Math Class: Adding and Multiplying Negatives

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Questions and Answers

What is the result of rewriting the expression $3 - (-7)$ as an addition problem?

  • 3 + 6 = 9
  • 3 + (-7) = -4
  • 3 + 7 = 10 (correct)
  • 3 - 7 = -4

What is the distance between the points -10 and -9?

  • 10
  • 0
  • 2
  • 1 (correct)

When multiplying two negative numbers, such as $(-4)(-3)$, what is the result?

  • $-7$
  • $12$ (correct)
  • $-12$
  • $0$

Which of the following expressions correctly rewrites $-480 - (-4)$ as an addition problem?

<p>$-480 + 4$ (C)</p> Signup and view all the answers

What is the absolute value distance between -4 and 5?

<p>9 (C)</p> Signup and view all the answers

How can you express the subtraction of a positive integer from a negative integer using addition?

<p>You can express it as the addition of the negative integer and the opposite of the positive integer.</p> Signup and view all the answers

What is the significance of absolute values in determining distances on a number line?

<p>Absolute values represent the non-negative distance between two points, regardless of their signs.</p> Signup and view all the answers

Discuss the result of multiplying two negative integers. What pattern do you notice?

<p>Multiplying two negative integers results in a positive integer, demonstrating that two negatives cancel each other out.</p> Signup and view all the answers

When rewriting the expression $-480 - (-4)$ as addition, what is the final result?

<p>The final result is $-476$, as it simplifies to $-480 + 4$.</p> Signup and view all the answers

Explain how the absolute value can be applied to find distances between two negative integers.

<p>The absolute value of the difference between two negative integers provides their distance on the number line.</p> Signup and view all the answers

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Study Notes

Adding Opposites

  • Subtracting a negative number is the same as adding its opposite.
  • For example, -4 - (-6) can be rewritten as -4 + 6.

Multiplying and Dividing Positive and Negative Numbers

  • The product of two negative numbers is positive.
  • The product of a positive and a negative number is negative.
  • Dividing a negative number by a positive number results in a negative number.

Distance Between Two Points

  • The distance between two points on a number line is found using the absolute value of their difference.
  • The absolute value of a number is its distance from zero.
  • For example, the distance between -10 and -9 is |-10 - (-9)| = 1.

Adding Opposites

  • When subtracting a negative number, you can rewrite the expression as addition
  • Adding the opposite of a negative number results in a positive number. For example, -4 + 6 = 2

Multiplying and Dividing Positive and Negative Numbers

  • The product of two negative numbers is always positive.
  • The product of a positive and a negative number is always negative.
  • Dividing a negative number by a negative number yields a positive result.

Distance Between Two Points

  • To find the distance between two points on a number line, use the formula: |a - b|, where 'a' and 'b' are the two points.
  • The absolute value represents the distance from zero.
  • The distance between two points is always a positive value.

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