Ms. Crusenberry 9-2013

Vocabulary Integers – all whole numbers and their opposites Positive numbers – whole numbers greater than zero Negative numbers – whole numbers less than zero Absolute value – the distance a number is from zero

Name their opposites -8 17 108 -238

Answers 8 -17 -108 238

Find the Sum 6 + -6 = -12 + 12 = -7 + 0 = 0 + 11 = 23 – 24 =

Answers -7 11 -1

Compare each pair Use > or < -3 _____ 2 6 _____ -9 -58 _____ -72 23 _____ 28

Answers < >

Find the sum -3 + -2 + 6 = 4 + - 8 + 7 = -5 + -3 + 6 = -8 + 5 + 7 =

Answers -5 + 6 = 1 -4 + 7 = 3 -8 + 6 = -2 -3 + 7 = 4

What is the absolute value? / -4 / / 8 / / -108 / / +3 /

Answers 4 8 108 3

Find the sum or difference /-3/ + /8/ = /+52/ + /-15/ = /-33/ - /16/ = /-2/ - /-1/ =

Answers 3 + 8 = 11 52 + 15 = 67 33 – 16 = 17 2 – 1 = 1

Subtracting Positive & Negative Numbers (-2) – (+5) = (-23) – (-16) = (+4) – (+1) = (-64) – (+31) = (-45) – (+26) =

Answers -7 3 -95 -71

Problem Solving On Monday, the temperature goes up 7 degrees, by Thursday the temperature goes up another 4 degrees, and by Sunday the temperature goes down 2 degrees. How much has the temperature changed over the course of the week? On Friday your checking account balance is $122. On Saturday you shop at the mall and write two checks for $17 and $31. What is your checking account balance now?

Answers 7 + 4 – 2 = 9 122 – 17 – 31 = 74

Multiplying Integers RULES Like Signs + x + = + - x - = + Unlike Signs

Find the Products (-2) x (-6) = (+3) x (-10) = (+15) x (+2) =

Answers 12 -30 30 -20

Find the Products (-4) x (-3) x (+3) = (+12) x (+4) x (-20) =

Answers 12 x 3 = 36 48 x -20 = -960 -10 x -5 = 50 -24 x -3 = 72

Properties of Addition & Multiplication Commutative Property of Addition 5 + 4 = 4 + 5 Commutative Property of Multiplication 4 x 6 = 6 x 4 Associative Property of Addition (2 + 3) + 4 = 2 + (3 + 4) Associative Property of Multiplication (4 x 5) x 2 = 4 x (5 x 2)

Continued… Distributive Property of Multiplication 2 x (4 + 3) = (2 x 4) + (2 x 3) 2 x 7 = 8 + 6 14 = 14

Name the Property 2 + 6 = 6 + 2 10 x 9 = 9 x 10 (9 + 2) + 3 = 9 + (2 + 3) (3 x 4) x 2 = 3 x (4 x 2) 3 x (5 + 4) = (3 x 5) + (3 x 4)

Answers Commutative Property of Addition Commutative Property of Multiplication Associative Property of Addition Associative Property of Multiplication Distributive Property of Multiplication

Dividing Positive & Negative Integers RULES The quotient of two numbers with like signs will be positive. (-15) ÷ (-5) = 3 The quotient of two numbers with unlike signs will be negative. (-12) ÷(4) = -3 (14) ÷ (-2) = -7

Solve for the Quotients (-16) ÷ (-8) = (88) ÷ (-11) = (-10) ÷ (-1) = (-90) ÷ (2) =

Answers 2 -8 10 -45

Vocabulary Variable – a symbol usually a letter, than can stand for different values Ordered pair – two numbers that give the location of a point on a grid Origin – the point on a grid with the coordinates (0,0) X-axis – the horizontal line on a grid that passes through the origin Y-axis – the vertical line on a grid that passes through the origin X-coordinate – the first number in an ordered pair describing the location of a point Y – coordinate – the second number in an ordered pair describing the location of a point

