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Chapter 1: Problem 21

Find each sum. $$ 6+(-6) $$

Short Answer

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Step by step solution

01

Identify the Numbers

Look at the numbers given in the expression. They are 6 and -6.
02

Understand the Addition of Opposites

When adding a number and its negative (opposite), the result is always 0. This is because moving positive 6 units and then moving negative 6 units will bring you back to the starting point.
03

Perform the Addition

Add 6 and -6 together: - 6 + (-6) = 0.
04

Verify the Result

Double-check the calculation. Adding a positive number and its exact negative always equals 0.

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Key Concepts

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

opposites in addition
When we talk about opposites in addition, we refer to a pair of numbers that are equal in magnitude but have opposite signs. For example, in the problem given, 6 and -6 are opposites. Adding these two together results in zero because they effectively cancel each other out. This happens because moving 6 units in the positive direction and then 6 units in the negative direction brings you right back to where you started.
Think of it like walking forward 6 steps and then walking backward 6 steps. You end up where you started, which is why the sum is zero.
zero property
The Zero Property of Addition states that the sum of any number and zero is the original number itself. However, there is another interesting facet of zero in addition, which we see in this exercise.
The Zero Property is highlighted when adding a number and its opposite. For example, adding 6 and -6 equals 0. You can see this as a way of balancing both positive and negative movements, leaving you at zero.
In general, whenever you're adding two exact opposites, your result will be zero due to the Zero Property!
integer operations
Understanding integer operations is crucial in solving problems with both positive and negative numbers like the one in the exercise. Integers include positive numbers, negative numbers, and zero. Here are some key points:
  • Adding Positive and Negative Numbers: When you add integers with different signs, you're essentially combining their directions. Like in our exercise, 6 (positive) and -6 (negative).
  • Adding Two Positive or Two Negative Numbers: When the signs are the same, you simply add their absolute values, and the result keeps that common sign. For instance, 3 + 4 = 7 and -3 + (-4) = -7.
  • Subtraction as Addition: Subtraction can be thought of as adding the opposite. For example, 6 - 6 can be written as 6 + (-6).

Mastering integer operations allows you to navigate more complex problems with confidence.

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Most popular questions from this chapter

Solve each problem. Nadine enjoys playing Triominoes every Wednesday night. Last Wednesday, on four successive turns, her scores were $$ \begin{array}{lllll} -19, & 28, & -5, & \text { and } & 13 . \end{array} $$ What was her final score for the four turns?

Use the distributive property to rewrite each expression. $$ 3(3 x+4) $$

Write each expression without parentheses. $$ -(-z+5 w-9 y) $$

Write a numerical expression for each phrase, and simplify the expression. 1.85 more than the sum of -1.25 and -4.75

Solve each problem. Linda owes \(\$ 870.00\) on her MasterCard account. She returns two items costing \(\$ 35.90\) and \(\$ 150.00\) and receives credit for these on the account. Next, she makes a purchase of \(\$ 82.50\) and then two more purchases of \(\$ 10.00\) each. She makes a payment of \(\$ 500.00\). She then incurs a finance charge of \(\$ 37.23 .\) How much does she still owe?
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