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Math Word Problems Solved Reproducible Worksheets Reproducible Worksheets for: Space Word Problems Starring Ratios and Proportions These worksheets are reproducible for educational use only and are not for resale. © 2009 Enslow Publishers, Inc. Math Word Problems Solved Reproducible Worksheets Reproducible Worksheets for: Space Word Problems Starring Ratios and Proportions These worksheets practice math concepts explained in Space Word Problems Starring Ratios and Proportions (ISBN: 978-0-7660-2921-7), written by Rebecca Wingard-Nelson. Math Word Problems Solved reproducible worksheets are designed to help teachers, parents, and tutors use the books from the Math Word Problems Solved series in the classroom and the home. The answers to the problems are contained in the Answers section starting on page 36. Teachers, librarians, tutors, and parents are granted permission and encouraged to make photocopies of these worksheets. These worksheets are reproducible for educational use only and are not for resale. © 2009 Enslow Publishers, Inc. Visit www.enslow.com and search for the Math Word Problems Solved series to download worksheets for the following titles: Amusement Park Word Problems Starring Pre-Algebra 978-0-7660-2922-4 Fun Food Word Problems Starring Fractions 978-0-7660-2919-4 Animal Word Problems Starring Addition and Subtraction 978-0-7660-2917-0 Space Word Problems Starring Ratios and Proportions 978-0-7660-2921-7 Big Truck and Car Word Problems Starring Multiplication and Division 978-0-7660-2918-7 Sports Word Problems Starring Decimals and Percents 978-0-7660-2920-0 Titles in this series can be purchased directly from: Enslow Publishers, Inc. 40 Industrial Road, Box 398 Berkeley Heights, NJ 07922-0398 Phone: 1-800-398-2504 email: [email protected] Web Page: http://www.enslow.com 1 Name _________________________________ Date ___________________ Problem-Solving Steps Here’s the problem. A three-day spaceflight is being planned. Each astronaut can pick 3 snacks per day. At this rate, how many snacks can each astronaut choose for the entire flight? Read and understand the problem. What do you know? What are you trying to find? Make a plan. How can you solve this problem? Solve the problem. Carry out your plan. Look back. Does your answer make sense? Is the math correct? What other plan could you use to solve this problem? © Enslow Publishers, Inc. Sheets are reproducible for educational use only. 2 Name _________________________________ Date ___________________ Problem-Solving Steps Here’s the problem. A ten-day spaceflight is being planned. Each astronaut needs 80 ounces of water per day. At this rate, how many ounces of water does each astronaut need for the entire flight? Read and understand the problem. Make a plan. Solve the problem. Look back. Want to try another one? Five astronauts are going on a mission. Each astronaut has permission to take personal items that weigh up to 12 pounds. How many pounds of personal items can be taken on the mission? © Enslow Publishers, Inc. Sheets are reproducible for educational use only. 3 Name _________________________________ Date ___________________ Read a Table Here’s the problem. There are 8 planets in our solar system. Some of the planets are made of rock. Others are made of gas. Use the table to find the ratio of the planets made of gas to the total planets in our solar system. Read and understand the problem. What do you know? Planet Material Earth rock Jupiter gas Mars rock Mercury rock Neptune gas Saturn gas Uranus gas Venus rock What are you trying to find? Make a plan. What plan does this problem tell you to use? Solve the problem. Carry out your plan. Look back. Could you have answered this problem a different way? © Enslow Publishers, Inc. Sheets are reproducible for educational use only. 4 Name _________________________________ Date ___________________ Read a Table Here’s the problem. There are 8 planets in our solar system. Some of the planets are made of rock. Others are made of gas. Use the table to find the ratio of the planets made of gas to the planets made of rock. Read and understand the problem. Planet Material Earth rock Jupiter gas Mars rock Mercury rock Neptune gas Saturn gas Uranus gas Venus rock Make a plan. Solve the problem. Look back. Want to try another one? Use the table to find the ratio of the total planets to the planets made of rock. © Enslow Publishers, Inc. Sheets are reproducible for educational use only. 5 Name _________________________________ Date ___________________ Comparison Sentences Here’s the problem. The distance from Earth to