Solving Equations - Vocabulary Equation – two or more mathematical expressions separated by equal signs 13 + 5 = 18 Open sentence – an equation with an unknown n + 5 = 18

Solving an Open Sentence Rule 1– you must get the variable by itself Rule 2 – what you do on one side of the equal marks you must do on the other side n + 5 = 18 x – 7 = 10 - 5 -5 +7 +7 n = 13 x = 17

Practice x + 2 = 10 s + 7 = 30 d – 5 = 30 m – 2 = 26 k – 5 = 2

Answers x + 2 = 10 5. k – 5 = 2 - 2 -2 + 5 +5 x = 8 k = 7 s + 7 = 30 - 7 -7 s = 23 d – 5 = 30 + 5 +5 d = 35 m – 2 = 26 +2 +2 m = 28

More Practice -5 + a = 12 8 + x = -10 -16 = x + 5 -7 = x – 5

Answers - 5 + a = 12 4. -7 = x - 5 +5 + 5 + 5 + 5 a = 17 -2 = x 8 + x = - 10 5. -25 + c = 50 -8 -8 +25 +25 x = -18 c = 75 - 16 = x + 5 - 5 - 5 -21 = x

Evaluating Expressions If x = 2, n = 3, y = 5 and m = 10 x + y = 3n + 4 = m/y = 2m = 6n + y = xm – 7 =

Answers 2 + 5 = 7 9 + 4 = 13 10/5 = 2 2 x 10 = 20 6 x 3 + 5 = 18 + 5 = 23 2 x 10 – 7 = 20 – 7 = 13

Problem Solving/Mathematical Expression You have $243 in your checking account. You need to write a check for $324. How much money do you need to deposit to prevent bouncing your check? You lost 25 pounds but you gained a few pounds on vacation. Now your net weight loss is 17 pounds. How many pounds did you gain on vacation? After selling 24 calendars for the community center fund-raiser, you have 14 left. How many calendars did you have before you sold any?

Answers To solve the problem, subtract 243 from 324. To put this into an equation, do 243 + n = 324 To solve the problem, subtract 17 from 25. To put this into an equation, do 17 + n = 25 To solve the problem add 24 and 14. To put this into an equation, do n – 14 = 24 or 14+24 = n

Evaluating Expressions Linda spent d dollars. Then she spent 15 dollars more. How many dollars did Linda spend? a. d > d b. d + 15 c. d/2 Aisha is 6 inches shorter than her husband. If Aisha is t inches tall, how many inches tall is her husband? a. t + 6 b. 6 – t c. t x 6

Answers B A

Solving Equations Using Multiplication or Division 2y = 12 2y is the same as 2 x y therefore, you must use division to get the (y) by itself. 2y = 12 divide each side by 2 2 2 y = 6

Continued a = 12 2 2 x a = 12 x 2 multiple each side by 2 2 to get the (a) by itself a = 24

Practice 5x = 40 3b = 96 4w = 16 13a = 130 2a = 56

Answers Divide each side by 5 to get 8 Divide each side by 3 to get 32

Practice b = 5 10 a = 3 21 n = 9 5 n = 6 10 t = 9 7

Answers Multiply each side by 10 to get 50

Practice with Integers 12x = -36 -3a = -24 -4v = 9 8p = -64 r/-10 = 4 x/4 = -3 w/16 = -4 n/7 = -4

Answers Divide each side by 12 to get -3 Multiply each side by -10 to get -40 Multiply each side by 4 to get -12 Multiply each side by 16 to get -64 Multiply each side by 7 to get -28

Solving Two-Step Equations 2x + 5 = 25 In a two-step equation, you must get the stand alone number on the side with variable out of the equation. 2x + 5 = 25 Step 1 – subtract 5 from both sides - 5 - 5 2x = 20 Step 2 – divide both sides by 2 2 2 x = 10

