Operations with Rational Numbers Worksheet PDF

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Practice materials for rational numbers for University of Nevada, REno Fund college math course...

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Track-and-Field Day The Harrison Creek Owls have been studying rational numbers. While participating in the annual track-and-field day at school, they are discovering that rational numbers are all around them! Let’s help them work with rational numbers during their events.

Photo by Gary Paulson

As you complete this task, keep this in mind: The seventh graders are competing against the eighth graders for the track-and-field day trophy. As you complete each problem, record the points earned by each team so you can determine who wins the trophy! Directions: Complete each of the following tasks, reading the directions carefully as you go. You will be graded on the work you show, or your solution process, in addition to your answers. Make sure to show all of your work and to answer each question as you complete the task. Type all of your work into this document so you can submit it to your teacher for a grade. You will be given partial credit based on the work you show and the completeness and accuracy of your explanations. Your teacher will give you further directions on submitting your work. You may be asked to upload the document, e-mail it to your teacher, or hand in a hard copy. Now let’s get started!

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Step 1: Calculating with rational numbers in real-world contexts

a) In the first event, the eighth graders are running a baton relay race with three other classmates. The team’s top speed for each leg is 56.81 seconds, 59.22 seconds, 57.39 seconds, and 60.11 seconds. Use the information to predict the team’s best time for the race. (2 points)

The best time for the race was 233.53 seconds or 3 minutes, 53.53 seconds

If the team’s best time for the race is less than 4 minutes, then the eighth graders earn 40 points. If not, the seventh graders earn 40 points. Which grade should be awarded 40 points? The eighth graders get 40 points

b) Each leg of the race from part a is the same distance. Calculate the team’s average time for each leg of the race. Show your work. (2 points) 56.81 + 59.22 + 57.39 + 60.11 = 233.53 233.53/4 = 58.38 The average time is 58.38 seconds

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c) d) e) f) g) h) i) j) k) If the team’s average time is less than one minute per leg, then the eighth graders earn 50 points. If not, the seventh graders earn 50 points. Which grade should be awarded 50 points? The eighth graders get 50 points Step 2: Using properties of operations to add and subtract with fractions 1 5 feet in the long-jump event. Jill’s best friend jumped 6 feet. 3 7 How much farther did Jill’s best friend jump? Describe in words the process you used to solve the problem. (2 points)

a) Jill jumped 6

Jill jumped 6 1/3 feet which is equal to 19/3 feet. Jill’s best friend jumped 6 5/7 feet which is equal to 47/7 feet. A common denominator is 21. So 19/3 is equal to 133/21 and 47/7 is equal to 141/21. So Jill’s bestfriend jumed 8/21 farther than Jill.

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If Jill’s best friend jumped farther than 6.5 feet, then she beat the school record and the seventh graders earn 50 points. If not, the eighth graders earn 50 points. Which grade should be awarded 50 points? The seventh graders get 50 points.

b) Claire and her partner, Grace, are throwing for the javelin event as a team. Claire 5 3 feet and Grace threw it 39 feet. How far did the team 8 5 throw the javelin? Show your work. (2 points) We added 42 and 39 to get 81. Using a common denominator of 40, we then converted 5/8 to 25/40 and 3/5 to 24/40. We added 25/40 and 24/40 and got 49/40. 49/40 is equal to 1 9/40. threw the javelin 42

Then we added 1 9/40 to 81 to get 82 9/40. The team threw 82 9/40 feet.

If the total distance of Claire and Grace’s javelin throw is greater than 82.5 feet, then the seventh graders earns 50 points. If not, the eighth graders earn 50 points. Which grade should be awarded 50 points? The eighth graders win 50 points l) For the high jump, each competitor receives multiple opportunities to clear the bar at each height. On average, Shane completes 2 out of 3 jumps on the lowest bar, 4 out of 6 jumps on the middle bar, and 1 out of 4 jumps on the highest bar. Write an equation that you could use to find Shane’s overall average number of jumps completed. Calculate Shane’s average using the equation. (2 points) Page 4 | © Edgenuity Inc.

2/3 + 4/6 + ¼ = 19/12 (19/12) / 3 = 19/36 Shanes average is 19/36.

If Shane’s average number of jumps completed is greater than one-half, then the eighth graders earn 50 points. If not, the seventh graders earn 50 points. Which grade should be awarded 50 points?

The eighth graders get 50 points.

Step 3: Using properties of operations to solve real-world problems with rational numbers a) The next event requires each runner to jump 8 hurdles that are spaced 12.3 meters apart. If there are 15 meters from the starting line to the first hurdle and 10.5 meters from the last hurdle to the finish line, how long is the race? Show your work. (2 points) 15 m Start

We looked at how many hurdles there are and in between each hurdle is 12.3 meters. There are 7 spaces in between

Myra won the hurdles event for the seventh graders. She completed the race in 22.8 seconds and knocked down 1 hurdle. Byron won the race for the eighth graders. He Page 5 | © Edgenuity Inc.

10.5 m Finish

completed the race in 20.3 seconds and knocked down 3 hurdles. If 2 seconds are added to the finishing time for each hurdle that is knocked down, what is the final time for each runner? Award 110 points to the team with the fastest time.

Step 4: Estimating with rational numbers 1 yards. If Jack and 4 4 other people each run a leg of the relay, how many yards will each runner run?

a) The relay race is just over one mile long, approximately 1,760

Justify your answer using an estimation strategy. (3 points)

The relay was an exciting event! The eighth graders earned 200 points. b) During the shot put event, Alayna throws the ball 32.45 feet while her teammates throw 28.34 feet, 26.59 feet, and 33.11 feet. Use an estimation strategy to determine about how many total feet were thrown by the team. Describe the estimation strategy you used to solve the problem. (2 points)

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If the team threw the shot put more than110 feet, then the seventh graders earn 110 points. If not, then the eighth graders earn 110 points. Which grade should be awarded 110 points?

Step 5: Adding and subtracting with rational numbers a) Alex, an eighth grader, and Eric, a seventh grader, need to determine who came closer to their grade’s state record for the triple jump. Alex jumped 39.85 feet and 1 inches. Who was closer to the state record if the 4 eighth-grade record is 42.25 feet and the seventh-grade record is 39 feet 3 inches? Eric jumped 37 feet and 1

(2 points)

If a seventh grader gets closer to the record-setting jump, then the seventh graders earn 100 points. If not, the eighth graders earn 100 points. Which grade should be awarded 100 points?

Step 6: Using the commutative and associative properties of multiplication to simplify multiplication of two rational numbers a) The event coordinator asks you to determine how many students participated in the track-and-field day. The total number of students in seventh and eighth grade combined is 584; graders. If

4 5

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5 8

of them are seventh graders and

3 8

of them are eighth

of the seventh graders participated in track-and-field day and

7 8

of the eighth graders participated, about how many total students participated? Describe the process you used to find your answer. (4 points)

b) Each team earns 1 point for each person who participated in the track-and-field day. Who wins the meet—the eighth graders or the seventh graders? Explain. (2 points)

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