Generate Equivalent Expressions

​Generate Equivalent Expressions

Chapter 2 Intervention Lesson 1​

ab = ba

a (b) = b (a)​

​ab (c) = a (bc)

​Distributive Property of Multiplication

a + b = b + a​

​a + b + c = c + b + a

​(a + b) + c = a + (b + c)

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​Distributive Property of Addition

​Any Order, Any Grouping

When just adding, or just multiplying, it can be in any order & any grouping.​

​Any Order, Any Grouping

​With Addition...

​#1. Rewrite 5𝑥 + 3𝑥 and 5𝑥 − 3𝑥 by combining like terms.

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Write the original expressions and expand each term using addition. What are the new expressions equivalent to?

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Make sure to write down your notes & problem solving in your notebook.

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$5x+3x\$  

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$5x-3x\$  

​Any Order, Any Grouping

​with Addition...

#2. Find the sum of 2𝑥 + 1 and 5𝑥.

Remember: When combining like terms, "and" = "add".​

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$2x+1\ and\ 5x$  

​Any Order, Any Grouping

​With Addition...

​#3. Find the sum of -3a + 2 and 5a - 3.

Remember: When combining like terms, "and" = "add".​

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$-3a+2\ and\ 5a-3$  

​Any Order, Any Grouping

​With Multiplication...

Find the product of 2x and 3. ​

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Remember: "product" is the result of multiplying two numbers.​

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$Find\ the\ product\ of\ 2x\ and\ 3.$  

​Any Order, Any Grouping

​Mixed Practice with Addition & Subtraction

Remember the Following:

• Parentheses imply ​multiplication.

• The floating dot is the algebraiac symbol for multiplication. ​

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Good Luck!

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$3\left(2x\right)$  

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$4y\left(5\right)$  

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$4\cdot2\cdot z$  

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$3\left(2x\right)+4y\left(5\right)$  

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$3\left(2x\right)+4y\left(5\right)+4\cdot2\cdot z$  

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Alexander says that 3x+4y is equivalent to (3)(4)+xy.

Is he correct? Why or why not?

​Combine Like Terms and Evaluate Expressions

​For each problem, follow these steps:

1. Write Equivalent Expressions by Combining Like Terms.

2. ​Evaluate the Expressions with the following variable values:

​ a = 2 b = 5 c = -3

Make sure you're writing all of this down in your math notebook!​

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$Simplify\ \ \ 3a+5a$  

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$Evaluate\ the\ \exp ression\ 3a+5a\ if\ a=2$  

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$Simplify\ the\ \exp ressions\ 3a+6+5a$  

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$Evaluate\ the\ \exp ression\ 3a+6+5a\ if\ a=2$  

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$Simplify\ the\ \exp ression\ 3a+6+5a-2$  

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$Evaluate\ the\ \exp ression\ 3a+6+5a-2\ if\ a=2$  

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$Simplify\ the\ \exp ression\ 8b+8-4b-3$  

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$Evaluate\ the\ \exp ression\ 8b+8-4b-3\ if\ b=5$  

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$Simplify\ the\ \exp ression\ 5c-4c+c-3c$  

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$Evaluate\ the\ \exp ression\ 5c-4c+c-3c\ if\ c=-3$  

​Simplify & Evaluate Expressions

​Example: 3(6a) ; for a = 3

​3(6⋅a)

​3(6⋅3)

3(18)

3⋅18

54​

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​Get Ready to Practice!

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$Simplify\ then\ Evaluate:\ 5d\left(4\right)\ ;\ for\ d=-2$  

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$Simplify\ then\ Evaluate:\ \left(5r\right)\left(-2\right)\ ;\ for\ r=-3$  

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$Simplify\ then\ evaluate:\ 3b\left(8\right)+\left(-2\right)\left(7c\right)\ ;\ for\ b=2,\ c=3$  

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$Simplify\ then\ evaluate:\ -4\left(3s\right)+2\left(-t\right)\ ;\ for\ s=\frac{1}{2};\ t=-3$  

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$Simplify\ then\ Evaluate:\ 9\left(4p\right)-2\left(3q\right)+p\ ;\ for\ p=-1,\ q=4$  

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$Simplify\ then\ evaluate:\ 7\left(4g\right)+3\left(5h\right)+2\left(-3g\right)\ ;\ for\ g=\frac{1}{2},\ h=\frac{1}{3}$