Whole Numbers

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Section 1

WHOLE NUMBERS

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Operations and Place Value

NAME DATE

1–1 THERE’S A PLACE FOR EVERYTHING

Find each sum, difference, product, or quotient. Then circle the indicated place in your answer. The numbers you circle in your answers should be a digit from 0 to 9. Each odd digit should appear twice in the circled numbers, and each even digit should appear only once.

1. 345 + 296 = ______Tens place

2. 531 – 456 = ______Tens place

3. 326 × 82 – 3,164 = ______Thousands place

4. 801 × 39 = ______Hundreds place

5. 684 ÷ 36 = ______Ones place

6. 3,015 – 498 = ______Hundreds place

7. 4,079 × 86 = ______Tens place

8. 34 + 30 + 69 + 128 = ______Tens place

11. 100 × 74 ÷ 10 × 427 = ______Ten thousands place

12. 687 – 488 = ______Hundreds place

13. 5,490 ÷ 305 = ______Ones place

14. 148 × 379 = ______Ten thousands place

15. 32,886 ÷ 9 = ______Thousands place

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Copyright © 2004 by Judith A. Muschla and Gary Robert Muschla AEDATE NAME Group 3 Group 2 Group 1 Find themissingnumberssothateachgroupofproblemshassameanswer. Section 1:WholeNumbers + + + 10 , 31 5 1 738 8 9 2 5 5 8 5 – FINDINGMISSINGNUMBERS 1–2 – – – 10 , 2 6 31 5 7 8 63 0 2 4 5 5 7 × 10 × , × 3 5 8 3 1 1 2 2 5 5 5 5 Operations withWholeNumbers 2 54 10 , ,5 15 3 5 15 2 8 6 2 5 3 03_970816 Ch01.qxd 6/2/04 10:43 AM Page 4

Operations with Whole Numbers

NAME DATE

1–3 FINDING THE LARGEST AND SMALLEST

Use the numbers below to ﬁll in each box according to the directions given.

234689

Find the largest odd sum. 1. 2. + +

Find the smallest difference. It must be larger than zero. 3. 4. – –

Find the smallest product. 7. 8. × ×

Find the smallest quotient. It must be Find the largest quotient. It must be a a whole number with no remainder. whole number with no remainder.

9. 10.

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Copyright © 2004 by Judith A. Muschla and Gary Robert Muschla AEDATE NAME .Thinkofafour-digit number. Write ithere.______Doublethenumber; add10; 4. Thinkofathree-digitnumber. Write ithere.______Multiplyby3;add18;multi- 3. Startwith706.Subtract398;add25;divideby111;multiply98;42; 2. Startwith26.Multiplyby13;add222;divide16;multiply18;9; 1. Follow thedirectionsofeachnumberchain.Write youranswersinthespacesprovided. Section 1:WholeNumbers ______How doesyouranswercomparetooriginal number?______multiply by12;divide8;9;add189; divideby27;subtract13.______How doesyouranswercomparetooriginalnumber?______ply by4;subtract6;dividemultiply8;add16;6.______by 128;divide56;multiply98;subtract1,492.______by 56;subtract392;divide126;2.______– ANUMBERCHAIN 1–4 Operations withWholeNumbers 5 03_970816 Ch01.qxd 6/2/04 10:43 AM Page 6

Operations and Rounding with Whole Numbers

NAME DATE

1–5 WHICH IS GREATER?

Find all the sums, differences, products, or quotients for the problems in columns A and B. Write your answers in the spaces provided. Compare the answers in both columns for each problem, and circle the larger answer. Then follow the special directions for problems 11 through 13.

