# Evaluating Expressions Worksheet, Examples, and Definition

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

### Key Points about Evaluating Expressions

- Evaluating expressions involves finding the value of an expression by substituting the given values for the variables and simplifying using the order of operations.
- The order of operations is a set of rules that dictate the order in which operations should be performed.
- Evaluating expressions is a fundamental skill in algebra and is used to solve equations, graph functions, and solve real-world problems.

## How to Evaluate Expressions using Arithmetic

Evaluating expressions is an essential skill in algebra and is used to simplify and solve mathematical problems. An expression is a combination of numbers, variables, and operations that can be evaluated to obtain a numerical result. Evaluating an expression involves substituting the given values for the variables and simplifying the expression using the order of operations.

The meaning of evaluating an expression is to find its value by performing the required operations in the correct order. This process is also known as simplifying an expression. Evaluating expressions is a fundamental skill in algebra and is used to solve equations, graph functions, and solve real-world problems. To evaluate an expression, one must follow the order of operations, which is a set of rules that dictate the order in which operations should be performed.

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

**Related Topics: **One Step Equations, Equivalent Expressions, Combining Like Terms, Distributive Property with Variables**Return To: **Home, 6th Grade

## Evaluate the Expression Meaning

When working with algebraic expressions, it is important to understand what it means to evaluate an expression. In simple terms, to evaluate an expression means to find the value of the expression when the variable is replaced by a given number.

An algebraic expression is made up of variables, constants, and mathematical operations. The variables can take on different values, and the expression can be evaluated for each value of the variable. For example, the expression `3x + 2`

can be evaluated for `x = 2`

by substituting `2`

for `x`

to get `3(2) + 2 = 8`

.

Evaluating an expression involves substituting the given value for the variable in the expression and then simplifying the expression using the order of operations. The order of operations is a set of rules that dictate the order in which mathematical operations should be performed. The order of operations is usually remembered using the acronym PEMDAS, which stands for Parentheses, Exponents, Multiplication and Division (from left to right), and Addition and Subtraction (from left to right).

It is important to note that the value of an expression may vary depending on the value of the variable. For example, the expression `x^2 - 4`

has different values for `x = 2`

and `x = -2`

. When `x = 2`

, the expression evaluates to `0`

, while when `x = -2`

, the expression evaluates to `0`

as well.

In summary, to evaluate an expression means to find the value of the expression when the variable is replaced by a given number. This involves substituting the given value for the variable in the expression and then simplifying the expression using the order of operations.

## Evaluating Expressions Definition

Evaluating expressions is a fundamental concept in algebra that involves finding the value of an expression when given the value of its variables. In other words, it is the process of substituting the given values of variables in an expression and simplifying it to obtain a numerical result.

Expressions can be simple or complex, involving one or more variables, constants, and mathematical operations such as addition, subtraction, multiplication, and division. Evaluating expressions is an essential skill that is used in solving algebraic equations, simplifying expressions, and solving real-world problems.

To evaluate an expression, one needs to follow the order of operations, also known as the PEMDAS rule, which stands for Parentheses, Exponents, Multiplication and Division (from left to right), and Addition and Subtraction (from left to right). It is crucial to follow this rule to avoid errors and obtain accurate results.

For example, consider the expression 3x + 2y – 5, where x = 2 and y = 4. To evaluate this expression, one needs to substitute the values of x and y in the expression and simplify it according to the order of operations.

- First, substitute x = 2 and y = 4 in the expression to obtain 3(2) + 2(4) – 5.
- Next, perform the multiplication and addition/subtraction operations according to the order of operations to obtain the final result.

Thus, 3x + 2y – 5 = 6 + 8 – 5 = 9.

In summary, evaluating expressions is an essential skill in algebra that involves substituting the given values of variables in an expression and simplifying it according to the order of operations to obtain a numerical result.

## How to Evaluate Expressions with Variables

Evaluating expressions with variables is an important skill in algebra. It involves substituting values for variables in the expression and simplifying the resulting expression. Here are the steps to evaluate expressions with variables:

- Identify the variables in the expression: Before evaluating the expression, it’s important to know which variables are involved. Variables are represented by letters or symbols and can take on different values.
- Substitute the values for the variables: Once you have identified the variables, you can substitute the given values for them. For example, if the expression is 2x + 3y and x = 5 and y = 2, you would substitute 5 for x and 2 for y to get 2(5) + 3(2).
- Simplify the expression: After substituting the values for the variables, simplify the expression by performing the operations in the correct order. Remember to use the order of operations (PEMDAS) to simplify the expression.
- Check your answer: Always check your answer to make sure it makes sense and is correct. You can do this by substituting the given values back into the original expression and verifying that the answer is the same.

Here is an example of evaluating an expression with variables:

Evaluate the expression 3x – 2y when x = 4 and y = 2.

- Identify the variables: The variables in this expression are x and y.
- Substitute the values: Substitute 4 for x and 2 for y to get 3(4) – 2(2).
- Simplify the expression: Following the order of operations, first multiply 3 and 4 to get 12, then multiply 2 and 2 to get 4, and finally subtract 4 from 12 to get 8.
- Check your answer: Substitute x = 4 and y = 2 back into the original expression to verify that the answer is correct: 3(4) – 2(2) = 12 – 4 = 8.

