space word problems starring ratios and proportions€¦ · space word problems starring ratios and...

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.

1

Math Word Problems Solved Reproducible Worksheets

Reproducible Worksheets for:

Space Word Problems Starring Ratios and Proportions

These worksheets practice math concepts explained in SSppaaccee WWoorrdd PPrroobblleemmssSSttaarrrriinngg RRaattiiooss aanndd PPrrooppoorrttiioonnss (ISBN: 978-0-7660-2921-7), written by RReebbeeccccaaWWiinnggaarrdd--NNeellssoonn.

MMaatthh WWoorrdd PPrroobblleemmss SSoollvveedd reproducible worksheets are designed to help teachers,parents, and tutors use the books from the Math Word Problems Solved series in theclassroom and the home. The answers to the problems are contained in the Answerssection starting on page 36.

Teachers, librarians, tutors, and parents are granted permission and encouraged tomake 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 MMaatthh WWoorrdd PPrroobblleemmss SSoollvveedd series todownload worksheets for the following titles:

AAmmuusseemmeenntt PPaarrkk WWoorrdd PPrroobblleemmss FFuunn FFoooodd WWoorrdd PPrroobblleemmssSSttaarrrriinngg PPrree--AAllggeebbrraa SSttaarrrriinngg FFrraaccttiioonnss

978-0-7660-2922-4 978-0-7660-2919-4

AAnniimmaall WWoorrdd PPrroobblleemmss SSppaaccee WWoorrdd PPrroobblleemmssSSttaarrrriinngg AAddddiittiioonn aanndd SSuubbttrraaccttiioonn SSttaarrrriinngg RRaattiiooss aanndd PPrrooppoorrttiioonnss

978-0-7660-2917-0 978-0-7660-2921-7

BBiigg TTrruucckk aanndd CCaarr WWoorrdd PPrroobblleemmss SSppoorrttss WWoorrdd PPrroobblleemmss SSttaarrrriinngg MMuullttiipplliiccaattiioonn aanndd DDiivviissiioonn SSttaarrrriinngg DDeecciimmaallss aanndd PPeerrcceennttss

978-0-7660-2918-7 978-0-7660-2920-0

Titles in this series can be purchased directly from:

Enslow Publishers, Inc.40 Industrial Road, Box 398Berkeley Heights, NJ 07922-0398 Phone: 1-800-398-2504email: [email protected] Page: http://www.enslow.com

Problem-Solving Steps

HHeerree’’ss tthhee pprroobblleemm..

A three-day spaceflight is being planned. Each astronautcan pick 3 snacks per day. At this rate, how manysnacks can each astronaut choose for the entire flight?RReeaadd aanndd uunnddeerrssttaanndd tthhee pprroobblleemm..What do you know?

What are you trying to find?

MMaakkee aa ppllaann..How can you solve this problem?

SSoollvvee tthhee pprroobblleemm..Carry out your plan.

LLooookk bbaacckk..Does your answer make sense?Is the math correct?

What other plan could you use to solve this problem?

Name _________________________________ Date ___________________

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© Enslow Publishers, Inc. Sheets are reproducible for educational use only.

Problem-Solving Steps


A ten-day spaceflight is being planned. Each astronautneeds 80 ounces of water per day. At this rate, howmany ounces of water does each astronaut need for theentire flight?RReeaadd aanndd uunnddeerrssttaanndd tthhee pprroobblleemm..

MMaakkee aa ppllaann..

SSoollvvee tthhee pprroobblleemm..

LLooookk bbaacckk..

Want to try another one? Five astronauts are going on a mission. Each astronaut haspermission to take personal items that weigh up to 12 pounds.How many pounds of personal items can be taken on the mission?

Name _________________________________ Date ___________________

3


Read a Table


There are 8 planets in our solarsystem. Some of the planets aremade of rock. Others are made ofgas. Use the table to find the ratioof the planets made of gas to thetotal planets in our solar system.RReeaadd aanndd uunnddeerrssttaanndd tthhee pprroobblleemm..What do you know?


