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Applications of Negative Numbers & Absolute Value In Algebra County Negative Numbers are found in weather reports, but not in sunny Florida! Zero Down here, temperatures are negative. Negative Numbers are found in stock market quotes There, the stock market went down. When losing weight, the weight loss is a negative number. The number of feet below sea level is a negative number. The number of feet below sea level is a negative number. The number of feet below sea level is a negative number. The number of feet below sea level is a negative number. Negative Numbers are found in banking. Checks are “subtracted” from the bank statement. Negative Numbers are found in Jeopardy scores. ADDING INTEGERS IN ALGEBRA COUNTY If it’s 70 degrees outside, and the temperature gets 10 degrees cooler, how can we write it? 70 10 60 If it’s 5 degrees outside, and the temperature gets 10 degrees colder, how can we write it? 5 10 5 A positive added to a negative takes the sign of the largest “number.” We subtract. If it’s -10 degrees outside, and the temperature goes down 10 degrees, how can we write it? 10 10 20 A negative added to a negative is a “larger” negative. We add the “numbers.” Another way to think of adding positive and negative numbers is by using red and yellow colored counters. 35 3 and -5 2 zero pairs 3 5 -3 and -5 No zero pairs 8 Write these in your notes pages 1. 2. 3. 4. 5. 6. 18 20 2 11 9 2 6 5 11 1 7 8 29 7 75 2 MULTIPLYING INTEGERS IN ALGEBRA COUNTY -5 TIMES 6 CAN BE WRITTEN: -5(6) (-5)(6) 2(3) MEANS: •2 GROUPS OF 3 •A 2 BY 3 ARRAY -5 ·6 WE CAN PICTURE 2(3): THESE ARE ALL ARRAYS WE CAN PICTURE 2(3) AS 2 GROUPS OF 3: Which? Group or array? Two rows of three kitchen tiles When we multiply: Positive X positive = Positive X negative = + - Negative X positive = Negative X negative = + Don’t get confused: Positive + positive = Positive + negative = + ?? Negative + positive = Negative + negative = ?? - Negative + positive = Why the question marks? -4+6 =2 (positive) -6+4 = -2 (negative) ?? Back to multiplication: -(-3) means: - 1(-3) Negative 1 times negative 3 =3 The number 1 is very important in Algebra County. Also: -(5) means: Negative 1 times 5 - 1(5) which is: -5 Let’s work some multiplication problems: -2(5) = -10 3(-5) -4(-2) = = -15 8 - (-6) = 6 -9(-11) = 99 - (-13) = 13