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1.1 Adding and Subtracting Integers Objective: Add and subtract integers.

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Definition Positive number – a greater than zero. 0123456

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Definition Negative number – a less than zero. 0123456-2-3-4-5-6

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Definition Opposite Numbers – numbers that are the same distance from zero in the opposite direction 0123456-2-3-4-5-6

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Definition Integers – are all the whole numbers and all of their opposites on the number line including zero.

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Definition Absolute Value – The distance a number is from zero on the number line. The absolute value of 9 or of –9 is 9.

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Negative Numbers Are Used to Measure Temperature

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Negative Numbers Are Used to Measure Under Sea Level 0 10 20 30 -10 -20 -30 -40 -50

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Negative Numbers Are Used to Show Debt Let’s say your parents bought a car but had to get a loan from the bank for $5,000. When counting all their money they add in -$5,000 to show they still owe the bank.

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Hint If you don’t see a negative or positive sign in front of a number it is positive. 9 +

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Integer Addition Rules Rule #1 – If the signs are the same, pretend the signs aren’t there. Add the numbers and then put the sign of the addends in front of your answer. 9 + 5 = 14 -9 + -5 = -14

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Solve the Problems -3 + -5 = 4 + 7 = (+3) + (+4) = -6 + -7 = 5 + 9 = -9 + -9 = -8 -18 14 -13 7 11

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Problems: 1. 8 + 13 = 2. -22 + -11 = 3. 55 + 17 = 4. -14 + -35 = 21 -33 72 -49

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Integer Addition Rules Rule #2 – If the signs are different pretend the signs aren’t there. Subtract the smaller from the larger one and put the sign of the one with the larger absolute value in front of your answer. -9 + 5 = 9 - 5 = 4 Larger abs. value Answer = - 4

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Solve These Problems 3 + -5 = -4 + 7 = (+3) + (-4) = -6 + 7 = 5 + -9 = -9 + 9 = -2 5 – 3 = 2 0 -4 1 3 9 – 9 = 0 9 – 5 = 4 7 – 6 = 1 4 – 3 = 1 7 – 4 = 3

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Problems 1. –12 + 22 = 2. –20 + 5 = 3. 14 + (-7) = 4. –70 + 15 = 10 -15 7 -55

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Integer Subtraction Rule Subtracting a negative number is the same as adding a positive. Change the signs and add. 2 – (-7) is the same as 2 + (+7) 2 + 7 = 9

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Many methods for solving integer problems Rules Money Zero Pairs Number Line (multiple techniques)

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Integer Addition Rule 1) When the signs are the same, ADD and keep the sign. (-2) + (-4) = -6 2) When the signs are different, SUBTRACT and use the sign of the larger number. (-2) + 4 = 2 2 + (-4) = -2

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Integer Addition – Same Sign ADD the absolute values and keep the original signs. The answer has the sign of the number that has the largest absolute value. Using the absolute value of each number, subtract the smaller from the larger. Integer Addition – Different Sign

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Zero Pair What happens when you add 1 and -1? 1 You get zero!

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1.1 Worksheet Homework

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One Way to Add Integers Is With a Number Line 0123456-2-3-4-5-6 When the number is positive, count to the right. When the number is negative, count to the left. +-

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One Way to Add Integers Is With a Number Line 0123456-2-3-4-5-6 + - +3 + -5 =-2

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One Way to Add Integers Is With a Number Line 0123456-2-3-4-5-6 + - +6 + -4 =+2

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One Way to Add Integers Is With a Number Line 0123456-2-3-4-5-6 + - +3 + -7 =-4

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One Way to Add Integers Is With a Number Line 0123456-2-3-4-5-6 - + -3 + + 7 =+4

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