MMaakkee aa ppllaann..What plan does this problem tell you to use?


LLooookk bbaacckk..Could you have answered this problem a different way?

Name _________________________________ Date ___________________

4


Planet Material

Earth rock

Jupiter gas

Mars rock

Mercury rock

Neptune gas

Saturn gas

Uranus gas

Venus rock

Read a Table


There are 8 planets in our solarsystem. Some of the planets aremade of rock. Others are made ofgas. Use the table to find the ratioof the planets made of gas to theplanets made of rock.RReeaadd aanndd uunnddeerrssttaanndd tthhee pprroobblleemm..



LLooookk bbaacckk..

Want to try another one? Use the table to find the ratio of the total planets to the planetsmade of rock.

Name _________________________________ Date ___________________

5


Planet Material

Earth rock

Jupiter gas

Mars rock

Mercury rock

Neptune gas

Saturn gas

Uranus gas

Venus rock

Comparison Sentences


The distance from Earth to the Sun is called anastronomical unit (AU). Jupiter is about 5 AUsfrom the Sun. Write a sentence using the words“as far as” to compare the distances from Jupiterand Earth to the Sun.RReeaadd aanndd uunnddeerrssttaanndd tthhee pprroobblleemm..What do you know?




LLooookk bbaacckk..Could you have solved this problem a different way?

Name _________________________________ Date ___________________

6


Comparison Sentences


Jupiter is about 5 AUs from the Sun. Neptune is30 AUs from the Sun. Write a sentence using thewords “as far as” to compare the distances fromJupiter to the Sun and from Neptune to the Sun.RReeaadd aanndd uunnddeerrssttaanndd tthhee pprroobblleemm..



LLooookk bbaacckk..

Want to try another one? Write a sentence using the problem above with the terms in adifferent order. Hint: Neptune is the first word of the sentence.

Name _________________________________ Date ___________________

7


Logical Reasoning


On Saturday night, Kory saw 3 B stars and 9 Kstars. On Sunday night, he saw zero B stars and12 K stars. Give the ratio of B stars to K stars forSaturday night, Sunday night, and the two nightscombined.RReeaadd aanndd uunnddeerrssttaanndd tthhee pprroobblleemm..What do you know?




LLooookk bbaacckk..Could you have solved this problem a different way?

Name _________________________________ Date ___________________

8


Logical Reasoning


On Monday, astronauts in training spent 4 hours in aclassroom and 3 hours in a flight simulator. On Tuesday,they spent 2 hours in a classroom and 6 hours in thesimulator. Give the ratio of classroom hours to simulatorhours for Monday, Tuesday, and the two days combined.RReeaadd aanndd uunnddeerrssttaanndd tthhee pprroobblleemm..



LLooookk bbaacckk..

Want to try another one?In a class of 32 students who took a test on rocket fuel types, thegrades were as follows: 24 As, 4 Bs, 3 Cs, and 1 D. Give the ratioof students who earned an A to the entire class, students whoearned a B to the entire class, and students who earned an A or aB to the entire class.

Name _________________________________ Date ___________________

9


Equivalent Ratios


A dog that weighs 12 pounds on Earth wouldweigh only 2 pounds on the Moon. Using thesame ratio, how much would a person whoweighs 180 pounds on Earth weigh on the Moon?RReeaadd aanndd uunnddeerrssttaanndd tthhee pprroobblleemm..What do you know?


MMaakkee aa ppllaann..What kind of model can you use to solve this problem?


LLooookk bbaacckk..Does your answer make sense?

Name _________________________________ Date ___________________

10


Equivalent Ratios


A dog that weighs 10 pounds on Earth wouldweigh 25 pounds on Jupiter. Using the sameratio, how much would a person who weighs 140 pounds on Earth weigh on Jupiter?RReeaadd aanndd uunnddeerrssttaanndd tthhee pprroobblleemm..



LLooookk bbaacckk..

