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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.

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?

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:

Substitute each variable with its given value.

Evaluate using the order of operations.

[FREE] Evaluate The Expression Worksheet (Grade 6 and 7)

Use this worksheet to check your 6th grade and 7th grade students’ understanding of evaluate the expression. 15 questions with answers to identify areas of strength and support!

Evaluate the expression examples

Example 1: one step, one variable.

Evaluate 4m when m=35.

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

4 \times 35

2 Evaluate 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.

3 \, (9+22)

\begin{aligned} & 3(9+22) \\\\ & =3(31) \quad \quad \text{ *Remember, } 3 \, (31) \text{ is the same as } 3 \times 31 \\\\ & =93 \end{aligned}

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

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

50-\cfrac{20}{2}

Because the numerator is larger than the denominator, the fraction can be simplified with division: \, \cfrac{20}{2}=20 \div 2.

\begin{aligned} & 50-\frac{20}{2} \\\\ & =50-10 \\\\ & =40 \end{aligned}

Example 4: two steps, two variables

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

11 \times 5-2 \times 6

\begin{aligned} & 11 \times 5-2 \times 6 \\\\ & =55-2 \times 6 \\\\ & =55-12 \\\\ & =43 \end{aligned}

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

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

5(3+11)-22 \, \cfrac{1}{3}

\begin{aligned} & 5(3+11)-22 \cfrac{1}{3} \\\\ & =5(14)-22 \cfrac{1}{3} \quad \quad \text{ **Remember } 5(14) \text{ is the same as } 5 \times 14 \\\\ & =70-22 \cfrac{1}{3} \\\\ & =47 \cfrac{2}{3} \end{aligned}

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

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

\begin{aligned} & 3^3(9-7) \\\\ & =3^3(2) \quad \quad \text{ **Remember } 3^3 \text{ is the same as } 3 \times 3 \times 3 \\\\ & =27(2) \quad \quad \text{ **Remember } 27(2) \text{ is the same as } 27 \times 2\\\\ & =54 \end{aligned}

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

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}

Related algebraic expressions lessons

Algebraic expression
Combining like terms
Simplifying expressions
Expanding expressions
Equivalent expressions

Practice evaluating the expression questions

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

Substitute the variable with its given value.

8 \times 3-10

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

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

\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} \, .

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

\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.

6 \times 1.3+7 \times 8

\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.

\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 .

\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

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.

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

The next lessons are

Math equations
Inequalities
Math formulas
Types of graphs

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Last modified on December 18th, 2023

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Evaluating algebraic expressions.

Evaluating an algebraic expression means finding the value of the given expression when a variable is substituted with its value and then performing the arithmetic operations to get the result.

Let us now evaluate the expression x + 2 for a) x = 15, b) x = 12

a) Substituting the given value of x = 15 in the given expression, we get,

15 + 2 = 17

b) Substituting the given value of x = 12 in the same expression, we get,

12 + 2 = 14

Now let us substitute x = 7 in the expression 2x – 5, we get,

2(7) – 5 = 14 – 5 = 9

After substitution, we simplify the expression using the order of operations (PEMDAS) rule.

Let us evaluate an algebraic expression ${4s^{2}-s+3}$, for s = 5

First, we will substitute ‘s’ with 5 in the given expression.

= ${4\left( 5\right) ^{2}-\left( 5\right) +3}$

The expression involves multiplication, an exponent, subtraction, and addition. According to the order of operations (PEMDAS), we simplify exponents and perform multiplication, addition, and subtraction.

Thus, we get ${4\times 25-5+3}$

Now, by multiplying, we get 100 – 5 + 3

By adding, we get 103 – 5

And finally, by subtracting, we get 98

Thus, the given expression ${4s^{2}-s+3}$ is evaluated to 98, when s = 5.

For More than One Variable

Now, let us evaluate the expression ${a^{2}+3bc}$, when a = 2, b = 6, c = 1

First, substitute a with 2, b with 6, and c with 1 in the given expression.

