Math Problem Statement

Which of the following are true statements about the expression 6 + (-6)?

Solution

Let's break down the given expression:

6+(6)6 + (-6)

Step-by-step Solution:

  1. 6+(6)6 + (-6) can be interpreted as adding the opposite of 6 to 6.

  2. The opposite of 6 is 6-6, so the expression becomes:

    66=06 - 6 = 0

Now, let's analyze the answer choices:

  • A. The expression describes the number that is 6 to the left of 6 on the number line.
    False: Adding 6-6 to 6 moves us left from 6, but it does not describe a number 6 units to the left of 6. It just equals 0.

  • B. The expression describes the number that is 6 to the right of 6 on the number line.
    False: The expression results in moving to the left, not to the right, of 6.

  • C. The expression equals 0.
    True: As we calculated, 6+(6)=06 + (-6) = 0.

  • D. The expression equals 12.
    False: The expression does not equal 12, but instead equals 0.

Conclusion:

The correct answers are:

  • C. The expression equals 0.
  • A. The expression describes the number that is 6 to the left of 6 on the number line.

Do you want further details or have any questions?

Here are some related questions you could consider:

  1. What is the rule for adding a negative number to a positive number?
  2. How would the expression change if the numbers were different?
  3. What is the graphical interpretation of adding numbers on the number line?
  4. How does subtracting a number relate to moving left on the number line?
  5. What happens if both numbers were negative instead?

Tip: Always visualize expressions on a number line when dealing with negative numbers for clarity.

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Math Problem Analysis

Mathematical Concepts

Arithmetic
Number Lines
Adding Negative Numbers

Formulas

Addition of Integers: a + (-b) = a - b

Theorems

Basic properties of integers

Suitable Grade Level

Grade 6-8