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Algebra 1 Chapter 1-2 The Commutative and Identity Properties Group Work True or False 1. 2. 3. 4. 3+8=8+3 6–3=3–6 10 / 5 = 5 / 10 4•6=6•4 Vocabulary Commutative Properties – we can change the order when adding or multiplying without changing the sum or product. Equivalent Expressions – expressions such as x + 2 and 2 + x, which always result in the same number when we substitute any value for their variables. Example…(Commutative Property) Write an expression equivalent to each using a commutative property: y+5 xy 5 + ab Try This… Use a commutative property to write an equivalent expression. 1. 2. 3. x+9 pq xy + t Vocabulary… Additive Identity – adding 0 to any number gives that number. Multiplicative Identity – multiplying 1 to any number gives that number (Dividing a number by itself gives 1) These all have the value of 1 n/n m+3/m+3 5y + 4 / 5y + 4 Examples… Write an equivalent expression for 2 / 3 by multiplying by 1. Try This… Write an equivalent expression for 7 / 5 by multiplying by 1. Write an equivalent expression for 3 / 8 by multiplying by 1. Examples… Write an expression equivalent to x / 2 by multiplying by 1. Use y / y for 1. Try This… Write an expression equivalent to y / 2x by multiplying by 1. Use z / z for 1. Write an expression equivalent to 2m / n by multiplying by 1. Use p / p for 1. Vocabulary… Factor – numbers that you multiply to find the product. Simplest Form – when the only common factor of the numerator and the denominator is 1. Simplifying – The process of finding the simplest form. Examples… (Simplifying Expressions) Simplify: 10 / 15 36 / 24 Try This… 18 / 27 48 / 18 56 / 49 More Simplifying Examples… 18 / 72 72 / 9 Try This 27 / 54 48 / 12 And Even More… xy / 3y x / 5xy 4cd / 2c Try This… 5xy / 3x m / 8 mn 14ab / 7b