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

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

    <p>9</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

    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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    Description

    Test your understanding of how to add and subtract negative numbers, as well as the rules for multiplying and dividing positive and negative values. This quiz also covers calculating distances between two points on a number line using absolute values.

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