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Complex Fractions and Unit Rates - Printable Mathematics Worksheets - Wayground

Complex Fractions and Unit Rates

20 questions

7th - 7th Grade

Mathematics

This free Grade 7 mathematics worksheet helps students simplify complex fractions and calculate unit rates when both quantities are fractions or mixed numbers. Its 20 multiple-choice questions ask students to identify a complex fraction, simplify nested fractions, and determine rates such as meters per hour, acres per hour, pages per hour, miles per hour, and ingredients per batch. Students apply fraction division in both numerical exercises and practical word problems, building accuracy with reciprocal relationships, rate units, and proportional reasoning. The varied contexts require students to interpret what a rate represents before selecting an answer, while the multiple-choice format provides focused practice and quick checks for understanding. The worksheet is available as a free printable worksheet and includes a complete answer key for efficient review or grading.

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Complex Fractions and Unit Rates

Total questions: 20

Name
Class
Date
1.
What is a complex fraction?
a)
A really hard fraction to figure out 
b)
A fraction with a fraction in the numerator, denominator, or both 
c)
A fraction multiplied by a decimal
d)
A fraction with an exponent 
2.

Simplify the complex fraction.

a)

20

b)

36/5

c)

1/20

d)

60/3

3.

Simplify the complex fraction.

a)

7/100

b)

35/20

c)

7/4

d)

21

4.

Simplify the complex fraction.

a)

6/5

b)

5/6

c)

15/128

d)

15/16

5.

If a snail can move 3/10 of a meter every 1/12 hour, what is the speed of the snail, in meters per hour?

a)

1/40

b)

5/18

c)

11/2

d)

33/5

6.
Sasha can mow 3/8 of an acre of grass in 3/4 an hour. How many acres of grass does Sasha mow per hour?
a)

2  acre/hr.

b)

1/2  acre/hr.

c)

9/24  acre/hr.

7.

A novelist can write 2¼ pages in 3/5 of an hour. What is her speed in pages per hour?

a)

4/15 pages per hour

b)

33/4 pages per hour

c)

20/27 pages per hour

d)

27/20 pages per hour

8.

It takes 31/5 teaspoons of syrup to make 13/4 strawberry milkshakes. Hany many teaspoons would you need to make one milkshake?

a)

129/35 teaspoons

b)

35/64 teaspoons

c)

28/5 teaspoons

d)

5/28 teaspoons

9.
If a dog can eat 1/3 of a bag of food in 1/2 week, how many bags of food can the dog eat in 1 week?
a)
1/6
b)
2/3
c)
3/2
d)
5/6
10.

Aliya hikes for 2 hours and goes a distance of 11/3 miles. What is her rate of speed in miles per hour?

a)

2/3 mph

b)

11/2 mph

c)

22/3 mph

d)

31/3mph

11.

Simplify the complex fraction

_3/4_

1/2

a)

3/4

b)

3/8

c)

11/2

d)

5/4

12.

Simplify the complex fraction.

a)

16/63

b)

14/72

c)

63/13

d)

72/14

13.

Simplify the following complex fraction.

a)

1/25

b)

25

c)

1/4

d)

4

14.

256\frac{2}{\frac{5}{6}}  

a)

35\frac{3}{5}  

b)

512\frac{5}{12}  

c)

106\frac{10}{6}  

d)

2252\frac{2}{5}  

15.

While exercising Logan walked 1⁄8 of a mile in 1⁄6 of an hour. At this rate, how far will he have traveled after an hour?

a)

1/48 of a mile

b)

3/4 of a mile

c)

1 mile

d)

5/8 of a mile

16.

797\frac{\frac{7}{9}}{7}  

a)

499\frac{49}{9}  

b)

9

c)

19\frac{1}{9}  

d)

949\frac{9}{49}  

17.

415\frac{4}{\frac{1}{5}}  

a)

120\frac{1}{20}  

b)

45\frac{4}{5}  

c)

20

d)

54\frac{5}{4}  

18.

A brownie recipe requires 2/3 cup of sugar for 1/3 batch of brownies. How much sugar is need for 1 batch of brownies

a)

2/9 cup

b)
1 cup
c)

11/3 cups

d)
2 cups
19.

Which of the following is a complex fraction?

a)

103\frac{10}{3}

b)

15\frac{1}{5}

c)

2357\frac{\frac{2}{3}}{\frac{5}{7}}

d)

5135\frac{1}{3}

20.

Simplify the complex fraction.

a)

21/3

b)

3/7

c)

100/21

d)

21/100

Answer Key

Complex Fractions and Unit Rates

Total questions: 20

1.
b) A fraction with a fraction in the numerator, denominator, or both 
2.
a)

20

3.
a)

7/100

4.
b)

5/6

5.
d)

33/5

6.
b)

1/2  acre/hr.

7.
b)

33/4 pages per hour

8.
a)

129/35 teaspoons

9.
b) 2/3
10.
a)

2/3 mph

11.
c)

11/2

12.
a)

16/63

13.
d)

4

14.
d)

2252\frac{2}{5}  

15.
b)

3/4 of a mile

16.
c)

19\frac{1}{9}  

17.
c)

20

18.
d) 2 cups
19.
c)

2357\frac{\frac{2}{3}}{\frac{5}{7}}

20.
a)

21/3

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FAQs

What does the Complex Fractions and Unit Rates worksheet cover?

This Grade 7 worksheet uses 20 multiple-choice questions to practice simplifying complex fractions and finding unit rates by dividing one fraction or mixed number by another. Students apply these skills to numerical fraction problems and contexts involving speed, production, food consumption, distance, and recipe quantities.

How can I use this worksheet to teach complex fractions and unit rates?

Begin by modeling a complex fraction as division of the numerator by the denominator, then connect that process to a unit-rate example such as finding meters per hour from a fractional distance and fractional hour. Have students identify the units before calculating, solve several of the multiple-choice items with written division steps, and explain why the selected answer has the correct rate unit.

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

Students may invert the wrong fraction when dividing a complex fraction, simplify only the numerator or denominator, or treat a fraction in the denominator as multiplication without using its reciprocal. In the unit-rate word problems, watch for reversing the quantities, failing to convert a mixed number before calculating, and choosing an answer with mismatched units, such as hours per mile instead of miles per hour.

How do I assign and grade this worksheet?

Wayground provides this worksheet as a printable PDF and as a digital quiz, and it includes a complete answer key for all 20 multiple-choice questions. You can grade printable submissions by scanning student work with the Wayground for Teachers app, or review responses through the digital quiz.

How can I differentiate this complex fractions and unit rates worksheet for my students?

Use the worksheet’s Advanced Settings to adjust font spacing and font size so the fraction expressions, answer choices, and unit-rate word problems are easier to read. You can also enable a dyslexia-friendly font or translate the worksheet into another language while keeping the same multiple-choice practice format.

Where can I find more 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 support essential skills and concepts. Browse more resources at https://wayground.com/en-us/worksheets.

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