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Chapter 1: Problem 45

Perform the indicated subtraction. $$-2.06-(-2.06)$$

Short Answer

Expert verified
The result is \( 0.00 \).

Step by step solution

01

Understanding Negative numbers subtraction

When subtracting a negative from a negative number, this essentially changes to addition. Conceptually, if we move in a negative direction, and then subtract a negative, it means we will be moving back in the positive direction. Therefore, \( -2.06 - (-2.06) \) becomes \( -2.06 + 2.06 \).
02

Perform Addition

Adding \( -2.06 \) and \( 2.06 \) gives result equals to \( 0.00 \).

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Key Concepts

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

Negative Numbers
Negative numbers represent values less than zero. They are the opposite of positive numbers. You can think of them like temperatures below freezing or debts in a bank account. For example, if it's 3 degrees below zero, you would write that as \(-3\). Similarly, having a debt of 5 dollars means you are \(-5\) dollars below having zero dollars. Negative numbers appear to the left of zero on the number line.
  • If you add negative numbers, you're essentially moving to the left on the number line.
  • Conversely, if you subtract them, you may move to the right, depending on the operation.
Understanding negative numbers is crucial before advancing to more complex arithmetic like subtraction and addition of negative numbers.
Addition of Negative Numbers
Adding negative numbers can seem tricky at first. However, it becomes straightforward when you consider the number line perspective. For instance:
  • If you add \(-3\) and \(-2\), think of starting at zero, moving left to \(-3\), and then moving left again by \(-2\). This lands you at \(-5\).
  • When adding a larger negative number to a smaller positive one, you effectively subtract the smaller from the larger and keep the negative sign. For example, \(5 + (-3) = 2\).
In essence, to add two negative numbers together, you add their absolute values and keep the negative sign. This is particularly important in scenarios requiring consistent direction measurement, like debts, where more debt (negative) results in a larger negative.
Basic Algebra
Basic algebra allows us to work with numbers in a generalized way. This involves using letters or symbols (like \(x\) or \(y\)) to represent numbers in equations or expressions. One key aspect in algebra is understanding operations like addition and subtraction, even with negative numbers.
  • When faced with expressions such as \(-x - (-y)\), the rules of arithmetic apply鈥攕ubtracting a negative is the same as adding the positive. For example, \(-2.06 - (-2.06)\) translates to \(-2.06 + 2.06\).
  • Evaluating expressions requires performing operations carefully according to the order of operations and managing the signs of numbers correctly.
Algebra is a powerful tool that helps us understand the relationships between numbers, enabling us to solve equations and predict outcomes. Comprehending these basics is essential for tackling more sophisticated algebraic concepts later.

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Most popular questions from this chapter

Explain how to simplify an algebraic expression in which a negative sign precedes parentheses.

Determine whether each statement "makes sense" or "does not make sense" and explain your reasoning. I found the sum of \(-13\) and 4 by thinking of temperatures above and below zero: If it's 13 below zero and the temperature rises 4 degrees, the new temperature will be 9 below zero, so \(-13+4=-9\)

Use a calculator to find a decimal approximation for each irrational number, correct to three decimal places. Between which two integers should you graph each of these numbers on the number line? $$2-\sqrt{5}$$

In Exercises \(109-116\), write a numerical expression for each phrase. Then simplify the numerical expression by performing the given operations. The quotient of \(-25\) and the sum of \(-21\) and 16

Simplify: \(-8-2-(-5)+11 .\) (Section \(1.6,\) Example 3 )
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