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Complete the pyramid by filling in the missing numbers. Each number is the sum of the numbers in the two boxes below it. -4 -8 –7 2 –9 4 –1 5 8 –3 You will need a pencil and a piece of paper. Title your paper “Chapter 11 Mid-Chapter Check” Page 173 1. 12 3. -12 5. -11 7. 2 9. 12 11. 14 13. 11 15. -11 17. 2 19. 16 21. -290 23. -7 + 12 = 5 Page 174 1. 3 spaces 3. -14 degrees 5. -14 + 6 = -8 cm 7. 1 foot Page 175 1. 3 3. -21 5. 7 7. 22 9. 10 11. 2 13. -12 15. 8 17. 19. Deandre, 12; Mazen, -9; Esme, 16; Shameeka, -2 -320 feet Page 176 1. 3. 5. $209, $110, -$40, -$52 $448 -29 degrees Page 640 #14-24, Even You have 15 minutes. Make sure your name is on it. How do I write 5+5+5 as multiplication? How do I write 6+6+6+6+6 as multiplication? How do I write (-6)+(-6)+(-6)+ (-6)+(-6)? as multiplication? The number of students who bring their lunch to Phoenix Middle School has been decreasing at a rate of 4 students per month. What integer represents the total change after three months? The integer -4 represents a decrease of 4 students each month. After 3 months, the total change will be 3(-4). You know that multiplying two positive integers together gives you a positive answer. Look for a pattern in the integer multiplication at right to understand the rules for multiplying two negative integers. 3(–200) = –600 2(–200) = –400 1(–200) = –200 0(–200) = 0 –1(–200) = 200 + 200 + 200 + 200 The product of –2(–200) = 400 two negative integers is a –3(–200) = 600 positive integer. Ways to express multiplication: ◦ x, parenthesis, ∙ + For even numbers of factors: ◦ Same (like) signs = POSITIVE ◦ Different (unlike) signs = NEGATIVE ◦ Or draw a triangle… Example: 3(4) =12 (-2)x(-7) = 14 (3)(-4) = -12 2(-7) = -14 - - Good Guys Leave town + - Result - Good Guys + Stay in town + Leave town - Result + Stay in town + Result - Bad Guys - Bad Guys - Result + (8)2 = ? (-8)2 = ? Write the rule for powers of 2! (2)3 = ? (-2)3 = ? Write the rule for powers of 3! Try powers of 4 and 5. Is there a pattern? Division can be written in two ways: ÷ or by a fraction (top divided by the bottom number) We call the answer to a division problem a Quotient For 2 factors: ◦ Like signs = POSITIVE ◦ Unlike signs = NEGATIVE Try this: (3)(-4)(4) ÷(-12) = (24 ÷(-3))(7) ÷ 2 = (-2)(-2)(4)(-2) ÷(-4)= (7)(-2)(4) ÷(-14)(-2)= # # # # of of of of negatives: negatives: negatives: negatives: 2 1 4 3 If your problem has only multiplication or division (no addition or subtraction signs) what do you notice about even and odd number of negatives? (5)(-8) Negative (-3)(-4)(5)(-2) Negative (-12)(3)(-2) Positive (–12)(5) ÷ (-10) Positive http://www.teachertube.com/video/integers121930 Evaluate x-y if x=12 and y = -7 Replace x and y with the numbers above and solve: x-y 12- (-7) 12+7 19 Evaluate 10 – x if x = (-8) -2 Replace x with the number above and solve: 10 – (-8) -2 18 -2 Notice that, in fraction form, we do everything on top first. The answer is -9 Evaluate ab ÷ c if a=5 and b= -12 and c= -4. Replace a, b and c with the numbers above and solve: (5)(-12) ÷ (-4) (-60) ÷ (-4) 15 Addition: Same sign: add and keep the sign Different sign: subtract and keep the sign of the number with the largest absolute value Subtraction: Change minus sign to a plus and flip the sign of the 2nd number: Ex: 5-2 become 5+(-2) or 6(-2) becomes 6+2, then follow the addition rules. ____________________________________________________ Multiplication/Division: Like sign: Positive Unlike sign: Negative If it is all multiplication/division, even negatives= positive odd negatives = negative Pages 177-178, Odd Pages 181-182, Odd Due at the start of next class.