# A Few Tips for finding Equivalent Expressions

Get the free Equivalent Expressions worksheet and other resources for teaching & understanding how to find Equivalent Expressions

**Here’s how to find Equivalent Expressions**

**Common Core Standard:**6.EE.3

**Related Topics:**One Step Equations, Evaluating Expressions, Combining Like Terms, Distributive Property with Variables

**The answer to what are Equivalent Expressions?**

Exactly what’s an equivalent expression anyway? Equivalent Expressions will be math statements that are equivalent to one another despite the fact that they may appear to be different from each other. For instance, you can substitute a similar value in for x into both statements and then simplify to see if they are actually the same value. Another way to find Equivalent Expressions is to use the Distributive Property. When using the Distributive Property you will distribute the number on the outside of the parenthesis to everything on the inside of the parenthesis using multiplication. Once simplified, the expression will be equivalent to the original expression, meaning that they are Equivalent Expressions.

**4 Easy Steps to Evaluate Equivalent Expression Examples**

- Equivalent Expressions Examples 6th grade are two expressions that look different but are actually the same.
- You must use the Distributive Property to see if the expressions are equivalent.
- You take the number on the outside of the parenthesis and you multiply it to everything on the inside of the parenthesis.
- You then simplify by combining like terms.

**Equivalent Expressions Practice Problems Quiz**

**Watch the video explanation of our Equivalent Expressions Worksheet**

Watch our free video on how to find Equivalent Expressions. This video shows how to solve problems that are on our free Equivalent Equations worksheet that you can get by submitting your email above.

**Watch the free Equivalent Expressions video on YouTube here: How to find Equivalent Expressions Video**

**Video Transcript:**

This video is about equivalent expressions. You can get the equivalent expressions worksheet 6th grade used in this video for free by clicking on the link in the description below. Equivalent expressions in math are mathematical expressions that represent the same value but may look different. Just to give you a quick example of two expressions that could represent the same value, if I were to write 5 plus 2 is equal to 4 plus 3. I know that these expressions are equivalent because 5 plus 2 is seven and four plus three is also seven even though I have four different numbers five plus two and four plus three. I know that they’re equivalent because if I were to simplify them I would end up with equal results in this case seven equals seven.

In terms of mathematical expressions like this one where we have three times the quantity nine plus five. In order to determine the expression that is equivalent to that you have to use what’s called the distributive property. The distributive property states that you take this number out in front, in this case 3, and you multiply it times the 9 and times the 5. I’m going to take this 3 and I’m going to multiply it times the first number inside of the parentheses, in this case which is 9. Then I’m going to add that 2 3 times the second number inside of the parentheses which in this case is 5. We’re going to do times 5. and then we’re going to simplify this 3 times 9 is 27 plus 3 times 5 which is 15. Now I know that 3 times the quantity 9 plus 5 is equal to 27 plus 15 because I distributed this 3 times 9 and then added it 3 times 5. Let’s do a couple practice problems on our equivalent expressions worksheet.

The first problem on our practice worksheet for showing you what are equivalent expressions gives us two times the quantity four plus one. Now we know according to the distributive property we have to take this term in front of the parentheses and distribute it to everything inside of the parentheses. We know that we’re going to take 2 and multiply it times the second term inside of the parentheses which in this case is 4 and that’s going to get added to 2 again times the second quantity in parentheses which in this case is 1. Then we’re going to simplify 2 times 4 and that’s 8 plus two times one which is two. Now I know two times the quantity four plus one is equivalent to eight plus two. This is an example of an equivalent expression.

Number three on showing you how to find equivalent expressions gives us ten times the quantity two plus eight. I’m going to take this ten which is outside of the parentheses and distribute it to everything inside of the parentheses. I’m going to say 10 times the first term inside the parentheses which is this 2. 10 times 2 plus 10 times the second term inside of the parentheses which in this case is 8 and then when I simplify this 10 times 2 that’s 20 plus 10 times 8 which is 80. I know that 10 times 2 plus 8 is equivalent to 20 plus 80 because they represent the same value or the same amount.

The last problem that we’re going to complete on our equivalent expressions worksheet is number seven. This problem gives us four times the quantity x plus one. I know that according to the distributive property I have to take this four and distribute it to everything inside of the parentheses. The first part is we’re going to take 4 times our first term which in this case is x 4 times x plus 4 times our second term which in this case is 1. 4 times x plus 4 times 1 now and then we’re going to simplify 4 times x well that’s 4x plus 4 times 1 which is 4. Now I know that 4 times the quantity x plus one is equal to four x plus four. Hopefully this video helped you in understanding what are equivalent expressions.

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