Algebra I in Simple English/Introduction to Basic Algebra Ideas/Working With Negative Numbers
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[edit] Vocabulary
Positive
Negative
[edit] Lesson
[edit] Negative Numbers
A positive number is a number more 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.
[edit] Adding and Subtracting
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
[edit] Multiplying and Dividing
Multiplying a negative number by a positive number, or a positive number by a negative number makes the answer negative.
- -2 * 3 = -6
- 2 * -3 = -6
Multiplying a negative number by a negative number makes the answer positive.
- -2 * -3 = 6
You do the same for dividing.
- -6 / 3 = -2
- 6 / -3 = -2
- -6 / -3 = 2
[edit] Exponentiating
Exponentiating a negative number to an even (a number you can divide by two) power makes a positive answer.
- (-3)2 = 9
- (-x)2 = -x * -x = x^2
Exponentiating a negative number to an odd (a number you can not divide by two) power makes a negative answer.
- (-2)3 = -8
- (-x)3 = -x * -x * -x = x^2 * -x = -x^3
[edit] Order of Operations
The negative operation has the same precedence as multiplying and dividing.
- 3 - -8 / 4 = 3 + 2 = 5
- -32 = -(3 * 3) = -9
- (-3)2 = (-3 * -3) = 9
[edit] Example Problems
1: 4 + (-4)
2: 4 + (-7)
3: 0 + (-2)
4: -5 + 7 - 2 * -4
Answers
1: 4 + (-4) = 4 - 4 = 0
2: 4 + (-7) = 4 - 7 = -3
3: 0 + (-2) = 0 - 2 = -2
4: -5 + 7 - 2 * -4 = -5 + 7 + (-2 * -4) = -5 + 7 + 8 = -5 + 15 = 10
