Integers and Absolute Value

Absolute value

Definition

| a | = {\begin{matrix} a & a \geq 0 \\ - a & a < 0 \end{matrix}

|a| ≥ 0 always

Distance on a number line

d = | a - b | = | b - a |

Add, same sign

(- a) + (- b) = - (a + b)

Add, different signs

subtract the absolute values; keep the sign of the larger one

Subtract

a - b = a + (- b)

Subtract a negative

a - (- b) = a + b

Same signs

(+) \times (+) = (+) (-) \times (-) = (+)

Different signs

(+) \times (-) = (-) (-) \times (+) = (-)

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