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Operations on Integers Number Line: Numbers increase to the right and decrease to the left. Note -2 is smaller than -1, therefore -2 is to the left of -1. -2 -1 0 1 2 3 4 Addition Integers Adding: If the signs are the SAME, just add and keep the sign the same. If the signs are different signs, do a “take away”, but keep the sign of the number with the larger absolute value. Add. 2 + -3 -4 + -7 5 + -1 Subtraction Integers Subtraction: DON’T subtract, change subtraction to adding the opposite of what follows. Subtract. 4 – (-3) -2 – 6 -3 + 5 Simplify. 4 – 5 – 12 -12 – (-3) – (-5) -4 + 6 – 8 – 2 Simplify. 11 – (-2) – 6 + 10 -1 – 8 + 6 – (-2) 6 + (-5) – 14 + 7 Multiply & Divide Integers Multiplication: COUNT the negative signs. If there is a EVEN number of negative signs being multiplied together, the result will be positive. If there is an ODD number of negative signs being multiplied together, the result will be negative. 2(-3) -2(-1)(3)(-1)(-2) -5(-8) -1(-1)(-1) 2(-1)(0)(-3)(-4)(5)(-6) Division could always be considered as multiplication of the reciprocal. Therefore, when dividing you can follow the multiplication rules. 6 3 18 3 Order of operations with Integers Order of Operations: Please Excuse My Dear Aunt Sally First: Do what is inside Parenthesis. Second: Do the Exponents; raise the base to the power. Third: Multiply and Divide in the order they appear from left to right. LAST: Add and Subtract in the order they appear from left to right. Simplify. -2 + -3 – 4 3 – -2 -32 ÷ -8 Order of Operations: Please Excuse My Dear Aunt Sally First: Do what is inside Parenthesis. Second: Do the Exponents; raise the base to the power. Third: Multiply and Divide in the order they appear from left to right. LAST: Add and Subtract in the order they appear from left to right. Simplify. (-9)(-1)(-2)(1)(2) (-5) + (-7) (-1)5 Order of Operations: Please Excuse My Dear Aunt Sally First: Do what is inside Parenthesis. Second: Do the Exponents; raise the base to the power. Third: Multiply and Divide in the order they appear from left to right. LAST: Add and Subtract in the order they appear from left to right. Simplify. 4 – (-5) – 2 – (-8 – 4) – 3 -24 ÷ (-6)(-2) Order of Operations: Please Excuse My Dear Aunt Sally First: Do what is inside Parenthesis. Second: Do the Exponents; raise the base to the power. Third: Multiply and Divide in the order they appear from left to right. LAST: Add and Subtract in the order they appear from left to right. Simplify. -3 · (-2)3 · 4 ÷ 8 – (-12) -3 + 2(-1) – 7