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Simplifying, Multiplying and Dividing Algebraic Fractions - Printable Math Worksheets 9th Grade - Wayground

Simplifying, Multiplying and Dividing Algebraic Fractions

Anthony Clark

Created by Anthony Clark

16 questions

9th Grade

Math

Updated Oct 2026

Designed for Grade 9 mathematics, this free printable worksheet with an answer key gives students focused practice simplifying, multiplying, and dividing algebraic fractions and rational expressions. Across 16 multiple-choice questions, students select equivalent simplified forms, perform multiplication and division with algebraic expressions, and apply coefficient and exponent rules to products and quotients such as 3x · 4x and 4x² ÷ 2x. Several items require students to factor or recognize cancellable factors before choosing a final expression. This worksheet is useful for guided practice, independent review, homework, or a quick formative assessment after instruction on rational expressions. Its multiple-choice format lets teachers check whether students can distinguish correct simplified results from common errors involving signs, coefficients, exponents, and incomplete cancellation. The included answer key supports efficient checking and targeted follow-up on the algebraic steps students find difficult.

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Simplifying, Multiplying and Dividing Algebraic Fractions

Total questions: 16

Name
Class
Date
1.
Multiply and Simplify

Multiply and Simplify

a)

4(x+3)/(x+2),

b)

(x+2)/4(x+1)

c)

(x+2)/4(x+3),

d)

4(x+1)/(x+2),

2.
Divide the Rational Expression

Divide the Rational Expression

a)

A

b)

B

c)

C

d)

D

3.
Multiply and Simplify

Multiply and Simplify 

a)

5a-25/ (a-5)(a+9)

b)

5/(a+9)

c)

5a-25/ (a+9)

d)

1/(a+9)

4.
Simplify.

Simplify. 

a)

(x+6)/(x+4)

b)

(x+6)(x+4)

c)

(x+6)

d)

(x+6)/(x-5)

5.
SIMPLIFY

SIMPLIFY

a)

A

b)

B

c)

C

d)

D

6.
Divide the Rational Expression

Divide the Rational Expression

a)

A

b)

B

c)

C

d)

D

7.

What is the product of 3x and 4x?

a)

12x

b)

7x

c)

x^2

d)

12x^2

8.

What is the quotient of 8y divided by 2y?

a)

6y

b)

4y

c)

4

d)

10y

9.

What is the result of dividing the expression 4x^2 by 2x?

a)

x

b)

2x^2

c)

8x

d)

2x

10.
Question Image
a)

2byc\frac{2by}{c}  

b)

4xbac\frac{4xb}{ac}  

c)

2xbac\frac{2xb}{ac}  

d)

acdc\frac{ac}{dc}  

11.
Question Image
a)

3c

b)

9b4a\frac{9b}{4a}  

c)

4a

d)

2cb\frac{2c}{b}  

12.
Question Image
a)

6am10a\frac{6am}{10a}  

b)

9

c)

9ma3a\frac{9ma}{3a}  

d)

6m

13.
Simplify the algebraic fraction.

Simplify the algebraic fraction.

a)

-m

b)

−1m\frac{-1}{m}  

c)

mn\frac{m}{n}  

d)

1mn\frac{1}{mn}  

14.

Multiply the two rational expressions and simplify the result:

a)

x−2x−5x\frac{x-2}{x-5x}  

b)

x−2x2−5x\frac{x-2}{x^2-5x}  

c)

x−2x−5\frac{x-2}{x-5}  

d)

x−4x2−5x\frac{x-4}{x^2-5x}  

15.

Multiply the two rational expressions and simplify the result: \frac{x^2-4}{x^2-9}\cdot\frac{x-3}{x+2}

a)

x−2x+3\frac{x-2}{x+3}  

b)

x+2x−3\frac{x+2}{x-3}  

c)

−23-\frac{2}{3}  

d)

x−2x−3\frac{x-2}{x-3}  

16.

Multiply the two rational expressions and simplify the result:

a)

(x−2)(x+6)(x−1)\frac{\left(x-2\right)}{\left(x+6\right)\left(x-1\right)}  

b)

(x−1)(x−2)(x−3)(x+2)\frac{\left(x-1\right)\left(x-2\right)}{\left(x-3\right)\left(x+2\right)}  

c)

(x−1)(x−3)(x−2)\frac{\left(x-1\right)}{\left(x-3\right)\left(x-2\right)}  

d)

(x−2)(x−1)(x+2)(x+3)\frac{\left(x-2\right)\left(x-1\right)}{\left(x+2\right)\left(x+3\right)}  

WaygroundAnswer Key

Simplifying, Multiplying and Dividing Algebraic Fractions

Total questions: 16

1.
b)

(x+2)/4(x+1)

2.
c)

C

3.
b)

5/(a+9)

4.
d)

(x+6)/(x-5)

5.
d)

D

6.
b)

B

7.
d)

12x^2

8.
c)

4

9.
d)

2x

10.
a)

2byc\frac{2by}{c}  

11.
a)

3c

12.
b)

9

13.
a)

-m

14.
b)

x−2x2−5x\frac{x-2}{x^2-5x}  

15.
a)

x−2x+3\frac{x-2}{x+3}  

16.
d)

(x−2)(x−1)(x+2)(x+3)\frac{\left(x-2\right)\left(x-1\right)}{\left(x+2\right)\left(x+3\right)}  

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FAQs

What does this worksheet cover?

This Grade 9 mathematics worksheet covers simplifying, multiplying, and dividing algebraic fractions and rational expressions through 16 multiple-choice questions. Students identify equivalent simplified forms, cancel common factors in factored expressions, and apply coefficient and exponent rules when finding products and quotients.

How can I use this worksheet to teach multiplying and dividing algebraic fractions?

Use the worksheet after modeling the process of factoring expressions, multiplying or inverting rational expressions, and canceling common factors. Have students explain why an option is equivalent rather than selecting an answer by appearance, then use the questions involving products such as 3x · 4x and quotients such as 4x² ÷ 2x to connect rational-expression work with basic monomial rules.

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

Watch for students adding or multiplying exponents incorrectly, confusing a product such as 3x · 4x with 12x, or treating a quotient such as 8y ÷ 2y as another variable expression instead of simplifying it. In the rational-expression items, students may also cancel individual terms rather than common factors, forget to invert the divisor, or stop before fully simplifying the result.

How do I assign and grade this worksheet?

This worksheet is available as a printable PDF and as a digital quiz on Wayground, so you can assign the format that fits your lesson. It includes a complete answer key, and printable submissions can be graded by scanning student work with the Wayground for Teachers app.

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

Under the worksheet’s Advanced Settings, adjust font spacing or choose a larger font size to make the multiple-choice expressions easier to read. You can also enable a dyslexia-friendly font or translate the worksheet into another language while keeping the algebraic-fraction practice format.

Where can I find more worksheets like this on Wayground?

Wayground offers a comprehensive collection of free printable worksheets and practice problems across all 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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