Algebra 1 – 2.5 Matching slides

1.The order in which you add numbers in a sum doesn’t matter. 2.If you add more than 2 numbers, the order in which you group them doesn’t matter. 3.When you add 0 to any number, the result is the number itself. 4.When you add any number to its opposite, the result is 0. When the sum of two numbers is 0, each number is the opposite of the other. A.For any three numbers, a, b, and c, a+(b+c)=(a+b)+c. B.For any number a, a+0=a. C.For any two numbers a and b, a+(-a)=0 and if a+b=0, b=-a. D.For any two numbers a and b, a+b=b+a.

1.The order in which you multiply two numbers doesn’t matter. 2.If you multiply more than 2 numbers, the order in which you group them doesn’t matter. 3.Multiplying a number by a sum is the same as multiplying the number by each term in the sum and then adding the result. 4.When you multiply 1 by any number, the result is that number. 5.When you multiply a nonzero number to its reciprocal, the result is 1. When the product of two numbers is 1, each number is the reciprocal of the other. A.For any three numbers, a, b, and c, a(bc)=(ab)c. B.For any number a, a·1=a. C.For any two numbers a and b, a· (1/a)=0 and if a·b=1, b=1/a. D.For any three numbers a, b, and c, a(b+c)=ab+ac. E.For any two numbers a and b, a·b=b·a.

They all have names, of course. Commutative Property of Addition Associative Property of Addition Commutative Property of Multiplication Associative Property of Multiplication Additive Identity Additive Inverse Multiplicative Identity Multiplicative Inverse Distributive Property

Rewrite these with letters. 1.Dividing is the same as multiplying by the reciprocal. 2.Subtracting is the same as adding the opposite. 3.If you have a product of two numbers, and you find the products of the opposites of the numbers, you get the same result. 4.If you multiply two numbers together and the result is 1, then the numbers are reciprocals.

Zero Product Property If ab=0, then a=0 or b=0.

Ok so prove it. Assume ab=0. If a=0, you can stop doing the proof. –WHY? Assume a isn’t zero. Then it has a reciprocal, 1/a. –WHY? Multiply both sides of the equation by 1/a. –What happens? How does this prove the property?

Making up new arithmetic. The binary operation ♥ is defined by the following rule: x ♥y = 3x + y Explain how to find 416 ♥18. Evaluate it. Is this property commutative? Is either 1 or 0 the ♥-identity?

REFLECTIONS To build a rectangular dog pen, Cheng uses a wall of his house for one of the long sides. Let L equal the length of the longer side. Let W be the length of the shorter. Write an expression for the amount of fencing Cheng needs to buy. How much should he buy if he wants a length of 8 ft and a width of 12 feet? How much should he buy if he wants a length of 5 ft and a width of 20 feet? Suppose the length is 9 ft more than the width. Use only ONE variable to write an expression.

Evaluate 4(2x+3) + 2(x+1) – 7 for… x= ½ Simplify the expression. When you evaluate the simplified expression for x=1 and x=6, do you get the same result this time?

Why are variables useful?

How can you invent a number trick that always gives you the same ending number?