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Published byJulian Mosley Modified over 8 years ago
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Schema: Simplify
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Combining Like Terms & Distributive Property Needed review from last year
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Some Things to Remember x 1x +1x +1x 1 1 Just Watch What Happens
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Terms vs. Factors
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How many terms?
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How many factors does the middle term have?
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Terms vs. Factors
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How many terms?
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Like Terms – have same variable with same exponent 6x + 2x = When combining like terms, only use the coefficients. 6x + 2x =8x 4x + 3y – 2x + 4y = Simplify 2x + 7y Simplify Never, NEVER, combine x’s and y’s or constant terms with variable terms. 2x + 7y ≠ 9xy and 3a + 6 ≠ 9a. Key Skills
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7x+ 3y+ 5y– 9x– 17y+ 7x = – 9y – 9x = – 2x + 5y+ 3y– 17y – 2x – 9y Just Watch What Happens
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TRY THESE 1) 3q + 7q = 10q 2) 4x + 8y – 10x + 3y = – 6x + 11y 4x + 8y – 10x + 3y = 3 + 5x = 3 + 5x ≠ 8x 3(5x) = Review Again 15x
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In algebraic terms, find the perimeter of the following shape. 2x 4x + 3y 3x – 2y To find the perimeter, add the sides together. P = 3x – 2y + 2x + 3x – 2y + 4x + 3y = 12x – y Key Skills What is the perimeter if x = 5 and y = 8? P = 12(5) – 8 = 52
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Find the perimeter of the following shape when x = 2. 6x – 2y 5x + y To find the perimeter, add the sides together. P = 5x + y + 5x + y + 6x – 2y = 16x TRY THIS 32 Does the value of y matter in this problem? Obviously Not!
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P total = 4x + 16 + 6x – 4 Schema: Field 2 Field 1 2x + 5 3 4 3x – 6 A farmer has two rectangular fields. P 1 = 3 + 3 + 2x + 5 + 2x + 5 P 2 = 4 + 4 + 3x – 6 + 3x – 6 P 1 = 4x + 16 P total = 10x + 12 How much fence would the farmer need if x = 5? P 2 = 6x – 4 P total = 10(5) + 12P total = 62 He wants to put a fence around both. In algebraic terms, how much fence would he need?
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Properties of Addition and Multiplication
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Commutative Property Commutative Property of Addition-- changing the order in which you add does not change the sum. So, More Examples:
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Commutative Property So, More Examples:
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Associative Property Associative Property of Addition-- changing the way the numbers are grouped does not change the sum. Add parenthesis to show Associative Property So,
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Associative Property Add parenthesis to show Associative Property
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Identity Property Identity Property of Addition-- if you add zero to a number, you get the same number! 0 is called the identity element of addition!!
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Identity Property 1 is called the identity element of multiplication!!
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Inverse Property
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Additive Inverse Property--a number plus its opposite equals 0.
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Identify the Property Commutative Prop. Of Multiplication Identity Prop. Of Addition Zero Property Associative Prop. Of Addition Identity Prop. Of Multiplication
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Distributive Property or Order of Operations Distributive Property It works! Why use the distributive property?
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Simplify using the distributive property. 1) 2) 3) 4) 5) 6)
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Simplify using the distributive property. 1) 2) 3) 4) 5) 6)
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Geometric Model for Distributive Property Two ways to find the area of the rectangle. 4 52 As a wholeAs two parts
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Geometric Model for Distributive Property Two ways to find the area of the rectangle. 4 52 As a wholeAs two parts same
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Find the area of the rectangle in terms of x, y and z in two different ways. x yz As a wholeAs two parts
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Find the area of the rectangle in terms of x, y and z in two different ways. x yz As a wholeAs two parts same
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Use the distributive property to write an equivalent variable expression. Then simplify. 1) 2) 3) 4) 5) 6)
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