Want to try another one?A student who can lift 60 pounds on Earth can lift 1,000 poundson a certain planet. Using the same ratio, how much can aweightlifter lift on that planet if he can lift 300 pounds on Earth?

Name _________________________________ Date ___________________

11


Use Mental Math


One night Charla saw 16 flying objects, but she could not identify 4. Write the ratio of the unidentified flyingobjects to the total number of flying objects she saw. Write the ratio in lowest terms.RReeaadd aanndd uunnddeerrssttaanndd tthhee pprroobblleemm..What do you know?


MMaakkee aa ppllaann..What plan does the problem tell you to use?




Name _________________________________ Date ___________________

12


Use Mental Math


One night David identified 25 stars and 5 constellationsby name. Write the ratio of stars to constellations heidentified that night. Write the ratio in lowest terms.RReeaadd aanndd uunnddeerrssttaanndd tthhee pprroobblleemm..



LLooookk bbaacckk..

Want to try another one?

Jennifer set up her camera to take 50 pictures of the Moon atten-minute intervals. In 20 of the pictures, the Moon was hiddenby clouds. Write the ratio in lowest terms of pictures with theMoon hidden to total pictures.

Name _________________________________ Date ___________________

13


Use Paper and Pencil


A rocket uses 260 kilograms of fuel in 60 seconds. Writea rate to show how fast the fuel is used by the rocket.Make sure the rate is in lowest terms.RReeaadd aanndd uunnddeerrssttaanndd tthhee pprroobblleemm..What do you know?




LLooookk bbaacckk..Did you include units in your answer?


Name _________________________________ Date ___________________

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Use Paper and Pencil


A rocket flew 135 kilometers in 15 seconds. Write a rateto tell how fast the rocket was moving. Make sure therate is in lowest terms.RReeaadd aanndd uunnddeerrssttaanndd tthhee pprroobblleemm..



LLooookk bbaacckk..


The diameter of Mercury is 4,800 km. The diameter of Mars is6,800 km. Write the ratio in lowest terms of Mercury’s diameterto Mars’ diameter.

Name _________________________________ Date ___________________

15


Use a Calculator


The glow of a huge explosion in space took 10.6 seconds to be seen on Earth. The explosionhappened 1,974,568 miles from Earth. Write a unitrate to the nearest mile for the speed of the light.RReeaadd aanndd uunnddeerrssttaanndd tthhee pprroobblleemm..What do you know?




LLooookk bbaacckk..Did you use mental math, paper-and-pencil, or a calculator? Why?

Name _________________________________ Date ___________________

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Use a Calculator


A rocket took 16 hours to travel 282,272 miles in space.Write a unit rate for the average speed of the rocket.RReeaadd aanndd uunnddeerrssttaanndd tthhee pprroobblleemm..



LLooookk bbaacckk..


A total of 250,560 hours were spent by 116 people preparing arocket for a flight into space. Write a unit rate for the amount oftime spent per person.

Name _________________________________ Date ___________________

17


Multiplying Rates


Uranus spins at a rate of 17 hours per full rotation.How many hours does Uranus take to rotate 6 times?RReeaadd aanndd uunnddeerrssttaanndd tthhee pprroobblleemm..What do you know?




LLooookk bbaacckk..

Is the math correct?


Name _________________________________ Date ___________________

18


Multiplying Rates


Venus orbits the Sun at a rate of 225 days per revolution.How long does Venus take to orbit the Sun twice? RReeaadd aanndd uunnddeerrssttaanndd tthhee pprroobblleemm..



LLooookk bbaacckk..


Uranus orbits the Sun at a rate of 84 years per revolution. Howlong does Uranus take to orbit the Sun 3 times?

Name _________________________________ Date ___________________

19


Use a Formula


A rocket traveled at a rate of 18,500 miles per hour for4 hours. How many miles did it travel? Use the formuladistance = speed �� time, or d = st.RReeaadd aanndd uunnddeerrssttaanndd tthhee pprroobblleemm..What do you know?


MMaakkee aa ppllaann..What plan does the problem tell you to use?