the Sun is called an astronomical unit (AU). Jupiter is about 5 AUs from the Sun. Write a sentence using the words “as far as” to compare the distances from Jupiter and Earth to the Sun. Read and understand the problem. What do you know? What are you trying to find? Make a plan. How can you solve this problem? Solve the problem. Carry out your plan. Look back. Could you have solved this problem a different way? © Enslow Publishers, Inc. Sheets are reproducible for educational use only. 6 Name _________________________________ Date ___________________ Comparison Sentences Here’s the problem. Jupiter is about 5 AUs from the Sun. Neptune is 30 AUs from the Sun. Write a sentence using the words “as far as” to compare the distances from Jupiter to the Sun and from Neptune to the Sun. Read and understand the problem. Make a plan. Solve the problem. Look back. Want to try another one? Write a sentence using the problem above with the terms in a different order. Hint: Neptune is the first word of the sentence. © Enslow Publishers, Inc. Sheets are reproducible for educational use only. 7 Name _________________________________ Date ___________________ Logical Reasoning Here’s the problem. On Saturday night, Kory saw 3 B stars and 9 K stars. On Sunday night, he saw zero B stars and 12 K stars. Give the ratio of B stars to K stars for Saturday night, Sunday night, and the two nights combined. Read and understand the problem. What do you know? What are you trying to find? Make a plan. What plan does this problem tell you to use? Solve the problem. Carry out your plan. Look back. Could you have solved this problem a different way? © Enslow Publishers, Inc. Sheets are reproducible for educational use only. 8 Name _________________________________ Date ___________________ Logical Reasoning Here’s the problem. On Monday, astronauts in training spent 4 hours in a classroom and 3 hours in a flight simulator. On Tuesday, they spent 2 hours in a classroom and 6 hours in the simulator. Give the ratio of classroom hours to simulator hours for Monday, Tuesday, and the two days combined. Read and understand the problem. Make a plan. Solve the problem. Look back. Want to try another one? In a class of 32 students who took a test on rocket fuel types, the grades were as follows: 24 As, 4 Bs, 3 Cs, and 1 D. Give the ratio of students who earned an A to the entire class, students who earned a B to the entire class, and students who earned an A or a B to the entire class. © Enslow Publishers, Inc. Sheets are reproducible for educational use only. 9 Name _________________________________ Date ___________________ Equivalent Ratios Here’s the problem. A dog that weighs 12 pounds on Earth would weigh only 2 pounds on the Moon. Using the same ratio, how much would a person who weighs 180 pounds on Earth weigh on the Moon? Read and understand the problem. What do you know? What are you trying to find? Make a plan. What kind of model can you use to solve this problem? Solve the problem. Carry out your plan. Look back. Does your answer make sense? © Enslow Publishers, Inc. Sheets are reproducible for educational use only. 10 Name _________________________________ Date ___________________ Equivalent Ratios Here’s the problem. A dog that weighs 10 pounds on Earth would weigh 25 pounds on Jupiter. Using the same ratio, how much would a person who weighs 140 pounds on Earth weigh on Jupiter? Read and understand the problem. Make a plan. Solve the problem. Look back. Want to try another one? A student who can lift 60 pounds on Earth can lift 1,000 pounds on a certain planet. Using the same ratio, how much can a weightlifter lift on that planet if he can lift 300 pounds on Earth? © Enslow Publishers, Inc. Sheets are reproducible for educational use only. 11 Name _________________________________ Date ___________________ Use Mental Math Here’s the problem. One night Charla saw 16 flying objects, but she could not identify 4. Write the ratio of the unidentified flying objects to the total number of flying objects she saw. Write the ratio in lowest terms. Read and understand the problem. What do you know? What are you trying to find? Make a plan. What plan does the problem tell you to use? Solve the problem. Carry out your plan. Look back. Does your answer make sense? What other plan could you use to solve this problem? © Enslow Publishers, Inc. Sheets are reproducible for educational use only. 12 Name _________________________________ Date ___________________ Use Mental Math Here’s the problem. One night David identified 25 stars and 5 constellations by name. Write the ratio of stars to constellations he identified that