We get ${\left( 2\right) ^{2}+3\left( 6\right) \left( 1\right)}$

Here, the expression involves addition, multiplication, and an exponent. According to the order of operations, we solve the exponent first, then multiply and add to simplify further.

Thus, we get ${4+3\left( 6\right) \left( 1\right)}$

Now, by multiplying, we get 4 + 18

By adding, we get 22

Thus, the given expression ${a^{2}+3bc}$ is evaluated to 22, when a = 2, b = 6, c = 1.

With Fractions

In the case of algebraic expressions with fractions, we always evaluate and simplify the numerator and the denominator separately. Then, we remove the common factor from both to get the required value.

Let us evaluate the expression ${\dfrac{a+3bc}{a^{2}}}$, when a = 2, b = 1, c = 6

First, substitute 2 for a, 1 for b, and 6 for c in the given expression.

We get ${\dfrac{\left( 2\right) +3\left( 1\right) \left( 6\right) }{\left( 2\right) ^{2}}}$

Here, the expression involves addition and multiplication in the numerator and an exponent in the denominator.

According to PEMDAS, we multiply and add in the numerator and solve the exponent in the denominator. Removing the common factor and rewriting the remaining terms to simplify further, we get,

= ${\dfrac{2+18}{4}}$

= ${\dfrac{20}{4}}$

Thus, the given expression ${\dfrac{a+3bc}{a^{2}}}$ is evaluated to 5, when a = 2, b = 1, c = 6.

Solved Examples

Evaluate: 4x + (12 – y) – 3z, when x = 2, y = 6, and z = -5

To evaluate the given expression 4x + (12 – y) – 3z, substituting the given values 2 for x, 6 for y, and -5 for z, we get, 4(2) + (12 – 6) – 3(-5) Now, solving using the order of operations, we get, 8 + 6 + 15 = 29 Thus, 4x + (12 – y) – 3z equals to 29, when x = 2, y = 6, and z = -5.

Evaluate the following algebraic expressions. a) ${\dfrac{3\left( a+c^{2}\right) }{12}}$, when a = -9 and c = 5 b) ${7x^{2}-11x+13}$, when x = 5

a) To evaluate the given expression ${\dfrac{3\left( a+c^{2}\right) }{12}}$, substituting the given values -9 for a and 5 for c, we get, ${\dfrac{3\left\{ \left( -9\right) +\left( 5\right) ^{2}\right\} }{12}}$ Now, solving using the order of operations, we get, ${\dfrac{3\left\{ -9+25\right\} }{12}}$ = ${\dfrac{3\times 16}{12}}$ = 4 Thus, ${\dfrac{3\left( a+c^{2}\right) }{12}}$ equals to 4, when a = -9 and c = 5. b) To evaluate the given expression ${7x^{2}-11x+13}$, substituting the given value 5 for x, we get, ${7\left( 5\right) ^{2}-11\left( 5\right) +13}$ Now, solving using the order of operations, we get, ${7\times 25-55+13}$ = 175 – 55 + 13 = 188 – 55 = 133 Thus, ${7x^{2}-11x+13}$ equals to 133, when x = 5.

Evaluate the algebraic expression: 5x + 2y – 4 a) When x = 3, y = 11 b) When x = -5, y = 7

The given expression is 5x + 2y – 4 a) Here, by substituting the values 3 for x and 11 for y, we get, 5(3) + 2(11) – 4 Now, solving using the order of operations, we get, 15 + 22 – 4 = 37 – 4 = 33 Thus, 5x + 2y – 4 = 133, when x = 3, y = 11. b) Here, by substituting the values -5 for x and 7 for y, we get, 5(-5) + 2(7) – 4 Now, solving using the order of operations, we get, -25 + 14 – 4 = 14 – 29 = -15 Thus, 5x + 2y – 4 = -15, when x = -5, y = 7.

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