LLooookk bbaacckk..

Does your answer make sense?


Name _________________________________ Date ___________________

20


Use a Formula


A rocket traveled at a rate of 12,200 miles per hour for30 hours. How many miles did it travel? Use theformula distance = speed �� time, or d = st.RReeaadd aanndd uunnddeerrssttaanndd tthhee pprroobblleemm..



LLooookk bbaacckk..


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 radiusof Mars at the equator is about 2,107 miles. To the nearest wholemile, find the distance around Mars at the equator.

Name _________________________________ Date ___________________

21


Change Units


A rocket travels at a speed of 310 kilometers per minute.What is the speed of the rocket in kilometers per hour?RReeaadd aanndd uunnddeerrssttaanndd tthhee pprroobblleemm..What do you know?




LLooookk bbaacckk..Check your math.

Name _________________________________ Date ___________________

22


Change Units


Mercury spins at a rate of 59 days per full rotation. Whatis Mercury’s rate in hours per rotation?RReeaadd aanndd uunnddeerrssttaanndd tthhee pprroobblleemm..



LLooookk bbaacckk..


The speed of sound is about 1,235,000 meters per hour. To thenearest whole number, what is the speed of sound in meters persecond? (Be careful, you are changing hours to seconds!)

Name _________________________________ Date ___________________

23


Use a Model


A teacher splits her class into groups to study Mars andits moons. They have models in a ratio of 2 plasticmoons for every one plastic Mars. If they use 27 plasticpieces in all, how many groups are there if each groupgets one Mars? Use a model to help solve this problem.RReeaadd aanndd uunnddeerrssttaanndd tthhee pprroobblleemm..What do you know?





Name _________________________________ Date ___________________

24


Use a Model


Hilda saw 3 B stars on Saturday for every B star shesaw on Friday. If she saw 16 B stars on both nightscombined, how many B stars did she see on Friday?Use a model to help solve this problem.RReeaadd aanndd uunnddeerrssttaanndd tthhee pprroobblleemm..



LLooookk bbaacckk..


A science classroom has three types of solar system models pertwo tables of students. There are 15 models in all. How manytables of students are there? Use a model to help solve thisproblem.

Name _________________________________ Date ___________________

25


Write a Proportion


Jupiter takes about 10 years to orbit the Sun. Saturntakes about 30 years. Is 1 to 3 the correct ratio for thetime it takes Jupiter to orbit the Sun to the time it takesSaturn to orbit the Sun? Write a proportion to solve thisproblem.RReeaadd aanndd uunnddeerrssttaanndd tthhee pprroobblleemm..

What do you know?





Name _________________________________ Date ___________________

26


Write a Proportion


If you weigh 100 pounds on Earth, your weight on Mars would be about 40 pounds. If a little boy weighs30 pounds on Earth, would his weight on Mars be about14 pounds? Use a proportion to solve this problem.RReeaadd aanndd uunnddeerrssttaanndd tthhee pprroobblleemm..



LLooookk bbaacckk..


A rocket uses 400 kilograms of fuel every 2 minutes. Jack says fora 5-minute flight, it will use 1,200 kilograms of fuel. Is thiscorrect? Use a proportion to solve this problem.

Name _________________________________ Date ___________________

27


Scale Drawings


The diameter of Mars is about 7,000 kilometers.Mercury’s diameter is about 5,000 kilometers. Beccamade a scale drawing of the solar system. Her drawingof Mars has a diameter of 14 millimeters. What shouldthe diameter of her drawing of Mercury be?RReeaadd aanndd uunnddeerrssttaanndd tthhee pprroobblleemm..What do you know?





Name _________________________________ Date ___________________

28


Scale Drawings


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 drawn45 millimeters from the Sun. How far should Uranus bedrawn from the Sun?RReeaadd aanndd uunnddeerrssttaanndd tthhee pprroobblleemm..



LLooookk bbaacckk..


