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Evaluate the expression

Evaluate the expression

Here you will learn how to evaluate the expression given a value for the variable.

Students will first learn how to evaluate the expression as part of expressions and equations in 6th grade.

Every week, we teach lessons on evaluating the expression to students in schools and districts across the US as part of our online one-on-one math tutoring programs. On this page we’ve broken down everything we’ve learnt about teaching this topic effectively.

What does it mean to evaluate the expression?

To evaluate the expression means to substitute the variable(s) of a polynomial with given value(s).

For example,

If x=6, what is the value of 6x+1?

Substitute 6 for x and follow the order of operations:

\begin{aligned} & 6(6)+1 \\\\ & =36+1 \\\\ & =37 \end{aligned}

The same process can be used when there is more than one variable.

For example,

If c=2 and t=4, what is the value of 3 \, (c-1)+t^2?

Substitute 2 for c and 4 for t , and follow the order of operations:

\begin{aligned} & 3(2-1)+4^2 \\\\ & =3(1)+4^2 \\\\ & =3(1)+16 \\\\ & =3+16 \\\\ & =19 \end{aligned}

What does it mean to evaluate the expression?

What does it mean to evaluate the expression?

Common Core State Standards

How does this relate to 6th grade math?

  • Grade 6 – Expressions and Equations (6.EE.B.5)
    Understand solving an equation or inequality as a process of answering a question: which values from a specified set, if any, make the equation or inequality true? Use substitution to determine whether a given number in a specified set makes an equation or inequality true.

How to evaluate the expression

In order to evaluate the expression:

  1. Substitute each variable with its given value.
  2. Evaluate using the order of operations.

[FREE] Evaluate the Expression Worksheet (Grade 6 to 8)

[FREE] Evaluate the Expression Worksheet (Grade 6 to 8)

[FREE] Evaluate the Expression Worksheet (Grade 6 to 8)

Use this worksheet to check your grade 6 – 8 students’ understanding of evaluating expressions. 15 questions with answers to identify areas of strength and support!

DOWNLOAD FREE
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[FREE] Evaluate the Expression Worksheet (Grade 6 to 8)

[FREE] Evaluate the Expression Worksheet (Grade 6 to 8)

[FREE] Evaluate the Expression Worksheet (Grade 6 to 8)

Use this worksheet to check your grade 6 – 8 students’ understanding of evaluating expressions. 15 questions with answers to identify areas of strength and support!

DOWNLOAD FREE

Evaluate the expression examples

Example 1: one step, one variable

Evaluate 4m when m=35.

  1. Substitute each variable with its given value.

Remember, numbers and letters written next to each other are being multiplied:

4 \times 35

2Evaluate using the order of operations.

There is only one step, multiply.

4 \times 35=140

Example 2: two steps, one variable

Evaluate 3 \, (h+22) when h=9.

Substitute each variable with its given value.

Evaluate using the order of operations.

Example 3: two steps, one variable, and a fraction

Evaluate 50-\cfrac{m}{2} when m=20.

Substitute each variable with its given value.

Evaluate using the order of operations.

Example 4: two steps, two variables

Evaluate 11x-2y , when x=5 and y=6.

Substitute each variable with its given value.

Evaluate using the order of operations.

Example 5: three steps, two variables, and a mixed number

Evaluate 5(3+p)-r , when p=11 and r=22 \, \cfrac{1}{3} \, .

Substitute each variable with its given value.

Evaluate using the order of operations.

Example 6: three steps, two variables, and an exponent

Evaluate a^3(n-7) , when a=3 and n=9.

Substitute each variable with its given value.

Evaluate using the order of operations.

Teaching tips for evaluating the expression

  • A great way to build the conceptual knowledge needed for evaluating algebraic expressions is with hands-on representations, like algebra tiles or other manipulatives. It is also a good idea to start with whole number coefficients and constants, as they are easier for students to make sense of and typically work better with manipulatives.

  • While “finding the answer” is an important part of this skill, it should not be the only focus. At this stage in their development, students are still building foundational ideas about algebraic expressions, so it is important to draw attention to all parts of the process and help them make mathematical connections. Give students time to find and explore different numbers in the solution set, and encourage them to look for patterns between an expression and its solution set.

  • Use expressions that come from real life scenarios when possible. This can help students think more deeply about how and why a solution set fits a given algebraic expression. For example, if the expression 8h is created to represent how many hotdogs there are based on h, the number of packets, students use the scenario to make connections between the expression and its solution set.