night. Write the ratio in lowest terms. Read and understand the problem. Make a plan. Solve the problem. Look back. Want to try another one? Jennifer set up her camera to take 50 pictures of the Moon at ten-minute intervals. In 20 of the pictures, the Moon was hidden by clouds. Write the ratio in lowest terms of pictures with the Moon hidden to total pictures. © Enslow Publishers, Inc. Sheets are reproducible for educational use only. 13 Name _________________________________ Date ___________________ Use Paper and Pencil Here’s the problem. A rocket uses 260 kilograms of fuel in 60 seconds. Write a rate to show how fast the fuel is used by the rocket. Make sure the rate is in lowest terms. Read and understand the problem. What do you know? What are you trying to find? Make a plan. How can you solve this problem? Solve the problem. Carry out your plan. Look back. Did you include units in your answer? What other plan could you use to solve this problem? © Enslow Publishers, Inc. Sheets are reproducible for educational use only. 14 Name _________________________________ Date ___________________ Use Paper and Pencil Here’s the problem. A rocket flew 135 kilometers in 15 seconds. Write a rate to tell how fast the rocket was moving. Make sure the rate is in lowest terms. Read and understand the problem. Make a plan. Solve the problem. Look back. Want to try another one? The diameter of Mercury is 4,800 km. The diameter of Mars is 6,800 km. Write the ratio in lowest terms of Mercury’s diameter to Mars’ diameter. © Enslow Publishers, Inc. Sheets are reproducible for educational use only. 15 Name _________________________________ Date ___________________ Use a Calculator Here’s the problem. The glow of a huge explosion in space took 10.6 seconds to be seen on Earth. The explosion happened 1,974,568 miles from Earth. Write a unit rate to the nearest mile for the speed of the light. Read and understand the problem. What do you know? What are you trying to find? Make a plan. How can you solve this problem? Solve the problem. Carry out your plan. Look back. Did you use mental math, paper-and-pencil, or a calculator? Why? © Enslow Publishers, Inc. Sheets are reproducible for educational use only. 16 Name _________________________________ Date ___________________ Use a Calculator Here’s the problem. A rocket took 16 hours to travel 282,272 miles in space. Write a unit rate for the average speed of the rocket. Read and understand the problem. Make a plan. Solve the problem. Look back. Want to try another one? A total of 250,560 hours were spent by 116 people preparing a rocket for a flight into space. Write a unit rate for the amount of time spent per person. © Enslow Publishers, Inc. Sheets are reproducible for educational use only. 17 Name _________________________________ Date ___________________ Multiplying Rates Here’s the problem. Uranus spins at a rate of 17 hours per full rotation. How many hours does Uranus take to rotate 6 times? Read and understand the problem. What do you know? What are you trying to find? Make a plan. How can you solve this problem? Solve the problem. Carry out your plan. Look back. Is the math correct? What other plan could you use to solve this problem? © Enslow Publishers, Inc. Sheets are reproducible for educational use only. 18 Name _________________________________ Date ___________________ Multiplying Rates Here’s the problem. Venus orbits the Sun at a rate of 225 days per revolution. How long does Venus take to orbit the Sun twice? Read and understand the problem. Make a plan. Solve the problem. Look back. Want to try another one? Uranus orbits the Sun at a rate of 84 years per revolution. How long does Uranus take to orbit the Sun 3 times? © Enslow Publishers, Inc. Sheets are reproducible for educational use only. 19 Name _________________________________ Date ___________________ Use a Formula Here’s the problem. A rocket traveled at a rate of 18,500 miles per hour for 4 hours. How many miles did it travel? Use the formula distance = speed ⫻ time, or d = st. Read and understand the problem. What do you know? What are you trying to find? Make a plan. What plan does the problem tell you to use? Solve the problem. Carry out your plan. Look back. Does your answer make sense? What other plan could you use to solve this problem? © Enslow Publishers, Inc. Sheets are reproducible for educational use only. 20 Name _________________________________ Date ___________________ Use a Formula Here’s the problem. A rocket traveled at a rate of 12,200 miles per hour for 30 hours. How many miles did it travel? Use the formula distance = speed ⫻ time, or d = st. Read and understand