Identifying & Applying Them

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Presentation transcript:

Identifying & Applying Them Algebraic Properties Identifying & Applying Them

Combining Like Terms Commutative Property Associative Property Distributive Property Key Vocabulary

2x² - 4x + 5x² + 3 Combining Like Terms To ‘Combine Like Terms’ it is essential to recall the definition of ‘terms’ & ‘coefficients.’ Terms: Parts of the expression separated by addition or subtraction. Ex: 2x; 4y; 5x; 3 Coefficients: The numbers in front of the variables. Ex: 2, 4, & 5 Combining Like Terms

2x² cannot be added or subtracted with 4x or with 3 2x² + 5x² - 4x + 3 { { 1st: Find each term with the same variable to the same power! Ex: 2x² & 5x² 4x 3 2nd: Simplify using the coefficients and operations. Ex: 2x² + 5x² = 7x² 4x = 4x 3 = 3 3rd: Unlike terms cannot be combined. 2x² cannot be added or subtracted with 4x or with 3 7x² - 4x + 3 Combining Like Terms

Combining Like Terms

x + x + x is the same as 3x x + y + y is the same as x + 2y 4y – y is the same as 3y Combining Like Terms

Combining like terms is essential to apply the algebraic properties.

A way to remember: Keep ‘order’ in the community! COMMUTATIVE PROPERTY (Ordering) Words Numbers You can add or multiply numbers in any order. 18 + 9 = 9 + 18 15  2 = 2  15 A way to remember: Keep ‘order’ in the community!

Examples of Applying the Commutative Property 5x + 2y + 4 = 2y + 4 + 5x 3 x 4 = 4 x 3 4x + 9 = 9 + 4x *All of the terms on one side of the equal sign are on the other side of the equal sign just in a different order.* Examples of Applying the Commutative Property

A way to remember! Be careful of the group you associate with! ASSOCIATIVE PROPERTY (Grouping) Words Numbers ONLY when you are adding or multiplying, you can group any of the numbers together. (17 + 2) + 9 = 17 + (2 + 9) (12  2)  4 = 12  (2  4) A way to remember! Be careful of the group you associate with!

Examples of Applying the Associative Property All of the terms on each side of the equal sign are the same. The order is the same. Examples of Applying the Associative Property

Caution! The Commutative and Associative Properties do not apply to subtraction or division.

Distributive Property Words Numbers To multiply a number by a sum, multiply by each number in the sum and then add. 6  (10 + 4) = (6  10) + (6  4) \ / \ / = 60 + 24 \ / = 84 Distributive Property

A way to remember! Distribute evenly to everyone.

A way to remember! Distribute evenly to everyone. 6(x + 7) (6· x) + (6 · 7) \/ \/ 6x + 42 Use the Distributive Property. Multiply. There are no like terms, so it stays the same. A way to remember! Distribute evenly to everyone.

A way to remember! Distribute evenly to everyone. 24 + 6x (24 ÷ 6) + (6x ÷ 6) \ / \ / (4 + x) 6 (4 + x) Factor out the GCF of each term. … in this case 6. Place the quotients in parenthesis. Place the GCF in front of the parenthesis of quotients. . A way to remember! Distribute evenly to everyone.

Let’s Practice! 3x + 7 + x 4n + 2n + 9 4(6x) (3 · n) · 11 x + x + x (14y + x) + 22y 4(2x + y) 27x + 18y 4(x + 1) + 2x 4x + 7 6n + 9 24x 33n 3x 4x + 3 36y + x 8x + 4y 27x + 18y 6x + 4 Let’s Practice!