Properties of Addition Lesson 1 4 Four Properties

Properties of Addition Lesson 1 -4

Four Properties of Addition 1. 2. 3. 4. Commutative Associative Identity Inverse

The Commutative Property • Background – The word commutative comes from the verb “to commute. ” – Definition on dictionary. com • Commuting means changing, replacing, or exchanging – People who travel back and forth to work are called commuters. • Traffic Reports given during rush hours are also called commuter reports.

Here are two families of commuters. Commuter B Commuter A & Commuter B changed lanes. Remember… commute means to change. Commuter B Commuter A

Here is another example…

Think of this hypothetical situation: Every day you ride your bike to school. The distance from home to school is 2 miles. The distance from school to home is also 2 miles. How do we know this? Did you notice that hypothetical and hypothesis look almost the same? Hmmmm. . . Think about what hypothesis means…

Home School The distance from Home to School is the same as the distance from school to home. Home + School = School + Home H+S=S+H A+B=B+A

The Commutative Property A+B=B+A

The Associative Property • Background – The word associative comes from the verb “to associate. ” – Definition on dictionary. com • Associate means connected, joined, or related – People who work together are called associates. • They are joined together by business, and they do talk to one another.

Let’s look at another hypothetical situation Three people work together. Associate B needs to call Associates A and C to share some news. Does it matter who he calls first?

Here are three associates. B calls A first He calls C last B A If he called C first, then called A, would it have made a difference? NO! C

(The Role of Parenthesis) • In math, we use parenthesis to show groups. • In the order of operations, the numbers and operations in parenthesis are done first. (PEMDAS) So….

The Associative Property The parenthesis identify which two associates talked first. (A + B) + C = A + (B + C) B A B THEN C A C

The Identity Property of Addition I am me! You cannot change My identity!

Zero is the only number you can add to something and see no change.

Identity Property of Addition +0= A+0=A

Inverse Property The sum of a number and its opposite is 0.

Examples 8 + (-8) = 0 -13 + (13) = 0 10+ (-10) = 0

Recall Commutative Property- The order in which you add two numbers does not change the sum. Associative Property – The way you group three numbers does not change the sum. Identity Property- The sum of a number and 0 is the number. Inverse Property- The sum of a number and its opposite is 0.

Let’s practice ! Look at the problem. Identify which property it represents.

(9 + 8) + 7 = 9 + (8 + 7) The Associative Property of Addition It is the only addition property that has parentheses.

12 + 0 = 12 The Identity Property of Addition It is the only addition property that has two addends and one of them is a zero.

9+7=7+9 The Commutative Property of Addition It is the only addition property that has numbers that change places.

4+6=6+4 The Commutative Property of Addition Numbers change places.

3+0=3 The Identity Property of Addition See the zero?

(4 + 3) + 2 = 4 + (3 + 2) The Associative Property of Addition It has parentheses!

a+0=a The Identity Property of Addition Zero!

Investigating Algebra Activity. Answer page 73 (Items 1 -14) Math UBD Book

Addition of Integers Rules in Addition • To add two numbers with the same sign, add their absolute values. The sum has the same sign as the numbers added. Examples: 8 + 7 = 15 -3 + (-5) = -8 -14 + (-20) = -34

Rules in Addition • To add two numbers with different signs, subtract the lesser absolute value from the greater absolute value. The sum has the same sign as the number with the greater absolute value. Examples: -12 + 7 = -5 18 + (-4) = 14

Remember! Absolute Value – The distance of a number from 0 on a number line. I 8 I=8 I -12 I = 12

Drill -11 + (-9)

Answer -20

Drill -24 + 8

Answer -16

Drill 9. 1 + (-2. 5)

Answer 6. 6

Drill 53 + (-37)

Answer 16

Drill -11. 4 + (-3. 8)

Answer -15. 2

Subtraction of Integers Rule in Subtraction In subtracting an integer from another integer, add the opposite of the subtrahend to the minuend. 14 – 8 = 14 + (-8) = 6 -2 – 7 = -2 + (-7) = -9

Drill 14 – (-5)

Answer 19

Drill 18 - 35

Answer -17

Drill -18 - 9

Answer -27

Drill -12 – (-9)

Answer -3

Drill -18. 2 – (-15. 4)

Answer -2. 8

Drill -98 – (-9)

Answer -89

Drill 32 – (-6)

Answer 38

Drill -89 – (-9)

Answer -80

Seatwork # 6 Perform the following operations 1) - 4 + (-9) 2) -19 + 23 3) 45 + (-10) 4)-12 + 3 5) -17 + 8

Homework Answer page 77 (Items 1 -15) Math UBD Book