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Learn how to add, subtract, multiply, and divide integers, understand properties and rules, solve examples step by step, and practice with real-world scenarios.
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Name: Date: Period: EOC Practice: 1. 2. Based on the diagram, what is the total number of students who did not participate in soccer or basketball?
Name: Date: Period: Topic: To find sums, differences, products, and quotients of real numbers Essential Question: How do the rules of integers relate to the properties of real numbers and the definitions of operations? Vocabulary: Integers = {…, -2, -1, 0, 1, 2, …} Whole Numbers = {0, 1, 2, …} Natural Numbers = {1, 2, 3, …}
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
1) (-4) + 8 = Examples: Use the number line if necessary. 4 2) (-1) + (-3) = -4 3) 5 + (-7) = -2
Answer Now -1 + 3 = ? • -4 • -2 • 2 • 4
Answer Now -6 + (-3) = ? • -9 • -3 • 3 • 9
When subtracting, change the subtraction to adding the opposite (keep-change-change) and then follow your addition rule. Example #1: - 4 - (-7) - 4+ (+7) Diff. Signs --> Subtract and use larger sign. 3 Example #2: - 3 - 7 - 3+ (-7) Same Signs --> Add and keep the sign. -10
Okay, here’s one with a variable! Example #3: 11b - (-2b) 11b+ (+2b) Same Signs --> Add and keep the sign. 13b
Answer Now Which is equivalent to-12 – (-3)? • 12 + 3 • -12 + 3 • -12 - 3 • 12 - 3
Answer Now 7 – (-2) = ? • -9 • -5 • 5 • 9
Simplify: • 8 – 7 = • 5 + (-3) = • 15 + 2 = • -6 + 4 = • -9 – 3 = • -2 + (-1) = • -10 – (-12) = • 17 – (-13) =
Review 1) If the problem is addition, follow your addition rule.2) If the problem is subtraction, change subtraction to adding the opposite (keep-change-change) and then follow the addition rule.
Same rule Applies to absolute value Absolute Value of a number is the distance from zero. Distance can NEVER be negative! The symbol is |a|, where a is any number.
Examples 7 = 7 10 = 10 -100 = 100 5 - 8 = -3= 3
Answer Now |7| – |-2| = ? • -9 • -5 • 5 • 9
Answer Now |-4 – (-3)| = ? • -1 • 1 • 7 • Purple
Independent Practice • 6 - 2 = • 8 - 15= • 7 + (-8) = • -82+ 3 = • 16- (-4) = • 9 – (-5) =
Multiplying and Dividing Integers If: Then: (+3) x (-7) = (-21) (-21) ÷ (+3) = (-7) (-5) x (-4) = (+20) (+20) ÷ (-5) = (-4) (-3) x (+8) = (-24) (-24) ÷ (-3) = (+8) (+5) x (+6) = (+30) (+30) ÷ (+5) = (+6) Are the rules the same? Yes!
Multiplying and Dividing Integers RULES: 1) When multiplying or dividing integers with the same signs, the answer will be positive. 2) When multiplying or dividing integers with different signs, the answer will be negative.
Multiplying & Dividing Rule: Just in case you didn’t get it! Positive times Positive = Positive ( + · + = +) Negative times Negative = Positive ( - · - = +) Positive times Negative = Negative ( + · - = -) Negative times Positive = Negative ( - · + = -)
Practice: 3 • -4 = -7 • -2 = 8 • 3 = -9 • 2 = 30 ÷ -2 = -24 ÷ -6 = -4 ÷ 2 = 14 ÷ 7 =
1. A deep-sea diver must move up or down in the water in short steps in order to avoid getting a physical condition called the bends. Suppose a diver moves up to the surface in five steps of 11 feet. Represent her total movements as a product of integers, and find the product. Multiply What does This mean? (11 feet) (5 steps) (55 feet) 5 · 11 = 55
2. At noon the temperature is 8°C. If the temperature decreases 4°C per hour, what is the temperature at 6 pm? How much does the temperature decrease each hour? How long Is it from Noon to 6 pm? 6 hours - 4 degrees (6 hours)(- 4 degrees per hour) Add this to the original temp. = - 24 degrees 8° + (- 24°) = - 16°C