Column A Column B

1. 85 × 89 = ______86 × 88 = ______

2. 312 × 57 = ______302 × 67 = ______

3. 1,704 + 3,060 = ______1,086 + 3,704 = ______

4. 3,079 – 2,076 = ______3,790 – 2,767 = ______

5. 83 + 124 + 764 = ______384 + 345 + 96 = ______

6. 8,424 ÷ 39 = ______8,232 ÷ 42 = ______

7. 36 × 89 = ______52 × 68 = ______

10. 1,007 – 447 = ______987 – 394 = ______

11. Round the answers you have circled in column A to the nearest ten. Estimate the sum.

12. Round each answer you have circled in column B to the nearest hundred. Estimate the sum.

13. Complete: “My answer to number 12 is about ______times my answer to number 11.”

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Copyright © 2004 by Judith A. Muschla and Gary Robert Muschla AEDATE NAME and writeyouranswersinthespacesprovided. number. Onecannot.Circlethethreenumbers thatcanberoundedtothesamenumber, In eachofthefollowingsetsnumbers,threenumberscanberoundedtosame 0 ,9 ,7 ,5 ,1 ______2,515 2,551 2,479 2,497 10. Section 1:WholeNumbers .180249199251______2,501 1,999 2,459 ______1,850 9. ______3,416 3,516 3,505 3,481 8. ______843 ______907 801 750 7. 1,059 1,358 1,755 550 6. ______989 985 ______943 991 5. 365 309 284 254 4. 8 15 9 12 3. 151 149 175 158 2. 25 18 24 15 1. – THETRIOROUNDSTO. 1–6 Rounded Number Rounding Numbers 7 03_970816 Ch01.qxd 6/2/04 10:43 AM Page 8

Factors and Perfect Squares

NAME DATE

1–7 A FACT ABOUT YOU

Answer each question and ﬁnd your answer in the Answer Bank. Write the letter of your answer in the space provided before each problem. Then read down the column to discover a fact that applies to you. Some answers will be used more than once; some answers will not be used.

1. _____ It has the fewest factors of any number.

2. _____ It is the smallest number that has only two factors.

3. _____ This one-digit number has the same number of factors as the number 6.

4. _____ It is the smallest number that has six factors.

5. _____ It is the smallest three-digit perfect square.

6. _____ It is the smallest three-digit number that has only two factors.

7. _____ It is the largest two-digit perfect square that has three factors.

8. _____ It is the smallest three-digit perfect square that has nine factors.

11. _____ It is a factor of half of all the numbers.

12. _____ It is the smallest perfect square that has nine factors.

Answer Bank D. 121 N. 101 E. 16 K. 90 F. 49 U. 8 Y. 1 C. 12 O. 2 M. 80 B. 9 R. 36 T. 144 S. 4 A. 100

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Copyright © 2004 by Judith A. Muschla and Gary Robert Muschla AEDATE NAME Answer thequestions.Write youranswersinthespacesprovided. 0 Iamthelargestone-digitnumberthathasonly threefactors.______10. 2 Iamthelargestcompositenumberbefore100. ______12. Iamtheﬁrstprimenumberafter100.______11. Section 1:WholeNumbers .I am aone-digitnumber. Ifyouadd all ofmyfactors,thesumequals12.______9. Iamnotthe number 1,butIamafactorof60and35.______8. IfIam the unitsdigitofanynumber, thenthenumberisdivisible by10.______7. The number59andIaretheonlytwoprimenumbersbetween5060.______6. Iamthelargest two-digitprimenumber. ______5. Iamtheonlyevenprimenumber. ______4. Ihaveonlyonefactor. ______3. Iamthesmallesttwo-digitprimenumber. ______2. Iamthelargestone-digitprimenumber. ______1. – WHOAMI? 1–8 Factors, Primes,andComposites 9 03_970816 Ch01.qxd 6/2/04 10:43 AM Page 10

Attributes of Numbers

NAME DATE

1–9 WHICH ONE DOES NOT BELONG?

In each set of numbers, one number does not belong. Circle this number and explain why it does not belong with the others. (Consider such things as primes, composites, factors, and even spelling!) Then replace the number that does not belong with a number that does.

1. 2, 4, 7, 10 ______

______

2. 3, 5, 7, 9 ______

______

3. 12, 20, 26, 38 ______

______

4. 3, 4, 6, 9 ______

______

5. 2, 6, 12, 20 ______

______

6. 15, 20, 35, 85 ______

7. 9, 16, 20, 25 ______

______

8. 313, 1001, 111, 1313 ______

______

9. 3, 13, 31, 47 ______

______

10. 28, 30, 31, 32 ______

______

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Copyright © 2004 by Judith A. Muschla and Gary Robert Muschla AEDATE NAME 3 5 13. Use thefollowingcluestosolvepuzzle. 4 6ls hnie 3Ars 2 4 4 340÷ 12. 52timesthe largestprimenumber 17. 8 16. 16lessthan item13Across 14. 1 h ags aidoels hn901.369+584287 10. Thelargest palindromelessthan900 11. Section 1:WholeNumbers .360dvddb .Thenextprimenumberafter67 1,287–548 Thenextoddnumberafter301 7. 9. 2. 7squared 6. 38times76 4. 29lessthana thousand 8. 3,690dividedby5 7. Theproductof76and4 5. 6lessthanitem1Across 3. 36+98 1. cosDown Across that islessthan20 × × 10 10 2 3 + 2 –0CROSSNUMBERPUZZLE: 1–10 × 10 2 + 8 12 16 13 × 10 012 10 567 WHOLE NUMBERS 1 + 7 × 10 11 89 0 14 1 ,3 36 3,132÷ 11. 5 Theproduct of118and6 15. 3 17 4 15 Number Puzzle 11 03_970816 Ch01.qxd 6/2/04 10:43 AM Page 12