the problem. Make a plan. Solve the problem. Look back. Want to try another one? The formula for the distance around a planet at its equator (circumference) is C = 2 r, where r is the radius at the equator. The symbol is called pi, and is approximately 3.14. The radius of Mars at the equator is about 2,107 miles. To the nearest whole mile, find the distance around Mars at the equator. © Enslow Publishers, Inc. Sheets are reproducible for educational use only. 21 Name _________________________________ Date ___________________ Change Units Here’s the problem. A rocket travels at a speed of 310 kilometers per minute. What is the speed of the rocket in kilometers per hour? Read and understand the problem. What do you know? What are you trying to find? Make a plan. How can you solve this problem? Solve the problem. Carry out your plan. Look back. Check your math. © Enslow Publishers, Inc. Sheets are reproducible for educational use only. 22 Name _________________________________ Date ___________________ Change Units Here’s the problem. Mercury spins at a rate of 59 days per full rotation. What is Mercury’s rate in hours per rotation? Read and understand the problem. Make a plan. Solve the problem. Look back. Want to try another one? The speed of sound is about 1,235,000 meters per hour. To the nearest whole number, what is the speed of sound in meters per second? (Be careful, you are changing hours to seconds!) © Enslow Publishers, Inc. Sheets are reproducible for educational use only. 23 Name _________________________________ Date ___________________ Use a Model Here’s the problem. A teacher splits her class into groups to study Mars and its moons. They have models in a ratio of 2 plastic moons for every one plastic Mars. If they use 27 plastic pieces in all, how many groups are there if each group gets one Mars? Use a model to help solve this problem. Read and understand the problem. What do you know? What are you trying to find? Make a plan. What plan does this problem tell you to use? Solve the problem. Carry out your plan. Look back. Does your answer make sense? © Enslow Publishers, Inc. Sheets are reproducible for educational use only. 24 Name _________________________________ Date ___________________ Use a Model Here’s the problem. Hilda saw 3 B stars on Saturday for every B star she saw on Friday. If she saw 16 B stars on both nights combined, how many B stars did she see on Friday? Use a model to help solve this problem. Read and understand the problem. Make a plan. Solve the problem. Look back. Want to try another one? A science classroom has three types of solar system models per two tables of students. There are 15 models in all. How many tables of students are there? Use a model to help solve this problem. © Enslow Publishers, Inc. Sheets are reproducible for educational use only. 25 Name _________________________________ Date ___________________ Write a Proportion Here’s the problem. Jupiter takes about 10 years to orbit the Sun. Saturn takes about 30 years. Is 1 to 3 the correct ratio for the time it takes Jupiter to orbit the Sun to the time it takes Saturn to orbit the Sun? Write a proportion to solve this problem. Read and understand the problem. What do you know? What are you trying to find? Make a plan. What plan does this problem tell you to use? Solve the problem. Carry out your plan. Look back. Does your answer make sense? © Enslow Publishers, Inc. Sheets are reproducible for educational use only. 26 Name _________________________________ Date ___________________ Write a Proportion Here’s the problem. If you weigh 100 pounds on Earth, your weight on Mars would be about 40 pounds. If a little boy weighs 30 pounds on Earth, would his weight on Mars be about 14 pounds? Use a proportion to solve this problem. Read and understand the problem. Make a plan. Solve the problem. Look back. Want to try another one? A rocket uses 400 kilograms of fuel every 2 minutes. Jack says for a 5-minute flight, it will use 1,200 kilograms of fuel. Is this correct? Use a proportion to solve this problem. © Enslow Publishers, Inc. Sheets are reproducible for educational use only. 27 Name _________________________________ Date ___________________ Scale Drawings Here’s the problem. The diameter of Mars is about 7,000 kilometers. Mercury’s diameter is about 5,000 kilometers. Becca made a scale drawing of the solar system. Her drawing of Mars has a diameter of 14 millimeters. What should the diameter of her drawing of Mercury be? Read and understand the problem. What do you know? What are you trying to find? Make a plan. How can you solve this problem? Solve the problem. Carry out your