A Quick Explanation of How to Evaluate Expressions

Get the free Evaluating Expressions Worksheet and other resources for teaching & understanding how to Evaluate Expressions

How to Evaluate the Expression using Arithmetic

To Evaluate Expressions, you have to substitute a number in for a variable. A variable is a letter that represents an unknown number, typically this letter is x. When Evaluating Expressions you will substitute in a number for the variable and then you will simplify the expression using either addition, subtraction, multiplication, or division. Sometimes you may have to use two or three of the rules to simplify the expression, if that is the case you will follow order to operations to solve. That means you do multiplication and division first and then addition and subtraction.
Common Core Standard: 6.EE.1
Return To: Home, 6th Grade


How to Evaluate Expressions

A Guide to Evaluating Expressions Example Problems

Read the guide below to learn how to evaluate an expression.

To Evaluate Expressions, you need to substitute a number in for a variable. A variable is a letter that is an unknown amount, regularly the letter that is used is x. When Evaluating Expressions you will substitute in a number for the variable and after that you will rearrange the expression by using either multiplication, division, addition, subtraction. In some cases you may need to utilize a few of the processes to rearrange the expression. In order to do this that means you will use Order of Operations to simplify.


How to Evaluate Expressions Solution

4 Quick Steps to answer Evaluate Expressions Practice Problems

  1. Use substitution to substitute the number value in for the variable.
  2. Once the number value has been substituted in you must simplify the expression.
  3. When simplifying, you should use addition, subtraction, multiplication, and division.
  4. If there are two or more steps you must follow Order of Operations.


Watch our video explanation of How to Evaluate Expressions Worksheet

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

Watch the free Evaluating Expressions video on YouTube here: How to Evaluate Expressions Video

Video Transcript:

This video is about how to evaluate expressions. You can get the evaluate the expression worksheet used in this video for free by clicking on the link in the description below.

In this video we’re going to talk about evaluating expressions with substitution. Now substitution is just when you take the variable and you substitute or you plug it in to the equation for what value is given to you. After you substitute the value in for the variable you will follow the order of operations to simplify the expression.

So how do you evaluate an expression anyway? In the case of this example expression that is 15 minus x and we know that x equals five. We’re going to take the value that represents our variable, which in this case, is five and we’re going to substitute it in for the variable. What we’re going to do is we’re going to take 5 and substitute it in for x by replacing x with the 5. After we’ve substituted 5 in, we will then simplify using order of operations. In the case of this one we have 15 minus x. This x is going to change to a 5 because 5 represents our variable. We know that x is equal to 5 so we’re going to swap out x for 5. Once we’ve done that, we can just simplify into 15 minus 5 which is 10. Now our expression is evaluated using substitution and we know that the solution is 10.

In this example we have a substitution symbol but you may be given addition subtraction multiplication or division in order to simplify using the order of operations let’s do a couple practice problems from our evaluating expressions worksheet

The first problem on our evaluating expressions worksheet gives us x plus 1 where x is equal to 5. We know that if x is equal to 5, we can replace x with 5 by using substitution. I can take this 5 and substitute it into the expression where x used to be. X plus 1 is going to change into 5 plus 1 because now our x has been substituted with a 5 and now it’s a 5. All we do after this point is use order of operations to simplify 5 plus 1 is equal to 6. After we evaluate this expression our answer is six.

Number two on our 6th grade evaluating expressions worksheet gives us three x and tells us that x is equal to seven. We’re going to take this seven and we’re going to substitute it in for x. Now 3x is like saying 3 times x, even though it’s not written there’s a multiplication symbol there. In this case we’re going to say 3 times x but x is now 7. We’re going to say three times seven so now the x is gone and it’s been replaced by seven and three times seven is equal to twenty-one. And that’s our answer for this expression.

The third problem on our evaluating expressions worksheet gives us 10 divided by x. This time x is equal to 2. We’re going to take this 2 and substitute it in for x. Our expression is now 10 divided by x but in this case, x is 2 so now it’s 10 divided by 2 and then 10 divided by 2 is equal to 5. Our expression is evaluated and our solution is 5.

The last problem we’re going to complete on our evaluating expressions worksheet is number five. This problem gives us the expression x plus x. In this case x is equal to three and we have two x’s in our expression. This means we’re going to take this 3 and substitute it in to both x’s in our expression. We know x is equal to 3 there are two x’s or two variables that means the 3 has to be substituted into both. Now it’s going to be instead of x plus x it will be 3 plus 3 which is equal to after you simplify 6. After our expression has been evaluated our solution is 6. You can try all the practice problems by downloading the free evaluating expressions worksheets above.


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Evaluating Expressions


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