Exponents

NAME DATE

1–11 THE POWERS OF PRIMES

Use the prime numbers 2, 3, 5, 7, and 11. Choose a base and an exponent from these numbers to equal the number in each problem. The ﬁrst problem is done for you.

Work Space 2 1. 25 = ______5

2. 8 = ______

3. 27 = ______

4. 32 = ______

5. 49 = ______

6. 125 = ______

7. 4 = ______

9. 343 = ______

10. 243 = ______

11. 121 = ______

12. 2,048 = ______

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Copyright © 2004 by Judith A. Muschla and Gary Robert Muschla AEDATE NAME Find thenumbersrelatedtosquaresandcubes. 0 Findatwo-digitnumber thatisonelessthanasquarenumber, andwhendoubledis 10. Section 1:WholeNumbers .Findthelargesttwo-digitnumberthatcanbewrittenassumoftwodifferent cubic 9. Findthesmallesttwo-digitnumberthatcanbewrittenassumoftwocubic 8. Findtheonlyone-digitnumberthatcanbewrittenassumoftwodifferentcubic 7. Findthesmallestthree-digitsquarenumberthatissumoftwo 6. Findthesmallesttwo-digitsquarenumberthatcanbewrittenassumoftwo square 5. Findatwo-digitnumberthatisonemorethan squarenumberandonelessthana 4. Findtheonlythree-digit numberthatisbothasquareandcubic 3. Findtheonlytwo-digitnumberthatisbothasquareandcubic 2. Findtheonlyone-digit numberthatisbothasquareandcubic 1. one lessthanasquarenumber. ______numbers. ______numbers. ______numbers. ______numbers. ______numbers. ______cubic number. ______number. ______number. ______number. ______–2CUBESANDSQUARES 1–12 Exponents 13 03_970816 Ch01.qxd 6/2/04 10:43 AM Page 14

Exponents

NAME DATE

1–13 AN EXPONENTIAL TYPO

In the equations below, every exponent that should have been raised was instead placed on the line by a careless typist. All of the other symbols are correct. Circle the exponent, or exponents, in each equation that should have been raised in order to correct the equation. Then rewrite the equations correctly.

Work Space

1. 23 + 74 = 82

2. 92 – (3 + 6)2 = 11

3. 24 ÷ 23 = 2

4. (3 + 5)2 – 62 – 7 × 22 = 0

5. 52 = 16 + 24

7. 24 = 6 × 22 – 23

8. 36 + 82 = 102

9. 32 = 20 + 23

10. 42 + 36 – 70 = 77

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Copyright © 2004 by Judith A. Muschla and Gary Robert Muschla AEDATE NAME Use Euclid’s methodtofindtheGCFofeachpairnumbers. Here isanexample.FindtheGCFof224and78.FollowEuclid’s steps: follow thesesteps: find theGCF(greatestcommonfactor)oftwonumbers.You canusethismethodtoday. Just More thantwothousandyearsago,Euclid,theGreekmathematician,devisedamethodto Section 1:WholeNumbers .10 1 C ___ 0 4,19GCF=______240,179 GCF=______10. 333,96 8. GCF=______GCF=______105,78 150,215 6. 9. GCF=______98,134 GCF=______4. 82,96 7. GCF=______GCF=______40,27 51,217 2. 5. GCF=______84,72 3. GCF=______105,27 1. .Divide8by2.Theansweris4;2theGCF. 5. Divide10by8.Theansweris1R2. 4. Divide68by10.Theansweris6R8. 3. Divide78by68.Theansweris1R10. 2. Divide224by78.Theansweris2R68. 1. ThelastdivisoristheGCFoforiginalnumbers. 4. Repeatthisprocess untilthere isnoremainder. 3. Dividethesmallernumberbyremainder inthefirststep. 2. Dividethelargernumberbysmallernumber. 1. –4EUCLIDANDTHEGCF 1–14 Greatest CommonFactor 15 03_970816 Ch01.qxd 6/2/04 10:43 AM Page 16

Least Common Multiple

NAME DATE

1–15 FINDING THE LCM USING THE GCF

A way to find the LCM (least common multiple) of two or more numbers is to find the product of the numbers and then divide the product by the GCF (greatest common factor). Use this method to find the LCM of each group of numbers below.

