Adding, Subtracting, Multiplying and Dividing Rational Numbers
11 questions
9th Grade
Mathematics
This Grade 9 mathematics worksheet gives students practice adding, subtracting, multiplying, and dividing rational numbers in practical situations. The 11-item set includes nine multiple-choice questions and two dropdown items covering fraction division with mixed numbers, fraction-sharing and measurement problems, fraction addition using a common denominator and the LCD, decimal addition and subtraction, and operation rules involving exponents. Students also translate a money situation into an inequality and identify when an inequality symbol changes.
The worksheet is designed for learners who need to connect computation rules with word-problem reasoning. Students must choose appropriate operations, interpret fractional and decimal quantities, and apply procedural rules rather than simply calculate. It works well for independent practice, review, or a short formative check after instruction on rational-number operations and inequalities. This is a free printable worksheet with a complete answer key, making it convenient for classroom practice, homework, or intervention.
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Adding, Subtracting, Multiplying and Dividing Rational Numbers
Total questions: 11
Name
Class
Date
1.
After a pizza party there are 4 2/3 pizzas left over. If the pizzas are divided so that party goers can take home 1/6 of a pizza, how many guests can take home pizza?
a)
26 guests
b)
28 guests
c)
8 guests
d)
33 guests
2.
Bob has a piece of wood that is 3/4 inches long. He decides to cut pieces that are 1/8 inches long. How many pieces can Bob cut?
a)
6
b)
9
c)
3
d)
12
3.
Sarah needs to cut 7 and a half feet of ribbon into 2 and 2/3 feet pieces. How many pieces will she be able to make?
a)
4 and 5/6
b)
2 and 13/16
c)
3
d)
20
4.
Sandy uses ⅛ of a pound of chocolate chips in each batch of cookies she makes. Yesterday Sandy used ⅘ of a pound to make all her batches. How many batches of cookies did Sandy make?
a)
4/40
b)
1/10
c)
6⅖
d)
5⅓
5.
When adding or subtracting fractions, I must always have a (a) . I then add or subtract the (b) and keep (c) the same.
Choose from the below words
Common Denominator
Numerators
Denominator
Common Numerators
Divisor
Dividend
6.
When (a) decimals, I must always (b) the decimals.
Choose from the below words
adding or subtracting
line up
multiplying or dividing
get rid of
7.
Sammy has 2 2/3 Hershey bars to share with 4 of her friends. How much of a Hershey bar will each of her 4 friends receive?
a)
1/3 Hershey bar each
b)
5/3 Hershey bar each
c)
2/3 Hershey bar each
d)
1 3/4 Hershey bar each
8.
When adding fractions, what does LCD mean?
a)
Least Common Denominator
b)
Lowest Common Divsion
c)
Last Corrective Divisor
d)
Least Correct Decision
9.
In what types of problems do you have to make sure the exponents are the same before beginning to compute?
a)
Adding and Subtracting
b)
Multiplying and Dividing
c)
Subtracting and Dividing
d)
Adding and Multiplying
10.
Last Friday Samantha had $22.50. Over the weekend, she received some money for cleaning. She now has more than $32.00. Which inequality represents this situation?
a)
22.50 - x > 32
b)
22.50x > 32
c)
22.50 + x > 32
d)
22.50 +x < 32
11.
When do we switch the inequality symbol?
a)
when multiplying or dividing by a NEGATIVE
b)
when adding and subtracting a NEGATIVE
c)
we never switch the inequality
d)
When there is a negative in the problem
Answer Key
Adding, Subtracting, Multiplying and Dividing Rational Numbers
Total questions: 11
1.
b)
28 guests
2.
a)
6
3.
b)
2 and 13/16
4.
c)
6⅖
5.
Common Denominator
,
Numerators
,
Denominator
6.
adding or subtracting
,
line up
7.
c)
2/3 Hershey bar each
8.
a)
Least Common Denominator
9.
a)
Adding and Subtracting
10.
c)
22.50 + x > 32
11.
a)
when multiplying or dividing by a NEGATIVE
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FAQs
What does this worksheet cover, and how does it help students use rational numbers?
This Grade 9 worksheet covers adding, subtracting, multiplying, and dividing rational numbers through nine multiple-choice problems and two dropdown items. Students solve fraction-based sharing and measurement situations, apply common-denominator and LCD rules, line up decimals, and represent a money situation with an inequality. The varied formats require students to select both the correct operation and the rule that supports it.
How can I use this worksheet to teach rational-number operations?
Introduce the worksheet by modeling one fraction-division situation, such as finding how many 1/6 portions are contained in 4 2/3 pizzas, and ask students to explain why division is appropriate. Then review the dropdown rules for common denominators and lining up decimals before students work through the application items. Use the inequality questions as a closing discussion about translating “more than” and switching the symbol when multiplying or dividing by a negative.
What mistakes should I watch for when students complete this worksheet?
Watch for students dividing fraction quantities without using the correct reciprocal, or treating a sharing problem as multiplication or subtraction. In the rule items, students may confuse the common denominator with the numerators or fail to line up decimal places. In the final inequality questions, check that students translate “more than” as a greater-than relationship and know that the symbol changes when multiplying or dividing by a negative.
How do I assign and grade this rational-numbers worksheet?
On Wayground, assign this worksheet as a printable PDF or as a digital quiz. The complete answer key supports grading the nine multiple-choice items and two dropdown items, and printable submissions can be graded by scanning student work with the Wayground for Teachers app. The printable format also gives schools an option for reducing screen time while students practise fraction, decimal, and inequality skills.
How can I differentiate this worksheet for my students?
Use the worksheet’s Advanced Settings to adjust font spacing and font size so the fraction, decimal, and inequality expressions are easier to read. You can also apply a dyslexia-friendly font or translate the worksheet into another language when that better supports access to its word problems and rule-based dropdown items.
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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