were charged for.
• So instead of subtracting, you add the opposite, turning the expression into an addition problem.
• For example, \(-17 - (-17)\) becomes \(-17 + 17\).

The original negative sign in front of the second number turns into a positive sign, effectively making it an addition scenario. This approach simplifies the subtraction of negative numbers, turning them into a more familiar and straightforward operation.

Addition of Integers

Adding integers is a fundamental arithmetic operation that involves combining numbers. When dealing with integers, pay attention to their signs as they dictate the type of arithmetic operation you will perform.

• If both numbers have the same sign, you simply add their absolute values and keep the sign.
• If they have different signs, you subtract the smaller absolute value from the larger one, and the result takes the sign of the number with the larger absolute value.

In the case of \(-17 + 17\), you have numbers with opposite signs:

• Calculate the absolute values, which are both \(17\).
• Since the absolute values are equal, their addition results in zero, effectively canceling each other out.

This example highlights how the addition of integers hinges largely on the understanding of their signs.

Algebraic Expressions

Algebraic expressions consist of numbers, variables, and operations. They form the building blocks of algebra, allowing mathematicians to represent and solve equations.

• Expressions can include a combination of addition, subtraction, multiplication, and division.
• Simplifying expressions often involves performing these operations in accordance with mathematical rules.

In simplifying an expression like \(-17 - (-17)\), recognizing how negative signs work in algebra is crucial.Simplifying involves rewriting the expression with the correct operations, as seen in the step-by-step process: \(-17 - (-17) = -17 + 17\).This progression shows how algebraic manipulation helps in understanding and breaking down problems into more manageable steps. Recognizing patterns in algebraic expressions can significantly enhance problem-solving skills.