Integers 2nd and 5th Hour notes

Section 2.1: Adding Integers Integers are the set of whole numbers, including 0, and their opposites. The absolute value of a number is its distance from 0 on the number line.

Example 1: Using a Number Line to Add Integers 4 + (-6) Try this one on your own… (-6) + 2 ?

Example 2: Using Absolute Value to Add Integers -3 + (-5) 4 + (-7) -3 + 6 Try these on your own… 1 + (-2) ? (-8) + 5 (-2) + (-4) 7 + (-1)

Example 3: Evaluating Expressions with Integers Evaluate b + 12 for b = -5 ? Try this one on your own… Evaluate c + 4 for c = -8 ?

Example 4: Health Application Monday Morning Calories Oatmeal 145 Toast with Jam 62 8 fl oz juice 111 Calories Burned Walked six laps 110 Swam six laps 40 Katrina wants to check her calorie count after breakfast and exercise. Use information from the journal entry to find her total. 145 + 62 + 111 – 110 – 40 168 calories

Try this one… Katrina opened a bank account. Find her account balance after the four transactions, listed below. Deposits: $200 and $20 Withdrawals: $166 and $38 ?

Subtracting Integers

Example 1: Subtracting Integers -5 – 5 2 – (-4) -11 – (-8) Try these on your own… -7 – 4 ? 8 – (-5) -6 – (-3)

Example 2: Evaluating Expressions with Integers 4 – t for t = -3 4 – (-3) ? -5 – s for s = -7 -5 – (-7) -1 – x for x = 8 -1 – 8 Try these on your own… 8 – j for j = -6 ? -9 – y for y = -4 n – 6 for n = -2

Example 3: Architecture Application The roller coaster Desperado has a maximum height of 209 feet and maximum drop of 225 feet. How far underground does the roller coaster go?

Try this one on your own… The top of Sears Tower, in Chicago, is 1454 feet above street level, while the lowest level is 43 feet below street level. How far is it from the lowest level to the top? 1454 – (-43) 1497 feet

Multiplying and Dividing Integers

Example 1: Multiplying and Dividing Integers Multiply or Divide. 6(-7) ? -45 / 9 -12 (-4) 18 / -6 Try these on your own… -6(4) ? -8(-5) -18/2 -25/-5

Example 2: Using the Distributive Property with Integers Simplify… -2(3 - 9) 4(-7 - 2) -3(16 - 8)

Try these… Simplify… 3(-6 - 12) ? -5(-5 + 2) -2(14 – 5)

Example 3: Plotting Integer Solutions of Equations. Complete a table of solutions for y = -2x – 1 for x = -2, -1, 0, 1, 2. Plot the points on a coordinate plane. x -2x – 1 y (x,y) -2 -2( ) – 1 -1 1 2 -2( ) - 1

Try this one on your own… Complete a table of solutions for y =3x – 1 for x = -2, -1, 0, 1, and 2. Plot the points on a coordinate grid. x 3x-1 y (x,y) -2 3( ) – 1 -1 1 2 3( ) - 1

Section 2.4: Solving Equations Containing Integers Example 1: Adding and Subtracting to Solve Equations Solve… y + 8 = 6 -5 + t = -25 x = -7 + 13

Try these on your own… x – 3 = -6 x = -5 + r = 9 r = -6 + 8 = n n = Z + 6 = -3 z =

Example 2: Multiplying and Dividing to Solve Equations Try these on your own… -5x = 35 x = z / -4 = 5 z = Solve… k / -7 = -1 -51 = 17b

Example 3: Problem Solving Application Net force is the sum of all forces acting on an object. Expressed in newtons (N), it tells you in which direction and how quickly the object will move. If two dogs are playing tug-of-war, and the dog on the right pulls with a force of 12 N, what force is the dog on the left exerting on the rope if the new force is 2N?

Try these… Sarah heard on the morning news that the temperature had dropped 26 degrees since midnight. In the morning, the temperature was -8 degrees. What was the temperature at midnight? -8 = x – 26 x =

Solving Inequalities Containing Integers Solve and Graph… w + 3 < -1 n – 6 > -5 Try these on your own… k + 3 > -2 ? r – 9 > u – 5 < 3 c + 6 < 2

Rules for Multiplying Inequalities by negative integers.

Example 2: Multiplying and Dividing to Solve Inequalities Solve and Graph… Try these on your own… Solve and Graph.

Properties of operation Associative property(+&X) Commutative property (+&X) Additive property Additive inverse property Multiplicative identity property Multiplicative inverse Grouping Moving Adding 0 Adding opposite=0 Multiply by #1. What do I multiply by to get

a⋅b = b⋅a (a⋅b)⋅c=a⋅(b⋅c) The commutative property of multiplication states that when finding a product, changing the order of the factors will not change their product. In symbols, the commutative property of multiplication says that for numbers a and b: a⋅b = b⋅a The associative property of multiplication states that when finding a product, changing the way factors are grouped will not change their product. In symbols, the associative property of multiplication says that for numbers a,b and c: (a⋅b)⋅c=a⋅(b⋅c)

What vocabulary do you see? Could we simplify before operating? How does the commutative property help us here? Think of GCF Let’s try another…

What property can we use here? What gives you the hint? What property can we use here and how will we evaluate?

Mastery Group work Use the properties to help write an equation that can be used to solve a real life scenario:

Explanation