plan. Look back. Does your answer make sense? Is the math correct? © Enslow Publishers, Inc. Sheets are reproducible for educational use only. 28 Name _________________________________ Date ___________________ Scale Drawings Here’s the problem. Earth is about 150 million kilometers from the Sun. Uranus is about 3,000 million kilometers from the Sun. In a scale drawing of the solar system, Earth is drawn 45 millimeters from the Sun. How far should Uranus be drawn from the Sun? Read and understand the problem. Make a plan. Solve the problem. Look back. Want to try another one? The Moon’s diameter is about 3,500 kilometers. The diameter of the dwarf planet Ceres is about 950 kilometers. A scale drawing of the Moon has a diameter of 70 millimeters. What should the diameter of the drawing of Ceres be? © Enslow Publishers, Inc. Sheets are reproducible for educational use only. 29 Name _________________________________ Date ___________________ Cross Multiply Here’s the problem. For every 7 parts of Earth’s surface that are covered by water, there are 3 parts covered by land. Elly is making a globe using small paper squares. She has 280 blue squares for the water, and 90 green squares for the land. Are the squares in the correct ratio? Read and understand the problem. What do you know? What are you trying to find? Make a plan. How can you solve this problem? Solve the problem. Carry out your plan. Look back. Does your answer make sense? Is the math correct? © Enslow Publishers, Inc. Sheets are reproducible for educational use only. 30 Name _________________________________ Date ___________________ Cross Multiply Here’s the problem. Jupiter is about 4 AUs from Earth. Neptune is about 30 AUs from Earth. In a drawing of the planets, Jupiter is drawn 6 inches from Earth and Neptune is 45 inches from Earth. Are the distances in the correct ratio? Read and understand the problem. Make a plan. Solve the problem. Look back. Want to try another one? For every 3 days on a spaceflight, each astronaut on a mission spent 28 hours monitoring equipment. If the mission was 24 days long, did each astronaut monitor equipment for 224 hours? © Enslow Publishers, Inc. Sheets are reproducible for educational use only. 31 Name _________________________________ Date ___________________ Scale Models Here’s the problem. In a scale model of the Solar System, Earth is 3 inches from the Sun and Neptune is 90 inches from the Sun. The actual distance from Neptune to the Sun is about 2,790 million miles. How many millions of miles is Earth from the Sun? Read and understand the problem. What do you know? What are you trying to find? Make a plan. How can you solve this problem? Solve the problem. Carry out your plan. Look back. Check your math. © Enslow Publishers, Inc. Sheets are reproducible for educational use only. 32 Name _________________________________ Date ___________________ Scale Models Here’s the problem. The diameter of Saturn is 120,000 kilometers. The largest dwarf planet in our solar system, Eris, has a diameter of about 2,500 kilometers. In a scale model of the solar system, Saturn has a diameter of 48 centimeters. What should the diameter of the model of Eris be? Read and understand the problem. Make a plan. Solve the problem. Look back. Want to try another one? In a one-kilometer-sized model of the Solar System, Venus is 18 meters from the Sun and Jupiter is 130 meters from the Sun. The actual distance of Venus from the Sun is about 108 million kilometers. About what is the actual distance from Jupiter to the Sun? © Enslow Publishers, Inc. Sheets are reproducible for educational use only. 33 Name _________________________________ Date ___________________ Estimation Here’s the problem. Most meteorites are gray and hard. A few are black and fragile. In one area, 12,876 meteorites were found. If 3 of every 1,000 meteorites found are the black fragile type, about how many of those found are the black fragile type? Read and understand the problem. What do you know? What are you trying to find? Make a plan. What plan does the problem ask you to use? Solve the problem. Carry out your plan. Look back. Does your answer make sense? Why or why not? © Enslow Publishers, Inc. Sheets are reproducible for educational use only. 34 Name _________________________________ Date ___________________ Estimation Here’s the problem. The distance around Earth at the equator is 24,901 miles. If a jet is flying at 1,000 miles per hour, how long will it take to fly the distance around the Earth? Read and understand the problem. Make a plan. Solve the problem. Look back. Want to try another one? An explosion in space happened 