Lesson 2-3 Adding and Subtracting Integers Objective Students will be able to: 1. State the coordinate of a point on a number line. 2. Graph integers on a number line. 3. Add and subtract integers.

Add or Subtract by Graphing on Number Line -5 5 Integers = {…, -2, -1, 0, 1, 2, …} Whole Numbers = {0, 1, 2, …} Natural Numbers = {1, 2, 3, …}

To GRAPH a set of numbers means to locate and mark the points on the number line. Graph {-1, 0, 2}. Be sure to put the dots on the line - not above or below. 5 -

Name the set of numbers graphed. {-2, -1, 0, . . . } The darkened arrow means that the graph keeps on going. When you see this, put 3 dots in your set.

Examples: Use the number line if necessary. 1) (-4) + 8 = 4 2) (-1) + (-3) = -4 3) 5 + (-7) = -2

SUBTRACT and use the sign of the larger number. 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

Karaoke Time! Addition Rule: Sung to the tune of “Row, row, row, your boat” Same signs add and keep, different signs subtract, keep the sign of the higher number, then it will be exact! Can your class do different rounds?

-22 + 39 = ? -61 32 17 -17 Answer Now

-10 + (-17) = ? -27 -7 3 7 Answer Now

The additive inverses (or opposites) of two numbers add to equal zero. Example: The additive inverse of 3 is -3 Proof: 3 + (-3) = 0 We will use the additive inverses for subtraction problems.

What’s the difference between 7 - 3 and 7 + (-3) ? The only difference is that 7 - 3 is a subtraction problem and 7 + (-3) is an addition problem. “ SUBTRACTING IS THE SAME AS ADDING THE OPPOSITE.” (Keep-change-change)

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

11b + (+2b) Same Signs --> Add and keep the sign. = 13b Okay, here’s one with a variable! Example #3: 11b - (-2b) 11b + (+2b) Same Signs --> Add and keep the sign. = 13b

Which is equivalent to -12 – (-3)? 12 + 3 -12 + 3 -12 - 3 12 - 3 Answer Now

7 – (-2) = ? -9 -5 5 9 Answer Now

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.

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 --250 = - 250

|7| – |-2| = ? -9 -5 5 9 Answer Now

|-4 – (-3)| = ? -1 1 7 Purple Answer Now

Lesson 2-3 Homework p. 90 # 24 – 54 every third problem

LESSON 2-5 ADDING AND SUBTRACTING RATIONAL NUMBERS Objective The students will be able to: 1. add and subtract rational numbers. 2. compare and order rational numbers.

A rational number is a number THAT CAN BE WRITTEN AS A FRACTION. HOW CAN THESE BE WRITTEN AS A FRACTION? 3 =

Inequality Symbols

Ordering Rational Numbers 2 ways to order from least to greatest Get a common denominator Change the fractions to decimals (numerator  denominator)

WHICH RATIONAL NUMBER IS BIGGER? 1) Get a common denominator. 2) or convert the fraction to a decimal. 0.363 < 0.375 4 1 < 3 8

Which rational number is bigger? 7 4 or 1 6 Get a common denominator or convert to a decimal 1.75 < 1.83 42 24 < 44

Line up the decimals and add (same signs). -2.564 Find the sum. 1) -2.304 + (-0.26) Line up the decimals and add (same signs). -2.564 2) Get a common denominator and subtract.

3) Change subtraction to adding the opposite. Find the difference. 3) Change subtraction to adding the opposite. Get a common denominator. Subtract and keep sign of the larger number.

4) Change subtraction to adding the opposite. Find the difference. 4) Change subtraction to adding the opposite. Get a common denominator and subtract.

5) Solve 6.32 – y if y = -3.42 Substitute for y: 6.32 - (-3.42) 6.32 + 3.42 9.74

Find the solution . Answer Now

Find the solution . Answer Now

Which symbol makes this true? 5 7 __ 3 4 < > = Answer Now

Which symbol makes this true? -2 -1 __ 9 4 < > = Answer Now

Lesson 2-5 Homework: p. 103 # 14 – 36 evens