USING THE IDENTITY & INVERSE TO WRITE EQUIVALENT EXPRESSIONS & PROOFS Engage NY: Lesson 5 Pink Packet pages 19-22

WRITE AN EXPRESSION TO REPRESENT THE TEMPERATURE CHANGE. In the morning, Harrison checked the temperature outside to find that it was -12°F. Later in the afternoon, the temperature rose 12°F. What was the afternoon temperature? Write an expression to represent the temperature change

WHAT IS THE TEMPERATURE CHANGE? In the morning, Harrison checked the temperature outside to find that it was -12°F. Later in the afternoon, the temperature rose 12°F. What was the afternoon temperature? What is the temperature change?

REWRITE SUBTRACTION AS ADDING THE INVERSE & FIND THE SUM A) – (-2) = 0

REWRITE SUBTRACTION AS ADDING THE INVERSE & FIND THE SUM B) -4 – (-4) (-4) + 4 = 0

REWRITE SUBTRACTION AS ADDING THE INVERSE & FIND THE SUM D) g – g g + (-g) = 0

THE SUM OF ADDITIVE INVERSES EQUALS___?

ADD OR SUBTRACT A) = 16

ADD OR SUBTRACT B) 0 – 7 = 0 + (-7) = -7

ADD OR SUBTRACT C) = = -4

ADD OR SUBTRACT D) 0 + d 0 + d = d

WHAT PATTERNS DO YOU NOTICE IN 4A – 4D? The sum of any quantity and zero is equal to the value of the quantity.

WHAT IS ANOTHER WORD FOR OPPOSITES?

WHAT IS THE ADDITIVE INVERSE OR OPPOSITE OF -12.5? = 0

WHAT IS THE SUM OF A NUMBER & ITS OPPOSITE?

GUESS MY NUMBER…

ADDITIVE IDENTITY PROPERTY OF ZERO  Zero is the only number that when summed with another number, results in that number again.  This property makes zero special among all the numbers, so special in fact, that mathematicians have a special name for zero, called the “additive identity”; they call that property the “Additive Identity Property of Zero.”  = 8

PROOFS… 1.Write down the problem 2.Work out each problem, showing every SINGLE LITTLE step 3.Write what property goes with each step you take 4.Use your pink packet vocabulary to help you.

 Additive Identity Property of Zero- The sum of any number and zero = ITSELF  0 + (-5) = -5  Additive Inverse- Opposites added together that have a sum of ZERO  2x + (-2x) = 0  Used when adding negative integers or subtracting integers  Associative Property- Any Grouping with parenthesis  (3x + 4) + 6 = 3x + (4 + 6)  Commutative Property- Any Order- Switch places of numbers  3x + 4 = 4 + 3x  Distributive Property- Expanded or standard form  4 (x + 6) = 4x + 24 ADDITION & SUBTRACTION PROPERTIES

WRITE THE SUM & THEN WRITE AN EQUIVALENT EXPRESSION BY COLLECTING LIKE TERMS. WRITE IN PROOF FORM.

2X – 7 AND THE OPPOSITE OF 2X

THE OPPOSITE OF (5X – 1) AND 5X

-4 AND 4B + 4

COMPLETE- PACKET PAGE 19

WHAT IS THE PRODUCT OF A MULTIPLICATIVE INVERSE?

MULTIPLICATIVE IDENTITY PROPERTY OF ONE

-1… IS A SPECIAL NUMBER

 Additive Identity Property of Zero- The sum of any number and zero = ITSELF  0 + (-5) = -5  Multiplicative Identity Property of One- The product of any number and its reciprocal = ITSELF  (-5) ● 1 = -5  Additive Inverse- Opposites added together that have a sum of ZERO  2x + (-2x) = 0  Used when adding negative integers or subtracting integers  Multiplicative Inverse- Opposites multiplied together that have a product of ONE  2x + (-2x) = 0  Used when adding negative integers or subtracting integers  Associative Property- Any Grouping with parenthesis  (3x + 4) + 6 = 3x + (4 + 6)  Commutative Property- Any Order- Switch places of numbers  3x + 4 = 4 + 3x  Distributive Property- Expanded or standard form  4 (x + 6) = 4x + 24

WRITE THE PRODUCT AND THEN WRITE THE EXPRESSION IN STANDARD FORM BY REMOVING PARENTHESES AND COMBINING LIKE TERMS. JUSTIFY EACH STEP.

THE OPPOSITE OF 4X AND X

THE OPPOSITE OF (– 7 – 4V) AND – 4V

3X + (1 – 3X)

THE OPPOSITE OF -10T AND T-10T

THE RECIPROCAL OF 3 AND -6Y – 3X