617,204 miles from Earth. The speed of light is about 186,282 miles per second. About how long will it be before the explosion can be seen from Earth? © Enslow Publishers, Inc. Sheets are reproducible for educational use only. 35 Answers Problem-Solving Steps Page 2: Each astronaut can choose 9 snacks. Page 3: Each astronaut needs 800 ounces of water. Want to try another one? 60 pounds of personal items can be taken on the mission. Read a Table Page 4: The ratio of planets made of gas to total planets is 4 to 8. Page 5: The ratio of planets made of gas to planets made of rock is 4 to 4. Want to try another one? The ratio of total planets to planets made of rock is 8 to 4. Comparison Sentences Page 6: Jupiter is 5 times as far as Earth from the Sun. Page 7: Jupiter is 5/30 (or 1/6) as far as Neptune from the Sun. Want to try another one? Neptune is 30/5 (or 6) times as far as Jupiter from the Sun. Logical Reasoning Page 8: The ratio of B stars to K stars Kory saw was 3 to 9 on Saturday night, 0 to 12 on Sunday night, and 3 to 21 on the two nights combined. Page 9: The ratio of classroom hours to simulator hours was 4 to 3 on Monday, 2 to 6 on Tuesday, and 6 to 9 on the two days combined.. Want to try another one? The ratio of students who earned an A to the entire class was 24 to 32. The ratio of students who earned a B to the entire class was 4 to 32. The ratio of students who earned an A or a B to the entire class was 28 to 32. © Enslow Publishers, Inc. Sheets are reproducible for educational use only. 36 Equivalent Ratios Page 10: A person who weighs 180 pounds on Earth would weigh 30 pounds on the Moon. Page 11: A person who weighs 140 pounds on Earth would weigh 350 pounds on Jupiter. Want to try another one? The weightlifter can lift 5,000 pounds on that planet. Use Mental Math Page 12: The ratio of unidentified flying objects to total flying objects is 1: 4. Page 13: The ratio of stars to constellations he identified that night is 5:1. Want to try another one? The ratio of pictures with the Moon hidden to total pictures is 2 :5. Use Paper and Pencil Page 14: The rocket used fuel at a rate of 13 kilograms per 3 seconds. Page 15: The rocket was moving at 9 kilometers per second. Want to try another one? The ratio of Mercury’s diameter to Mars’ diameter is 12 to 17. Use a Calculator Page 16: The speed of the light was 186,280 miles per second. Page 17: The average speed of the rocket was 17,642 miles per hour. Want to try another one? The average time spent was 2,160 hours per person. Multiplying Rates Page 18: Uranus takes 102 hours to rotate 6 times. Page 19: Venus takes 450 days to orbit the Sun twice. Want to try another one? Uranus takes 252 years to orbit the Sun 3 times. © Enslow Publishers, Inc. Sheets are reproducible for educational use only. 37 Use a Formula Page 20: The rocket traveled 74,000 miles. Page 21: The rocket traveled 366,000 miles. Want to try another one? Mars is about 13,232 miles around at the equator. Change Units Page 22: The rocket speed is 18,600 kilometers per hour. Page 23: Mercury spins at a rate of 1,416 hours per full rotation. Want to try another one? The speed of sound is about 343 meters per second. Use a Model Page 24: The class is split into 9 groups. Page 25: Hilda saw 4 B stars on Friday. Want to try another one? There are ten tables of students. Write a Proportion Page 26: Yes, the ratio of times for Jupiter and Saturn to orbit the Sun is 1 to 3. Page 27: No, the little boy would weigh about 12 pounds on Mars. Want to try another one? No, for a 5-minute flight, the rocket will use 1,000 kilograms of fuel. Scale Drawings Page 28: Becca’s drawing of Mercury should have a diameter of 10 millimeters. Page 29: Uranus should be drawn 900 millimeters from the Sun. Want to try another one? The diameter of Ceres in the drawing should be 19 millimeters. © Enslow Publishers, Inc. Sheets are reproducible for educational use only. 38 Cross Multiply Page 30: Elly does not have the correct ratio of blue to green paper squares. Page 31: Yes, the distances are in the correct ratio. Want to try another one? Yes, each astronaut spent 224 hours monitoring equipment. Scale Models Page 32: Earth is 93 million miles from the Sun. Page 33: The diameter of the model of Eris should be 1 centimeter. Want to try another one? Jupiter is about 780 million kilometers from the Sun. Estimation Page 34: About 36 of the meteorites are the black fragile type. Page 35: It will take about 25 hours. Want to try another one? It will be about 3 seconds before the explosion can be seen from Earth. © Enslow Publishers, Inc. Sheets are reproducible for educational use only. 39