# Generating Equivalent Expressions Worksheets

Understanding how to manipulate expressions and make them bend to your will is a skill that will take a great deal of time to master. One of the first steps in this process is to be able to simplify and reduce values to be repurpose or repackage them in a manner that makes them simple to work with. When we start to do this, it is helpful to think back to what we know about the property of operations. When we have a solid handle on those, it becomes clear. On this topic students will begin to generate their own expressions from a starting expression. This is a great skill because it leads us it more advanced algebra skills. This is a very important unit that you want to make sure that you have a good handle on.

### Aligned Standard: Grade 6 Expressions and Equations - 6.EE.A.3

- Simplifying Expressions Step-by-step Lesson- Expressions that include exponents and compounded variables.
- Guided Lesson - Rewriting expressions and using the distributive property to create equal expressions.
- Guided Lesson Explanation - I might have not provided enough steps. I just never really see have students have trouble with these types of problems.
- Practice Worksheet - The entire sheet is dedicated to creating equivalent expressions.
- Visual Expressions Five Pack - I haven't seen questions like these before. So, I made them.
- Matching Worksheet - Match the expression that are equal. A really nice way to practice.

- Answer Keys - These are for all the unlocked materials above.

### Homework Sheets

You will find that each sheet is progressively easier, 1 being the hardest in the set.

- Homework 1 - Multiply a sum by multiplying each addend separately.
- Homework 2 - Find a common number or variable that you can use. We are looking for an integer that can easily be divided.
- Homework 3 - Simply (a + a + a)/ 4

### Practice Worksheets

I tried to make this section slightly more difficult than the basic old problems I see everywhere.

- Practice 1 - Choose and apply the distributive property to the expression to produce an equivalent expression: 2(4 + x)
- Practice 2 - Rewrite the expression: (5a + 50b)
- Practice 3 - Choose and apply the distributive property to the expression to produce an equivalent expression: 5(6 + x)

### Math Skill Quizzes

You should find as nice mix of difficulty here. 2 easy problems, 2 hard problems and the rest somewhere in between.

- Quiz 1 - Simplify the expression. 5(5
^{2}+ 5x) - Quiz 2 - Rewrite the expression: (8a + 40 b)
- Quiz 3 - Apply the properties of operations to produce an equivalent expression: (e + e + e) / 4

### What Does Simplifying an Expression Mean?

When we are dealing with algebraic expressions, it is possible that you get expressions that very lengthy. Lengthy expressions are difficult to even understand. However, with the help of simplification, you can make the expression most compact; without changing its original value. This includes taking common terms or adding or subtracting similar values in order to get a simplified form. Below we will discuss some steps that can be considered when you want to simplify an expression.

**Similar Terms:** Similar or like terms can have same powers on same variables, even if their coefficients are different. This is the only difference. 3x, 2x, 5x are like terms.

**Combining Similar Terms:** Combining those similar terms is the next step towards getting a simplified expression. (3x) ^{2} + (5x) ^{2} + 5x +3 will get a simplified answer of (8x)^{2} + 5x + 3.

**Parentheses:** Parentheses are multiplied beforehand in order to get similar terms; which can then be combined.

### How to Use the Distributive Property to Generate Equivalent Expressions

If we remember back to our properties of math operations, we will be reminded of how a factor can be distributed over the course of a sum or difference problem. This distributive property of multiplication can be used to help us simply or reduce expression and help us work with simpler numbers for quicker calculations. When properly stated this property tells us that the product of a difference or sum is equal to the difference or sum of the products. For example, if we are given this expression: 5(3 + 4), it would have the same outcome or solution as breaking those operations up into: 5(3) + 5(4). While we have been using this property of multiplication to help make our math easier to work with, there is also another great use for this. In certain situations, we can use the distributive property to generate expressions that have the same end value.

We can use this in simple cases as we have already demonstrated, but where this truly shines is when working with expressions that have multiple unknown variables. Take a look the expression below and see if you can follow the steps through exploring the distributive property:

3(6x + 4y)

Step 1) Applying Distributive Property.

3(6x + 4y) = 18x + 12y

Step 2) Reduce (6 is GCF)

18x + 12y = 3x + 2y

See how you can take something that is rather complex and looks like you might need to break out the calculator but using this property of math it settles as something rather plain.