The Moon’s diameter is about 3,500 kilometers. The diameter ofthe dwarf planet Ceres is about 950 kilometers. A scale drawingof the Moon has a diameter of 70 millimeters. What should thediameter of the drawing of Ceres be?

Name _________________________________ Date ___________________

29


Cross Multiply


For every 7 parts of Earth’s surface that are covered bywater, there are 3 parts covered by land. Elly is makinga globe using small paper squares. She has 280 bluesquares for the water, and 90 green squares for the land. Are the squares in the correct ratio?RReeaadd aanndd uunnddeerrssttaanndd tthhee pprroobblleemm..What do you know?





Name _________________________________ Date ___________________

30


Cross Multiply


Jupiter is about 4 AUs from Earth. Neptune is about 30 AUs from Earth. In a drawing of the planets, Jupiteris drawn 6 inches from Earth and Neptune is 45 inchesfrom Earth. Are the distances in the correct ratio?RReeaadd aanndd uunnddeerrssttaanndd tthhee pprroobblleemm..



LLooookk bbaacckk..

Want to try another one?For every 3 days on a spaceflight, each astronaut on a missionspent 28 hours monitoring equipment. If the mission was 24 days long, did each astronaut monitor equipment for 224 hours?

Name _________________________________ Date ___________________

31


Scale Models


In a scale model of the Solar System, Earth is 3 inchesfrom the Sun and Neptune is 90 inches from the Sun.The actual distance from Neptune to the Sun is about2,790 million miles. How many millions of miles isEarth from the Sun?RReeaadd aanndd uunnddeerrssttaanndd tthhee pprroobblleemm..What do you know?




LLooookk bbaacckk..Check your math.

Name _________________________________ Date ___________________

32


Scale Models


The diameter of Saturn is 120,000 kilometers. The largestdwarf planet in our solar system, Eris, has a diameter ofabout 2,500 kilometers. In a scale model of the solarsystem, Saturn has a diameter of 48 centimeters. What should the diameter of the model of Eris be?

RReeaadd aanndd uunnddeerrssttaanndd tthhee pprroobblleemm..



LLooookk bbaacckk..


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 millionkilometers. About what is the actual distance from Jupiter to theSun?

Name _________________________________ Date ___________________

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Estimation


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 fragiletype, about how many of those found are the blackfragile type?RReeaadd aanndd uunnddeerrssttaanndd tthhee pprroobblleemm..What do you know?


MMaakkee aa ppllaann..What plan does the problem ask you to use?



Why or why not?

Name _________________________________ Date ___________________

34


Estimation


The distance around Earth at the equator is 24,901miles. If a jet is flying at 1,000 miles per hour, how longwill it take to fly the distance around the Earth?RReeaadd aanndd uunnddeerrssttaanndd tthhee pprroobblleemm..



LLooookk bbaacckk..


An explosion in space happened 617,204 miles from Earth. Thespeed of light is about 186,282 miles per second. About howlong will it be before the explosion can be seen from Earth?

Name _________________________________ Date ___________________

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AAnnsswweerrss

PPrroobblleemm--SSoollvviinngg SStteeppssPage 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.

RReeaadd aa TTaabblleePage 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.

CCoommppaarriissoonn SSeenntteenncceessPage 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.

LLooggiiccaall RReeaassoonniinnggPage 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.

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EEqquuiivvaalleenntt RRaattiioossPage 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.

UUssee MMeennttaall MMaatthhPage 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.

UUssee PPaappeerr aanndd PPeenncciillPage 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.

UUssee aa CCaallccuullaattoorrPage 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.

MMuullttiippllyyiinngg RRaatteessPage 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.

37


UUssee aa FFoorrmmuullaaPage 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.

CChhaannggee UUnniittssPage 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.

UUssee aa MMooddeellPage 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.

WWrriittee aa PPrrooppoorrttiioonnPage 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.

SSccaallee DDrraawwiinnggssPage 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.

38


CCrroossss MMuullttiippllyyPage 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.

SSccaallee MMooddeellssPage 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.

EEssttiimmaattiioonnPage 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.

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