Work Space

1. 36, 80 LCM = ______

2. 24, 86 LCM = ______

3. 70, 45 LCM = ______

4. 54, 64 LCM = ______

5. 93, 60 LCM = ______

7. 49, 27 LCM = ______

8. 38, 46 LCM = ______

9. 12, 45, 63 LCM = ______

10. 56, 12, 16 LCM = ______

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Copyright © 2004 by Judith A. Muschla and Gary Robert Muschla AEDATE NAME the workspace. For someequations,youmayalsoneedtoinsert Place addition,subtraction,multiplication,ordivisionsignstomakeeachexpressioncorrect. 10.15348= 11 Section 1:WholeNumbers 9. 15 5 3 7 = = 7 3 2 5 15 9. 8.1 863= 7.7411 3 =6.12322= 9 0 5.3 323= 4.9831 2= 3.16461=7 = 4 32 6 2 3 102. 1.826 3= 14 –6THEMISSINGSYMBOLS 1–16 Work Space parentheses. Write the Order ofOperations revised equationsin 17 03_970816 Ch01.qxd 6/2/04 10:43 AM Page 18

Order of Operations

NAME DATE

1–17 WHAT A MIX-UP!

The problems below are missing their problem numbers and are out of order. Solve the problems, and write the correct problem number before each. (Remember to follow the order of operations.)

Work Space

_____ 9 + 5 – (1 + 4)

_____ 10 ÷ 2 + 8 ÷ 4

_____ 10 ÷ (2 + 8) + 3

_____ 4 × 2 – 3 × 1

_____ (4 + 3 × 2) ÷ 5

_____ 10 – (8 + 1) + 5

_____ 2(3 + 4) – 4 × 3 – 1

_____ 2(3 + 4) – (4 × 3 – 1)

_____ 10 – 2 × 4 + 6(9 – 8)

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Copyright © 2004 by Judith A. Muschla and Gary Robert Muschla AEDATE NAME equal 1,andthencontinue. must useeachdigitonce(andonlyonce!)inproblem. use addition,subtraction,multiplication,anddivision.You mayalsouseparentheses.You Using thedigits2,4,6,and8,createequationswithanswersrangingfrom1to10.You may 10 =______Section 1:WholeNumbers 8 =______7 =______6 =______5 =______4 =______3 =______2 =______1 =______9 =______eei neape 8–4 (6–2).Startbyﬁndinganequationofyourownto Here isanexample:1=(8–4)÷ –8APERFECT10 1–18 Order ofOperations 19 03_970816 Ch01.qxd 6/3/04 5:41 PM Page 20

Order of Operations

NAME DATE

1–19 NOT-SO-FAMOUS FIRSTS FOR PRESIDENTS

Simplify the expression beneath the name of the president, and write your answer in the space provided. Match your answers to the numbers in the Fact Bank to learn an interest- ing fact about these men.

1. John Adams 2. John Quincy Adams 13 – 4 × 2 = ______(8 – 3) × 5 = ______3. Martin Van Buren 4. William Henry Harrison 6 + 3 × 4 = ______28 – 3 × 5 = ______5. John Tyler 6. Millard Fillmore (8 + 4) ÷ 4 = ______13 × 2 – 3 × 4 = ______7. Abraham Lincoln 8. Grover Cleveland (9 + 4) × 2 = ______40 ÷ 2 × 4 – 3 = ______9. William H. Taft 10. Woodrow Wilson 7 + 9 × 3 + 2 = ______7 × 8 – 5 × 3 = ______11. Herbert C. Hoover 12. Dwight D. Eisenhower 45 – 7 × 5 – 4 = ______3 × 6 – 2 = ______

