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Positive and Negative Number Theory

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**y x Rise on the y Positive up Run on the x Negative to the left**

Positive to the right Negative down

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**Only the sign moves the number on the number line.**

Mathematicians are Lazy. We only write the signs of negative numbers. Subtraction is the addition of the opposite sign Addition combines numbers

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Plot -3 Start at the origin Negative moves to the left

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Plot 7 Start at the origin Positive to the right

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**x = -3 + 7 x = 4 Solve for x Start at the origin**

Negative moves to the left Positive moved to the right x = x = 4

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**x = -2 - 7 x = -2 + - 7 x = -9 Solve for x Start at the origin**

Negative moves to the left Positive moved to the right x = x = x = -9

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**x = -2 - -7 x = -2 + 7 x = 5 Solve for x Start at the origin**

Subtraction is the addition of the opposite sign Negative to the left Positive to the right x = x = x = 5

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**Adding and Subtracting**

Addition does not change the sign of a number Example: = x = x 5 = x = x Subtraction is the addition of the opposite sign Example: – 3 = x = x = x = x -1 = x 1 = x

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**Multiply and Divide If the signs are the same**

(both positive or both negative), the answer will be positive. + * + = * - = + If the signs are different (one positive and one negative), the answer will be negative. + * - = * + = -

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Multiply and Divide Two like signs make a positive sign. Two unlike signs make a negative sign.

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Example Solve for x. Subtraction sign Negative sign x = 18 – (–16) – 3 – (–5) + 2 = – = (–3) = 41 + (–3) [I added all the positive numbers.] = 41 – 3 [The addition of a negative is the same as the subtraction of a positive.] = 38

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