Equivalent Expressions Objective To create identify equivalent expressions

Equivalent Expressions Objective: To create & identify equivalent expressions by simplifying.

Standards: MCC 6. EE. 2 b, MCC 6. EE. 3 and MCC 6. EE. 4 (Identify parts of an expression, apply math properties to generate equivalent expressions, and identify when two expressions are equivalent) Essential question: How can I tell when two expressions are equivalent?

Equivalent Expressions In the expression 7 x + 9 y + 15, 7 x, 9 y, and 15 are called terms. See if you can create a definition for the word term given the examples on this page. 7 x term + 5 term – 3 y 2 + y + x 3 term

Let’s look at some vocabulary A term can be a number, a variable, or the product of numbers and variables. How close was your definition to the actual definition? 2 c 3 c 2 a 2 d -2 5 b 35 d

Let’s look at some vocabulary An expression is a collection of terms and operations. Terms in an expression are separated by + and –. a 2 + 5 3 3 c + 2 4 c 2 c 7 2 c + 5 c 2 2 5 d + 2 d 2(a + 15)

Let’s look at some vocabulary A coefficient is the number multiplying the variable. A variable standing alone, like y, is said to have a coefficient of 1. So y = 1 y k 3 c 5 c 12 a 4 2 c 15 q 2 d

Let’s look at some vocabulary Like terms are terms with same variable raised to the same power. Constants, like 5, ½, and 3. 2, are also like terms. k + 2 k 3 c+2 c 15 a – 5 a 12 + 3 4 2 c + 4 c 2 2 d + 2 d

You try… Work with a partner to simplify each expression. In other words, combine like terms!!!

Let’s look at some vocabulary What would be the definition of unlike terms be now that you know what like terms are? Like Terms 3 x and 2 x w and 3 w 5 and 1. 8 Unlike Terms 5 x 2 and 2 x 6 a and 6 b 3. 2 and n The exponents are different. The variables are different Only one term contains a variable

Kicking things up a notch! • A number and a variable are unlike terms. 7 and x are unlike terms. • Terms that use different variables are unlike terms. 3 z, b and 2 x are unlike terms. • Terms that use the same variable but different powers are unlike terms. 5 x, x 2, and 2 x 3

Jack put the fruit shown above in his grocery cart. The cashier needs all of the same fruit together in piles. Combine the fruit correctly and count the total for each fruit. 2 apples 3 bananas 4 strawberries

x 2 x 1 2 x x 2 3 Combining like terms in algebra is really the same idea, but instead of combining the same fruit, we combine like (same) terms. 2 x 2 3 x 4

Identifying Like Terms Identify like terms in the list. Look for like variables with like powers. 3 t 5 w 2 7 t 9 v 4 w 2 8 v Identify like terms in the list. 2 x 4 y 3 8 x 5 z 5 y 3 8 z

When like terms are added or subtracted…. …the coefficient changes 6 t – 4 t An expression is simplified when… ü There are no ( ) or other grouping symbols. ü When there are NO like terms left to be combined.

Let’s Try More Problems Together 45 x – 37 y + 87 An expression is simplified when… ü There are no ( ) or other grouping symbols. ü When there are NO like terms left to be combined.

Let’s Try More Problems Together 5 y + 3 y An expression is simplified when… ü There are no ( ) or other grouping symbols. ü When there are NO like terms left to be combined.

Let’s Try More Problems Together 3 a 2 + 5 b + 11 b 2 – 4 b + 2 a 2 – 6 An expression is simplified when… ü There are no ( ) or other grouping symbols. ü When there are NO like terms left to be combined.

Let’s Try More Problems Together Write an expression for the perimeter of the triangle. Then simplify the expression. An expression is simplified when… 2 x + 1 x ü There are no ( ) or other grouping symbols. ü When there are NO like terms left to be combined.