Fact Bank Copyright © 2004 by Judith A. Muschla and Gary Robert Muschla 13 president who had the shortest presidency 25 first president to have his photo taken 36 first president to throw out the first pitch to start the baseball season 5 first president to live in the White House 14 president who started the White House library 16 first president to have a pilot’s license 77 candy bar Baby Ruth named to honor this president’s daughter 26 first president to patent an invention 3 president who had the most children 6 asteroid was named for this president 41 first president to speak on the radio 18 first president to be born a U.S. citizen, not a British subject

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Copyright © 2004 by Judith A. Muschla and Gary Robert Muschla AEDATE NAME Find themissingnumberstocompletepatterns. 10. 4, ______, ______, ______, ______, 4, 10. Section 1:WholeNumbers 8. ______, ______, 8. ______, ______, 9, 7. 9, ______, ______, 6. ______, ______, ______, 2, 5. ______, ______, 0, 4. 4 ______, ______, ______, 8, 9, 3. 32 ______, ______, ______, 2, 1, 2. 10 ______, 8, ______, ______, 5, 1. .2,5,11, 9. ______, ______, ______, ______, 240, 120, –0WHAT’S NEXT? 1–20 ______, ______, 15, 16, 10, 18, 21, ______, 25 ______, ______, 36 ______, ______, 19 ______, ______30, ______11, 13 Patterns 21 03_970816 Ch01.qxd 6/2/04 10:43 AM Page 22

Types of Numbers

NAME DATE

1–21 NUMBERS OF ALL KINDS

All of the words below relate to some type of number. Use the clues to unscramble these “number” words. Read carefully!

1. smtocoipe: having three or more factors ______

2. starofc: 4 has three of these ______

3. veen: can be divided by 2 ______

4. eruﬁgat: in great shape ______

5. ntadunab: plentiful ______

6. imrep: having only two factors ______

7. suliptmel: every number has these ______

8. dod: peculiar ______

9. minadepolr: can also be a word or phrase ______

11. fereptc: far better than good ______

12. ceindieft: lacking in some way ______

13. preim: backwards prime ______

14. ialndarc: a red bird ______

15. tulanar: not artiﬁcial ______

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Copyright © 2004 by Judith A. Muschla and Gary Robert Muschla AEDATE NAME amount ofmoneysheexpectedtoearnforthetwonightsbaby-sitting. the night. planned tobebackabout11:00 bor, Mrs.Taylor. Mrs.Taylor offered topayVal $3perhourforeachgirl.SinceMrs.Taylor just ______hoursfromnow, shewouldbeginbaby-sittingthetwodaughtersofherneigh- she left,Mrs.Taylor askedVal ifshecouldwatchthegirlsnextSaturdayfrom6:30 expected toearn,butshedidnothavewatchbothgirlsaslonghadthought.Before to 11:00. Val watchedErin,theyoungerdaughter, from7:00until11:00andwatchedSarah9:00 Taylor’s older daughter, wasvisitingafriendanddidnotreturnhome untilnineo’clock. Complete the story byﬁllingintheblankswithcorrectnumbers. Complete thestory 12:30 Section 1:WholeNumbers As Val left,shethoughtaboutthethingscouldbuywith$______,total Val arrivedattheTaylor houseat6:45 Including a$3tip,Mrs.Taylor paidVal $______.Thiswas$______lessthanVal had Valerie satintheschoolcafeteria andnoticedthatitwaseleveno’clock.At7:00 A . M . ShewouldpayVal thesamerateforatotalof$______. –2VAL’S BABY-SITTING JOB 1–22 P . M ., Val ﬁguredthatshewouldearnatotalof$______for P . M ., ______minutesaheadoftime.Sarah,Mrs. Application ofNumbers P . M . until P . 23 M ., 03_970816 Ch01.qxd 6/2/04 10:43 AM Page 24

Number Sense

NAME DATE

1–23 IS THE PRICE RIGHT?

The owners of the stores in Skattersville, a somewhat unusual town, price their goods in an unusual way. The consonants and vowels in the name of an item have a monetary value. The cost of an item is found by multiplying the number of consonants in the name of the item by the value of the consonants, and then adding the product of the number of vowels and the value of the vowels. For example, if consonants were worth $1 and vowels were worth $2, the cost of an eraser would be $9.

Find the value of the third item in the problems that follow.

1. If a book costs $12 and a pencil costs $22, a pen costs ______.

2. If a pair of sneakers costs $19 and a pair of socks costs $11, shorts cost ______.

3. If a newspaper costs $27 and a magazine costs $20, a book costs ______.

4. If a protractor costs $17 and a ruler costs $8, a compass costs ______.

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