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Integers Definition Positive integer – a number greater than zero. 0 1 2 3 4 5 6 Definition Negative number – a number less than zero. -6 -5 -4 -3 -2 -1 0 1 2 3 4 5 6 Place the following integers in order from least to greatest: 297 -56 39 -125 78 0 Place the following integers in order from least to greatest: 297 -125 -56 -56 39 0 -125 39 78 78 0 297 Definition Opposite Numbers OR Additive Inverse – numbers that are the same distance from zero in the opposite direction -6 -5 -4 -3 -2 -1 0 1 2 3 4 5 6 Definition Integers – all whole numbers and their opposites on the number line, including zero. 7 opposite -7 Definition Absolute Value – The distance a number is from zero on the number line The absolute value of 9 or of –9 is 9. Negative Numbers Are Used to Measure Temperature Negative Numbers Are Used to Measure Below Sea Level 30 20 10 0 -10 -20 -30 -40 -50 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. Hint If you don’t see a negative or positive sign in front of a number, it is ALWAYS positive. +9 Integer Addition Rules Rule #1 – When adding two integers with the same sign, ADD the numbers and keep the sign. 9 + 5 = 14 -9 + -5 = -14 Solve the Following Problems: -3 + -5 = 4 + 7 = (+3) + (+4) = -6 + -7 = 5 + 9 = -9 + -9 = Check Your Answers: -3 + -5 = -8 +11 4 + 7 = +7 (+3) + (+4) = -13 -6 + -7 = 14 5 + 9 = -18 -9 + -9 = Solve the following: 1. 2. 3. 4. 8 + 13 = –22 + -11 = 55 + 17 = –14 + -35 = Check Your Answers 1. 2. 3. 4. 8 + 13 = –22 + -11 = 55 + 17 = –14 + -35 = +21 -33 +72 -49 Integer Addition Rules Rule #2 – When adding two integers with different signs, find the difference (SUBTRACT) and take the sign of the larger number. -9 + +5 = 9 - 5 = 4 Answer = - 4 Larger absolute value: Solve These Problems 3 + -5 = 5 – 3 = 2 -2 -4 + 7 = 7 – 4 = 3 +3 (+3) + (-4) = 4 – 3 = 1 -1 7 – 6 = 1 +1 -6 + 7 = 5 + -9 = -4 9–5=4 0 9–9=0 -9 + 9 = Solve the following: 1. 2. 3. 4. –12 + 22 = –20 + 5 = 14 + (-7) = –70 + 15 = Check Your Answers 1. 2. 3. 4. –12 + 22 = –20 + 5 = 14 + (-7) = –70 + 15 = +10 -15 +7 -55 One Way to Add Integers Is With a Number Line When the number is positive, count to the right. When the number is negative, count to the left. - + -6 -5 -4 -3 -2 -1 0 1 2 3 4 5 6 One Way to Add Integers Is With a Number Line + -6 -5 -4 -3 -2 -1 0 1 2 3 4 5 6 One Way to Add Integers Is With a Number Line Answer: +3 + -5 = -2 + -6 -5 -4 -3 -2 -1 0 1 2 3 4 5 6 One Way to Add Integers Is With a Number Line + -6 -5 -4 -3 -2 -1 0 1 2 3 4 5 6 One Way to Add Integers Is With a Number Line Answer: +6 + -4 = +2 - + -6 -5 -4 -3 -2 -1 0 1 2 3 4 5 6 One Way to Add Integers Is With a Number Line + -6 -5 -4 -3 -2 -1 0 1 2 3 4 5 6 One Way to Add Integers Is With a Number Line Answer: +3 + -7 = -4 + -6 -5 -4 -3 -2 -1 0 1 2 3 4 5 6 One Way to Add Integers Is With a Number Line + - -6 -5 -4 -3 -2 -1 0 1 2 3 4 5 6 One Way to Add Integers Is With a Number Line Answer: -3 + +7 = +4 + - -6 -5 -4 -3 -2 -1 0 1 2 3 4 5 6 Integer Subtraction Rule Subtracting a negative number is the same as adding a positive one. Change the sign and add. “Keep, change, change.” is the same as 2 – (-7) 2 + (+7) 2 + 7 = 9 Here are some more examples. 12 – (-8) -3 – (-11) 12 + (+8) -3 + (+11) 12 + 8 = 20 -3 + 11 = 8 Solve the following: 1. 8 – (-12) = 2. 22 – (-30) = 3. – 17 – (-3) = 4. –52 – 5 = Check Your Answers 1. 8 – (-12) = 8 + 12 = +20 2. 22 – (-30) = 22 + 30 = +52 3. – 17 – (-3) = -17 + 3 = -14 4. –52 – 5 = -52 + (-5) = -57 Integer Multiplication Rules Rule #1 When multiplying two integers with the same sign, the product is always positive. Rule #2 When multiplying two integers with different signs, the product is always negative. Rule #3 If the number of negative signs is even, the product is always positive. Rule #4 If the number of negative signs is odd, the product is always negative. Solve the following: 1. +8 x (-12) = 2. -20 x +30 = 3. – 17 x (-3) = 4. +50 x +5 = Check Your Answers: 1. +8 x (-12) = -96 2. -20 x +30 = -600 3. – 17 x (-3) = +51 4. +50 x +5 = +250 Integer Division Rules Rule #1 When dividing two integers with the same sign, the quotient is always positive. Rule #2 When dividing two integers with different signs, the quotient is always negative. Solve the following: 1. (-36) ÷ 4 = 2. 200 ÷ -5 = 3. – 18 ÷ (-9) = 4. +50 ÷ +5 = Check Your Work: 1. (-36) ÷ 4 = -9 2. 200 ÷ -5 = -40 3. – 18 ÷ (-9) = +2 4. +50 ÷ +5 = +10 Evaluate the following: 1. -45 + 10 3² - 2 2. 7 + -4(9 – 4) = 3. -50 ÷ 5² + (3 - 6) = Check Your Work: 1. -45 + 10 3² - 2 -35 = -5 7 2. 7 + -4(9 – 4) = 3. -50 ÷ 5² + (3 - 7) = -13 -6 Evaluate the following if n = -2 : 1. -5 (2n – 2)² 2. -48 n-6 Check Your Work: 1. -5 (2n – 2)² 2. -48 n-6 -180 6 Aren’t integers interesting?