Easy mistakes to make

  • Not following order of operations (pemdas)
    The order of operations should always be used to evaluate the expression. For any given expression, this means solving within the parentheses, then the exponents, then multiplying or dividing from left to right, and finally adding or subtracting left to right. Not following this order will give the incorrect answer.

    For example,
    Evaluate x -3y when x=10 and y=2.

    Evaluate the expression image 1Evaluate the expression image 2

  • Confusing the values of the variables when there is more than one
    Always pay attention to which value is assigned to each variable. Mixing them up will result in a different answer.

    For example,
    Evaluate 5x+y when x=3 and y=4.

    Evaluate the expression image 3Evaluate the expression image 4

  • Confusing the meaning of a number next to a parenthesis
    Remember in an expression when there is a number next to parenthesis, the operation is multiplication.

    For example,
    If 4 \, (k+10), evaluate the expression when k=1.

    \begin{aligned} & 4(1+10) \\ & =4(11) \\ & =44 \end{aligned}

Practice evaluating the expression questions

1. Evaluate 8x-10 when x=3.

73
GCSE Quiz False

1
GCSE Quiz False

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14
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Substitute the variable with its given value.

 

8 \times 3-10

 

Evaluate using the order of operations.

 

\begin{aligned} & 8 \times 3-10 \\\\ & =24-10 \\\\ & =14 \end{aligned}

2. Evaluate \, \cfrac{x}{5} \, when x=23.

115
GCSE Quiz False

4 \, \cfrac{3}{5}
GCSE Quiz True

18
GCSE Quiz False

28
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Substitute the variable with its given value.

 

\cfrac{23}{5}

 

To simplify, \, \cfrac{23}{5} \, can be converted into a mixed number or written as decimal by working out 23 \div 5.

 

23 \div 5=4 \, \cfrac{3}{5}

3. Evaluate 9(12-f) when f=2 \, \cfrac{1}{2} \, .

85 \, \cfrac{1}{2}
GCSE Quiz True

90
GCSE Quiz False

130 \, \cfrac{1}{2}
GCSE Quiz False

99 \, \cfrac{1}{2}
GCSE Quiz False

Substitute the variable with its given value.

9\left(12-2 \, \cfrac{1}{2}\right)

 

Evaluate using the order of operations.

 

\begin{aligned} & 9\left(12-2 \, \cfrac{1}{2}\right) \\\\ & =9\left(9 \, \cfrac{1}{2}\right) \quad \quad \text{ **Remember } 9\left(9 \, \cfrac{1}{2}\right) \text{ is the same as } 9 \times 9 \, \cfrac{1}{2}\\\\ & =85 \, \cfrac{1}{2} \end{aligned}

4. Evaluate 6 z+7 r when r=8 and z=1.3.

57.1
GCSE Quiz False

139.3
GCSE Quiz False

22.3
GCSE Quiz False

63.8
GCSE Quiz True

Substitute each variable with its given value.

 

6 \times 1.3+7 \times 8

 

Evaluate using the order of operations.

 

\begin{aligned} & 6 \times 1.3+7 \times 8 \\\\ & =7.8+7 \times 8 \\\\ & =7.8+56 \\\\ & =63.8 \end{aligned}

5. Evaluate w-2(b+3) when w=44 and b=4.

17
GCSE Quiz False

42
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30
GCSE Quiz True

20
GCSE Quiz False

Substitute each variable with its given value.

 

44-2(4+3)

 

Evaluate using the order of operations.

 

\begin{aligned} & 44-2(4+3) \\\\ & =44-2(7) \quad \quad \text{ **Remember } 2(7) \text{ is the same as } 2 \times 7\\\\ & =44-14 \\\\ & =30 \end{aligned}

6. Evaluate 5 t^4+t when t=3 .

63
GCSE Quiz False

584
GCSE Quiz False

408
GCSE Quiz True

515
GCSE Quiz False

Substitute each variable with its given value.

 

5(3)^4+3

 

Evaluate using the order of operations.

 

\begin{aligned} & 5 \times 3^4+3 \quad \quad \text{ **Remember } 3^4=3 \times 3 \times 3 \times 3 \\\\ & =5 \times 81+3 \\\\ & =405+3 \\\\ & =408 \end{aligned}

Evaluate the expression FAQs

How are numerical expressions similar to algebraic expressions?

When evaluating for a specific value, you use only numbers, so the variables in an algebraic expression need to be substituted. Then you evaluate both types of expressions by following the order of operations.

How do you evaluate equations and inequalities?

You can evaluate them in the same way that you do expressions, by substituting a value for the variable(s).

Still stuck?

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