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Chapter 1: Problem 17

Add and subtract. $$ 5-(-2)+(-6) $$

Short Answer

Expert verified
The result of the expression is 1.

Step by step solution

01

Identify and Rewrite Negatives

The original expression is \(5 - (-2) + (-6)\). We know that subtracting a negative number is the same as adding its positive counterpart. Therefore, rewrite the expression as:\(5 + 2 - 6\).
02

Perform Addition

Start with the first two terms of the expression from Step 1:\(5 + 2\).Calculate this to get:\(7\).
03

Perform Subtraction

Now, subtract the last term of the expression from Step 2:\(7 - 6\).Calculate this to obtain the final result:\(1\).

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Key Concepts

These are the key concepts you need to understand to accurately answer the question.

Addition and Subtraction
When performing operations involving addition and subtraction, it's important to remember that these are the basic building blocks of arithmetic. With addition, we are combining values, while subtraction means finding the difference between them. Think of addition and subtraction as moving forward and backward on a number line.

For effective calculations:
  • Always pay attention to the signs of the numbers involved.
  • Start by simplifying the expression step by step.
  • If needed, rewrite the expression for easier calculations.
In our example, after rewriting the problem as \(5 + 2 - 6\), we add \(5\) and \(2\) to get \(7\). Then, subtract \(6\) from \(7\) to find the result of \(1\). Each operation is performed in steps, ensuring clarity and accuracy.
Negative Numbers
Negative numbers are an essential part of arithmetic as they help in representing values less than zero, often seen in real-world scenarios, like temperatures below freezing or financial debts. Understanding how to work with negative numbers is critical for accurate calculations.

Key points about negative numbers:
  • A negative sign in front of a number indicates it is below zero.
  • Subtracting a negative number is equivalent to adding its positive counterpart (e.g., \(-(-2)\) turns into \(+2\)).
  • When adding two negative numbers, the result is a negative.
In our exercise, we used the rule that subtracting a negative transforms into addition, turning \(5 - (-2)\) into \(5 + 2\). This small adjustment simplifies dealing with negative values.
Algebraic Expressions
Algebraic expressions involve numbers, variables, and operations. Learning to simplify these expressions is crucial in mathematics, helping us solve problems efficiently. While our example doesn't include variables, it illustrates how to handle expressions.

To manage algebraic expressions effectively:
  • Identify and understand each part of the expression.
  • Use properties of numbers, such as the commutative and associative properties, to simplify calculations.
  • Simplify by performing one operation at a time. This is especially useful if the expression is complex.
In our task, the expression \(5 - (-2) + (-6)\) was simplified by first addressing the negative signs, manifesting an essential lesson in simplifying and solving such expressions methodically.

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