Factors and Multiples Chapter Questions

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1 Factors and Multiples Chapter Questions 1. What is the divisibility rule for 3? 2. What is the divisibility rule for 9? 3. Explain LCM. 4. Explain GCF. NJ Center for Teaching and Learning ~ 1 ~

2 Chapter Problems Even and Odd Numbers Classwork Determine whether each sum or product will be even or odd. Explain your reasoning. 1) 42, ,243 2) 983 x 455 3) 6, ,227 4) 54,294 x 31,871 5) 1, ) 7,330 x 318 7) 81, ,316 8) 2,773 x 6,228 9) ) 3 x 4 x 5 x 6 x 7 Homework Determine whether each sum or product will be even or odd. Explain your reasoning. 11) 72, ,101 12) 458 x ) 3, ,422 14) 10,234 x 11,329 15) ) 1,945 x 3,734 17) 8, ,338 18) 313 x ) ) 8 x 9 x 10 x 11 x 12 NJ Center for Teaching and Learning ~ 2 ~

3 Divisibility Rules for 3 & 9 Classwork 21) If the number to the left of each row is divisible by the number at the top of the column, put a check mark in the box ,205 20, ,032 4,128,796 22) Which of the following numbers are divisible by 3? Explain. 94, 36, 64, 21, 91, 48, 74, 28, 75, 19 23) Which of the following numbers are divisible by 9? Explain. 72, 66, 45, 144, 171, 234, 245, 559, 612, ) Is 4,314 divisible by 3? If it is, write the number as the product of 3 and another factor. If not, explain. 25) Is 2,376 divisible by 9? If it is, write the number as the product of 9 and another factor. If not, explain. 26) Explain why 5,868 is divisible by both 3 and 9. NJ Center for Teaching and Learning ~ 3 ~

4 Homework 27) If the number to the left of each row is divisible by the number at the top of the column, put a check mark in the box ,132 13, ,880 4,031, ) Which of the following numbers are divisible by 3? Explain. 15, 54, 43, 51, 91, 57, 76, 23, 35, ) Which of the following numbers are divisible by 9? Explain. 63, 89, 108, 261, 139, 432, 216, 639, 910, ) Is 21,069 divisible by 3? If it is, write the number as the product of 3 and another factor. If not, explain. 31) Is 4,608 divisible by 9? If it is, write the number as the product of 9 and another factor. If not, explain. 32) Explain why 3,042 is divisible by both 3 and 9. Greatest Common Factor Classwork Find the Greatest Common Factor of each set of numbers. 33) 72 and 64 34) 15 and 16 35) 14 and 49 36) 15 and 75 37) 66 and ) 78 and 42 NJ Center for Teaching and Learning ~ 4 ~

5 39) 75 and 18 40) 98 and 66 41) 27 and 72 42) 18 and 21 Homework Find the Greatest Common Factor of each set of numbers. 43) 30 and 45 44) 70 and ) 98 and 30 46) 45 and 66 47) 77 and 21 48) 63 and 45 49) 36 and 63 50) 21 and 40 51) 6 and 51 52) 63 and 99 Least Common Multiple Classwork Find the Least Common Multiple of each set of numbers. 53) 9 and 21 54) 12 and 80 55) 6 and 10 56) 14 and 12 57) 15 and 36 58) 8 and 20 59) 9 and 6 60) 15 and 10 61) 8 and 14 62) 55 and 22 NJ Center for Teaching and Learning ~ 5 ~

6 Homework Find the Least Common Multiple of each set of numbers. 63) 9 and 15 64) 4 and 7 65) 12 and 15 66) 10 and 9 67) 8 and 14 68) 11 and 13 69) 42 and 21 70) 4 and 6 71) 14 and 63 72) 22 and 8 GCF/LCM Applications Classwork 73) Kiara baked 30 oatmeal cookies and 48 chocolate chip cookies to package in plastic containers for her friends at school. She wants to divide the cookies into identical containers so that each container has the same number of each kind of cookie. a. If she wants each container to have the greatest number of cookies possible, how many plastic containers does she need? b. How many of each cookie will she put in each container? 74) Beginning at 8:30 A.M., tours of the National Capitol and the White House begin at a tour agency. Tours for the National Capitol leave every 8 minutes. Tours for the White House leave every 10 minutes. How often do the tours leave at the same time? 75) Joe is making key chains with beads. He wants each key chain to have the same number of beads. He has 90 blue beads and 72 yellow beads. a. What is the greatest number of key chains he can make that are exactly the same? b. How many of each color bead will be on each key chain? 76) A florist has 36 roses, 27 tulips, and 18 carnations she must use to create bouquets. a. What is the largest number of bouquets she can make without having any flowers left over? b. How many of each flower will she put in each bouquet? NJ Center for Teaching and Learning ~ 6 ~

