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Order of Operations and Evaluating Algebraic Expressions - Printable Mathematics Worksheets - Wayground

Order of Operations and Evaluating Algebraic Expressions

15 questions

9th - 9th Grade

Mathematics

This Grade 9 mathematics worksheet helps students evaluate algebraic expressions by substituting given values, applying PEMDAS, and performing operations in the correct sequence. It also reinforces essential vocabulary and properties, including variables, coefficients, algebraic expressions, the Commutative Property of Addition, and the Inverse Property of Multiplication. Students work through 15 questions: 13 multiple-choice items and 2 fill-in-the-blank items. Use this free printable worksheet with direct instruction, guided practice, independent work, or a review of order of operations and introductory algebraic language. The evaluation questions include powers, parentheses, multiplication and division, and addition and subtraction, while the substitution items ask students to evaluate expressions such as a² + b² and 5a + b using specified values. A complete answer key is included to support efficient checking, feedback, and assessment.

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Worksheets

Order of Operations and Evaluating Algebraic Expressions

Total questions: 15

Name
Class
Date
1.

 a2+b2 when a=3 and b=−4a^2+b^2\ when\ a=3\ and\ b=-4  

a)

 −1-1  

b)

 −7-7  

c)

 2525  

d)

 4949  

2.

When solving expressions with series of operations, which of the following is correct?

a)

Add and subtract from right to left

b)

Multiply and divide from left to right

c)

Add and multiply from left to right

d)

Subtract and divide from right to left

3.

Evaluate x+3x−2x+3x-2  when  x=3x=3  

(a)  

4.

In the acronym for the order of operation PEMDAS, what does E stands for?

(a)  

5.

Evaluate the expression using the correct order of operations.

 48÷22×3+1248\div2^2\times3+12  

a)

72

b)

720

c)

36

d)

48

6.

Evaluate the expression

[(12 ÷ 2) - 4] + (8 x 2)

a)

20

b)

17

c)

16

d)

18

7.

When evaluating an expression, which operation should be considered last?

a)

powers

b)

brackets

c)

addition and subtraction

d)

multiplication and division

8.

When evaluating an expression, following the order of operations, which

operation should be considered first?

a)

multiplication and division

b)

addition and subtraction

c)

powers

d)

parenthesis

9.
What are the coefficients in the expression
8a + b + 9?
a)
8 only
b)
1 and 8
c)
8 and 9
d)
1, 8, and 9
10.

Letters used to represent amounts

a)

Expressions

b)

Equations

c)

Symbols

d)

Variables

11.
b2 + 4
when b = 3
a)
10
b)
12
c)
13
d)
11
12.

Numbers, symbols, and operations that are grouped together

a)

Evaluation

b)

Algebraic Expression

c)

PEMDAS

d)

Order of Operations

13.

Evaluate the expression: 5a + b for a= 6 and b= 3

a)

33

b)

36

c)

30

d)

59

14.

What property allows for two or more numbers to be added in any order without changing the sum?

a)

Associative Property of Addition

b)

Commutative Property of Multiplication

c)

Commutative Property of Addition

d)

Distributive Property

15.

What property states that the product of a number and its reciprocal is always 1?

a)

Identity Property of Multiplication

b)

Distributive Property

c)

Inverse Property of Multiplication

d)

Commutative Property of Multiplication

Answer Key

Order of Operations and Evaluating Algebraic Expressions

Total questions: 15

1.
c)

 2525  

2.
b)

Multiply and divide from left to right

3.
10
4.
Exponent, Exponents
5.
d)

48

6.
d)

18

7.
c)

addition and subtraction

8.
d)

parenthesis

9.
b) 1 and 8
10.
d)

Variables

11.
c) 13
12.
b)

Algebraic Expression

13.
a)

33

14.
c)

Commutative Property of Addition

15.
c)

Inverse Property of Multiplication

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FAQs

What does this worksheet cover, and how does it help students evaluate algebraic expressions?

This Grade 9 worksheet focuses on evaluating algebraic expressions by substituting values for variables and following PEMDAS, including powers, parentheses, multiplication and division from left to right, and addition and subtraction. Its 15 items combine 13 multiple-choice questions with 2 fill-in-the-blank questions, so students practise both procedural evaluation and key terms such as variables, coefficients, and algebraic expressions.

How can I use this worksheet to teach evaluating algebraic expressions?

Introduce PEMDAS and model one expression with parentheses and powers, explicitly showing why multiplication and division are completed from left to right. Then use the worksheet’s substitution items, such as evaluating 5a + b for given values, for guided practice before assigning the remaining multiple-choice and fill-in-the-blank questions independently. Ask students to explain which operation they completed first and why.

What mistakes should I watch for when students complete this order of operations worksheet?

Watch for students treating multiplication as always preceding division instead of completing those operations from left to right, or adding and subtracting before resolving powers and parentheses. In the substitution questions, students may replace a variable incorrectly, omit the coefficient of an implied term such as b, or confuse coefficients with constants. Students may also select the wrong property when distinguishing commutative, associative, distributive, and inverse multiplication rules.

How do I assign and grade this worksheet?

This worksheet is available as a printable PDF and as a digital quiz on Wayground, with a complete answer key for all 15 questions. You can grade digital responses through Wayground and scan printable student work with the Wayground for Teachers app for faster review.

How can I differentiate this algebraic expressions worksheet for my students?

Use the worksheet’s Advanced Settings to adjust font spacing and font size so powers, parentheses, and substitution expressions are easier to follow. You can also enable a dyslexia-friendly font or translate the worksheet into another language, depending on student needs.

Where can I find more free worksheets like this on Wayground?

Wayground offers a broad collection of free printable worksheets and practice problems across subjects, with downloadable PDFs and answer keys to help students master essential skills and concepts. Browse more resources at https://wayground.com/en-us/worksheets.

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