Another Example Using Integers -25 = 3a – 2 Step 1 – add 2 to both sides + 2 +2 -23 = 3a Step 2 – divide both sides by 3 3 3 -23 = a **Leave as an improper fraction 3 44 – x = 1 Step 1 – add x to both sides + x + x 44 = 1 + x Step 2 – subtract 1 from both sides -1 -1 43 = x

Practice 2a – 6 = 30 5y + 10 = - 20 2c – 1 = 9 3a + 3 = -15 3 + 2n = 31 -8 - 11n = 25 -55 – x = 1 -5x + 51 = 141

Answers Add 6 to each side then divide each side by 2 to get 12 Subtract 10 from each side then divide each side by 5 to get -6 Add 1 to each side then divide each side by 2 to get 5 Subtract 3 from each side then divide each side by 3 to get -6 Add 1 to each side then divide each side by 3 to get 4 Add 4 to each side then divide each side by 7 to get 34/7 Subtract 3 from each side then divide each side by 2 to get 14 Add 8 to each side then divide each side by – 11 to get 3 Add x to each side then subtract 1 from each side to get 56 Two ways : 1st – Subtract 51 from both sides then divide both sides by -5 to get x = -18 2nd = Add 5x to both sides, subtract 141 from both sides, then divide both sides by 5 to get -18

Combining Like Terms Remember (-2) + (-5) = -7 Then (-2a) + (-5a) = -7a or -2a – 5a = -7a -3a – 6a = -9a -4a + 5a = 1a or just a -9x + 2x = -7x

Practice 3a – 4a 6x – 4x 9y – 3y + 2y y + 2y 8c – 2c -10x – 10x -15c + 5c – 5c 16a – 20a

Answers -1a or –a 2y 8y 3y 6c -20x -15c -4a

Simplifying Mixed Terms 7a + 3c + 4a – 9c Combine like terms 7a + 4a + 3c – 9c Arrange the like terms 11a – 6c -8x + 3y – 2x -10x + 3y 5a + 2c – 8a + 5c + 6 – 8 5a – 8a + 2c + 5c + 6 – 8 -3a + 7c - 2

Practice -3a + 9c + 8c 4x + 2 + 5x -5c + 7c + 6c 4a – 6a – 2a + 3 30c + 2c – 6c + 4c -6x + 2y + 8y – 3x 5 - 8x – 2x + 3x + 7x + 6 -6y – 3y + 6y + 6x

Answers -3a + 17c 9x + 2 8c -4a + 3 30c -9x + 10y 11 -3y + 6x

Input/Output Input 3 5 7 9 Output 15 19 What’s the rule? Is it x3 or + 10? Input 7 8 11 14 Output 4 5.5 What’s the rule? Is it -4 or ÷2?

More Practice Input 5 2 4 3 6 Output 9 What’s the rule? -2, x3 or -4, x9 Input 4 10 8 6 Output 42 What’s the rule? -3, x6 or +2, x12

Answers Add 10 Divide by 2 Subtract 2, multiply by 3

Numerical Patterns 1, 6, 11, 16, 21, 26 What is the pattern? Complete the following: 500, 100, _____, _____ 7, 22, 37, 52, _____, _____ 1, 3, 9, 27, _____, _____

Answers + 5 ÷ 2 ÷ 5 + 15 x 3

Solving Inequalities If m + 5 > 8, find the value of m m + 5 > 8 - 5 -5 m > 3 Special Situation -2x > 4 -2 <-2 divide each side by -2 and flip the inequality x < -2

Practice x – 7 < 25 m + 14 < 52 23 + p > 50 y/3 – 4 < 27

Answers Add 7 to both sides to get x < 32 Subtract 14 from both sides to get m < 38 Subtract 23 from both sides to get p > 27 Multiply both sides by 3 to get y < 63 Divide both sides by -3 then flip the inequality to get x < 4