7 77) A radio station is giving away prizes to its callers. Depending on what number caller you are, you receive a different prize. Prizes Caller Hat Every 3 rd caller T-shirt Every 5 th caller Backpack Every 6 th caller What number caller will be the first to receive all 3 prizes? Homework 78) Two neon lights are turned on at the same time. One blinks every 4 seconds and the other blinks every 6 seconds. In 60 seconds, how many times will they blink at the same time? 79) Shannon is making identical balloon arrangements for a party. She has 32 maroon balloons, 24 white balloons, and 16 orange balloons. She wants each arrangement to have the same number of each color. a. What is the greatest number of arrangements that she can make if every balloon is used? b. How many balloons of each color will be in each arrangement? 80) At a display booth at an amusement park, every visitor gets a gift bag. Some of the bags have items in them as shown in this table. Items Bags Hat Every 2 nd visitor T-shirt Every 7 th visitor Backpack Every 10 th visitor What number visitor will be the first to receive all 3 items in the gift bag? 81) There are 48 girls and 64 boys in the school choir. The choir teacher plans to arrange the students in equal rows. The same number of boys and the same number of girls will be in each row. What is the greatest number of rows the teacher can arrange? 82) Mike can buy red push pins in packages of 10 and yellow push pins in packages of 12. What is the least amount of packages of each color he must buy in order to have the same number of pins? NJ Center for Teaching and Learning ~ 7 ~

8 Factors and Multiples Chapter Review Multiple Choice Questions 83) Find the Greatest Common Factor of 24 and 72. a. 12 b. 24 c. 6 d ) What is the Least Common Multiple of 3 and 18? a. 36 b. 6 c. 3 d ) 4 is the GCF of which two numbers? a. 8 and 16 b. 16 and 32 c. 8 and 12 d. 24 and 36 86) 48 is the LCM of which two numbers? a. 16 and 48 b. 12 and 4 c. 6 and 8 d. 2 and 24 87) Which of the following numbers is divisible by both 3 and 9? a. 15 b. 89 c. 102 d. 234 Short Constructed Response Questions 88) What is the GCF of 15 and 54? 89) What is the LCM of 16 and 36? NJ Center for Teaching and Learning ~ 8 ~

9 Extended Constructed Response Questions 90) Miriam s uncle donated 120 cans of juice and 90 packs of cheese crackers for the school field trip. Each student is to receive the same number of cans of juice and the same number of packs of crackers. a. What is the greatest number of students that can go on the field trip and share the food equally with no food left over? b. How many cans of juice and how many packs of crackers will each student receive? Explain. 91) Jeremy and his little sister, Deborah, are at a carnival. There are both a large and a small Ferris wheel. Jeremy gets on the large Ferris wheel at the same time his sister gets on the small Ferris wheel. The rides begin at the same time. The large wheel makes one revolution in 10 seconds and the small wheel makes one revolution in 7 seconds. a. How many seconds will pass before Jeremy and Deborah are at the bottom at the same time again? b. How many times will each Ferris wheel go around before Jeremy and his sister are both on the ground again? NJ Center for Teaching and Learning ~ 9 ~

10 Answer Key 1) Odd 2) Odd 3) Even 4) Even 5) Odd 6) Even 7) Even 8) Even 9) Even 10) Even 11) Even 12) Even 13) Even 14) Even 15) Even 16) Even 17) Odd 18) Odd 19) Odd 20) Even 21) ,205 20, ,032 4,128,796 22) 36, 21, 48, 75 23) 72, 45, 144, 171, 234, ) 3 x 1,438 25) 9 x ) The sum of the digits is 27 and it is divisible by both 3 and 9. 27) ,132 NJ Center for Teaching and Learning ~ 10 ~

11 13, ,880 4,031,037 28) 15, 54, 51, 57, ) 63, 108, 261, 432, 216, ) 3 x 7,023 31) 9 x ) The sum of the digits is 9 and it is divisible by both 3 and 9. 33) 8 34) 1 35) 7 36) 15 37) 3 38) 6 39) 3 40) 2 41) 9 42) 3 43) 15 44) 10 45) 2 46) 3 47) 7 48) 9 49) 9 50) 1 51) 3 52) 9 53) 63 54) ) 30 56) 84 57) ) 40 59) 18 60) 30 61) 56 62) ) 45 64) 28 65) 60 66) 90 67) 56 68) ) 42 70) 12 71) ) 88 73) a. 6 containers b. 5 oatmeal and 8 chocolate chip 74) Every 40 minutes 75) a. 18 key chains b. 5 blue, 4 yellow 76) a. 9 bouquets b. 4 roses, 3 tulips, 2 carnations 77) 30 th caller NJ Center for Teaching and Learning ~ 11 ~

12 78) 5 times 79) a. 8 arrangements b. 4 maroon, 3 white, 2 orange 80) 70 th visitor 81) 16 rows 82) 6 packages of red, 5 packages of yellow Fraction and Decimal Computations Unit Review Multiple Choice Questions Answer Key 83) b 84) d 85) c 86) a 87) d Short Constructed Response Questions Answer Key 88) 3 89) 144 Extended Constructed Response Questions Answer Key 90) a. 30 students can go on the field trip. b. Each student will get 4 cans of juice and 3 packs of crackers; 30 is the GCF, so 4 x 30 = 120 (juice) and 3 x 30 = 90 (crackers) 91) a. It will be 70 seconds before they are both on the bottom again. b. The large Ferris Wheel will go around 7 times, small will go 10 times. NJ Center for Teaching and Learning ~ 12 ~

7) Use a place value chart to solve. Then, write your answer in standard form. 15 and 2 tenths 9 thousandths + 2 and 3 hundredths 2 thousandths =

7) Use a place value chart to solve. Then, write your answer in standard form. 15 and 2 tenths 9 thousandths + 2 and 3 hundredths 2 thousandths = Decimal Operations Addition Classwork Solve the following problems: PMI 5 th Grade, Unit 2 Decimal Computation 1) 65.24 + 72.11 = 4) 34.12 + 0.9 = 2) 8.29 + 0.31 = 5) 0.234 + 0.541 = 3) 159.34 + 2.64 =