GOSEA 3 - Properties of Operations

GOSEA 3

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Properties of Operations

By continuing to the next slide and completing this lesson, you testify that you are the student who is enrolled in GOSEA at BCHS with Mrs. Haley and that you are doing the lesson for yourself and no one else.

More than just numbers

Mathematics contains many properties (rules) that ensure we all come up with the same answer when operations are carried out correctly.

Order of Operations (PEMDAS)

• P - Parentheses - simplify any operations located inside of ( ) first

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• E - Exponents - simplify any exponential expression

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• MD - complete Multiplication AND Division in order from LEFT to RIGHT

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• AS - complete Addition AND Subtraction in order from LEFT to RIGHT

Follow the directions.

Directions for problems involving order of operations should say to "simplify" or "evaluate". One can not "solve" expressions.

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"Simplify" means to simply do the operations that are indicated (in the correct order - PEMDAS).

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"Evaluate" means to 'find the value of'.

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"Solve" is done to equations (which contain equals signs).​

When doing the following problems, do them WITHOUT a calculator.

Calculators know the order of operations.

I need to know that YOU know the order of operations.

You are only hurting yourself if you do them with a calculator.

Multiple Choice

Simplify: 4 + 3 x 2

• 10

• 14

• 49

• 9

Multiple Choice

Evaluate:   $$4\div4+5$$  

• $$\frac{4}{9}$$  

• 6

Multiple Choice

Find the value of the expression:    $$2\cdot6-4$$  

• 4

• 6

• 8

• 3

Multiple Choice

Simplify:                   $$5-9\div\left(6-3\right)$$  

• $$-\frac{4}{3}$$  

• 2

• $$-\frac{11}{3}$$  

• -4

Multiple Choice

Evaluate:

               $$12\div2^2+3$$  

• 7

• $$\frac{12}{7}$$  

• 39

• 6

"Commutative" Properties

The root word in COMMUTATIVE is "commute" which means to move round. When you see a commutative property, it just means the numbers can move around in any order.

Commutative Property of Addition

• a + b = b + a

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• This property means that the order that two numbers are added in does not affect the sum.

  ("Sum" is the answer to an addition problem.)

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• 3 + 4 = 4 + 3

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• 7 = 7

Commutative Property of Multiplication

• ab = ba

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• This property means that the order two numbers are multiplied in does not affect the product.

  ("Product" is the answer to a multiplication problem.)

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• 5 x 6 = 6 x 5

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• 30 = 30

"Associative" Properties

The root word in ASSOCIATIVE is "associate". When you associate yourself with other people, you are grouping yourself with them. When you see associative properties, it just means numbers are being grouped together. When adding a bunch of numbers, you will group two numbers together to add first. Then you will group another two and so on. The same is true when multiplying a bunch of numbers.

Associative Property of Addition

• (a + b) + c = a + (b + c)

• This property means that when adding three or more numbers, it does not matter which two numbers are added first. Follow the order of operations on each side to see that the two sides equal each other.

• (7 + 2) + 5 = 7 + (2 + 5)

  (9) + 5 = 7 + (7) ........ inside the ( ) was simplified first

  14 = 14

Associative Property of Multiplication

Distributive Property of Multiplication

• a ( b + c ) = ab + ac

• This property means that any number (a) multiplied by an expression containing two terms (b + c) must be multiplied by BOTH terms in the parentheses with the resulting products being added together.

  The following example shows how both sides are equal.

• 3 ( 4 + 5 ) = 3 (4) + 3 (5) Distributive Property applied

  3 (9) = 12 + 15 Order of Operations applied to both sides

  27 = 27

Directions for problems requiring distributing may say to....

• "Simplify by using the Distributive Property"

• "Distribute"

• "Simplify each expression"

• "Simplify"

Multiple Choice

Simplify:

3 (m + 2)

• 3m + 2

• 3m + 6

• 3m + 5

• m + 5

Multiple Choice

Simplify:

7 (8n - 2)

• 8n - 14

• 56n - 2

• 56n - 14

• 15n + 5

Multiple Choice

Simplify:

10 ( 1 + 9p )

• 10 + 9p

• 1 + 90p

• 100p

• 10 + 90p

Multiple Choice

Simplify:

-8 ( 9 + 7x )

• -72 - 56x

• -72 + 56x

• -72 + 7x

• -1 - 1x

Multiple Choice

Simplify:

-2 ( -7 - 5n )

• -9 - 7n

• 14 - 10n

• 14 + 10n

• -14 + 10n

Multiple Choice

Simplify:

- ( -7 + 9x )

• 7 - 9x

• 7 + 9x

• -2x

• 16x

Multiple Choice

Simplify:

( x + 10 ) 10

• 10x + 10

• 10 ( x + 10)

• x + 100

• 10x + 100

Multiple Choice

Simplify:

( -10n - 10 ) $$\cdot$$  5

• 5( -10n - 10)

• -50n - 10

• -50n - 50

• -5n - 5

Multiple Choice

Simplify:

( 5n - 9) ( -6 )

• -30n + 54

• 5n + 54

• -1n - 15

• 24n

Multiple Choice

Simplilfy:

( x - 7 )  $$\cdot$$   -3

• x + 21

• -3x + 21

• -3x - 7

• 12n

Multiple Choice

Simplify: ( 1 - 5r)  $$\cdot$$  -9

• -8 - 14r

• -9 - 45r

• -9 + 45r

• 36r

Keep redoing this assignment until you make a 100. That is the only way to get a 100 for Geometry class in the Fall.

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