By following these steps, anyone can evaluate expressions with variables accurately and confidently.

## How to Evaluate Expressions with Exponents

Evaluating expressions with exponents is a fundamental skill in mathematics. It involves simplifying expressions with variables raised to a power. Here are the steps to evaluate expressions with exponents:

- Identify the base and the exponent of the term. The base is the number or variable that is being raised to a power, and the exponent is the number that indicates how many times the base is being multiplied by itself.
- Substitute the value of the variable, if given, into the expression. If the expression contains more than one variable, substitute the value of each variable one at a time.
- Simplify the expression by performing the indicated operations. If there are multiple terms with exponents, simplify each term separately before combining them.

For example, consider the expression `3x^2 + 2y^3 - 4z^2`

. To evaluate this expression when `x=2`

, `y=3`

, and `z=1`

, follow these steps:

- Identify the base and exponent of each term. The base of the first term is
`x`

, and the exponent is`2`

. The base of the second term is`y`

, and the exponent is`3`

. The base of the third term is`z`

, and the exponent is`2`

. - Substitute the values of
`x`

,`y`

, and`z`

into the expression:`3(2)^2 + 2(3)^3 - 4(1)^2`

- Simplify each term separately:
`3(4) + 2(27) - 4(1)`

- Combine like terms:
`12 + 54 - 4 = 62`

Therefore, the value of the expression `3x^2 + 2y^3 - 4z^2`

when `x=2`

, `y=3`

, and `z=1`

is `62`

.

It is important to understand the order of operations when evaluating expressions with exponents. The order of operations is Parentheses, Exponents, Multiplication and Division (from left to right), and Addition and Subtraction (from left to right). Use parentheses to group terms that should be evaluated together before raising them to a power.

In summary, evaluating expressions with exponents involves identifying the base and exponent of each term, substituting the values of the variables into the expression, simplifying each term separately, and combining like terms. Remember to use the order of operations and parentheses when necessary.

## 4 Quick Steps for Evaluating Expressions Examples

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

### Concept of Evaluating Expressions

Evaluating expressions involves finding the value of an expression by replacing variables with given values and simplifying the resulting expression. This process is useful in solving equations, simplifying algebraic expressions, and solving real-life problems.

For example, consider the expression 2x + 3. To evaluate this expression for x = 4, substitute 4 for x to get 2(4) + 3 = 8 + 3 = 11. Therefore, the value of the expression 2x + 3 for x = 4 is 11.

### Order of Operations

The order of operations is a set of rules that dictate the order in which operations should be performed in an expression. The order of operations is as follows:

- Perform any calculations inside parentheses first.
- Exponents (ie. powers and square roots, etc.)
- Multiplication and Division (from left to right)
- Addition and Subtraction (from left to right)

For example, consider the expression 2 + 3 * 4. According to the order of operations, multiplication should be performed before addition. Therefore, 3 * 4 = 12, and 2 + 12 = 14. Therefore, the value of the expression 2 + 3 * 4 is 14.

Another example is the expression (2 + 3) * 4. According to the order of operations, the addition inside the parentheses should be performed first. Therefore, 2 + 3 = 5, and (5) * 4 = 20. Therefore, the value of the expression (2 + 3) * 4 is 20.

In summary, evaluating expressions involves replacing variables with given values and simplifying the resulting expression. The order of operations is a set of rules that dictate the order in which operations should be performed in an expression. By following these rules, one can accurately evaluate expressions and solve complex problems.

## How to Evaluate Expressions FAQ

### What is the process for evaluating algebraic expressions?

To evaluate an algebraic expression, you need to substitute the given values for the variables and simplify the expression using the correct order of operations.

### How do you evaluate expressions with variables?

To evaluate expressions with variables, you need to substitute the given values for the variables and simplify the expression using the correct order of operations.

### What are some examples of evaluating expressions?

Here are some examples of evaluating expressions:

- Evaluate 3x + 2 when x = 4.

Substitute x = 4 into the expression:

3(4) + 2 = 14

- Evaluate 2y – 5 when y = -3.

Substitute y = -3 into the expression:

2(-3) – 5 = -11

### What is the correct order of operations for evaluating expressions?

The correct order of operations for evaluating expressions is:

- Parentheses
- Exponents
- Multiplication and Division (from left to right)
- Addition and Subtraction (from left to right)

### How do you evaluate expressions with fractions and decimals?

To evaluate expressions with fractions and decimals, you need to follow the same order of operations as with whole numbers. You can also convert fractions to decimals or decimals to fractions to make the calculations easier.

### What is the meaning of evaluating an expression?

Evaluating an expression means finding the numerical value of the expression by substituting the given values for the variables and simplifying the expression using the correct order of operations.

### What is the correct sequence of evaluating expressions?

The correct sequence of evaluating expressions is to first substitute the values for the variables and then simplify the expression using the correct order of operations.

## How to Evaluate Expressions Worksheet Video Explanation

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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