Basic Algebra/Introduction to Basic Algebra Ideas/Working With Negative Numbers

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Vocabulary[edit]

Positive
Negative

Lesson[edit]

Negative Numbers[edit]

A positive number is a number greater than zero.

A negative number is a number less than zero. You make a negative number by doing the negative operation on a positive number. You use the " – " sign for the negative operation. This sign is the same you use for subtracting.

Adding and Subtracting[edit]

Adding a negative number is the same as subtracting a positive number.

  •  7 + (-4) = 7 - 4
  •   x + (-y) = x - y

Subtracting a negative number is the same as adding a positive number.

  •  7 - (-4) = 7 + 4
  •  x - (-y) = x + y

Multiplying and Dividing[edit]

Multiplying a negative number by a positive number, or a positive number by a negative number makes the result negative.

  •  (-2) \times 3 = -6
  •  2 \times (-3) = -6

Multiplying a negative number by a negative number makes the result positive.

  •  (-2) \times (-3) = 6

You do the same for dividing.

  •   (-6) \div 3 = -2
  •   6 \div (-3) = -2
  •  (-6) \div (-3) = 2

Exponentiating[edit]

Exponentiating a negative number to an even (a number you can divide by two) power makes the result positive.

  •  (-3)^2 = 9
  •  (-x)^2 = (-x) \times (-x) = x^2

Exponentiating a negative number to an odd (a number you can not divide by two) power makes the result negative.

  •  (-2)^3 = -8
  •  (-x)^3 = (-x) \times (-x) \times (-x) = x^2 \times (-x) = -x^3

Order of Operations[edit]

The negative operation has the same precedence as multiplying and dividing.

  •  3 + 8 \div 4 = 3 + 2 = 5
  •  -3^2 = -(3 \times 3) = -9
  •  (-3)^2 = (-3) \times (-3) = 9

Example Problems[edit]

  1. 4 + (-4) = 0
  2. 4 + (-7) = -3
  3. 0 + (-2) = -2
  4. -5 + 7 - 2 \times (-4) = 10

Practice Games[edit]

none

Practice Problems[edit]

  1. 6 + (-3) =
  2. 3 + (-9) =
  3. -4 \times 4 =
  4.  4 \times (-9) =
  5. -2 \times (-4) =
  6.  \frac{-25}{5^2} =
  7. -4 \div 2=
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