Extra Practice 1. Name Date. Lesson 1.1: Patterns in Division

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1 Master 1.22 Extra Practice 1 Lesso 1.1: Patters i Divisio 1. Which umbers are divisible by 4? By 5? How do you kow? a) 90 b) 134 c) 395 d) 1724 e) 30 f) 560 g) 3015 h) 74 i) Write a 5-digit umber that is divisible by 8. How did you choose the umber? 3. A umber is missig the tes digit. The umber is What could the tes digit be if the umber is divisible by 2? By 4? By 8? 4. Which umbers are divisible by 4? By 8? By 10? How do you kow? a) 80 b) 216 c) 132 d) 350 e) 2160 f) Adrew ad Matthew discuss divisibility. Adrew says, 280 is divisible by 5 ad by = 40, so 280 is also divisible by 40. Matthew says, 296 is divisible by 4 ad by = 32, so 296 is also divisible by 32. Are both Adrew ad Matthew correct? Explai your thikig. 6. Explai why a umber with 0 i the oes place is divisible by 5.

2 Master 1.23 Extra Practice 2 Lesso 1.2: More Patters i Divisio 1. Which umbers are divisible by 0? By 6? By 9? How do you kow? a) 92 b) 114 c) 216 d) 420 e) 636 f) 675 g) 1026 h) 1252 i) Draw a Ve diagram with 2 loops. Label the loops Divisible by 3 ad Divisible by 5. Place the umbers from 1 to 50 i the correct loop. What is true about all the umbers i the regio where the loops overlap? 3. Use divisibility rules to fid the factors of 132. How do you kow you have foud all the factors? 4. Write three 4-digit umbers that are divisible by 9. How did you choose the umbers? 5. Which of these umbers is divisible by? How do you kow? a) 2 b) 3 c) 4 d) 5 e) 6 f) 8 g) 9 h) 10 i) 0 6. Suppose you have 60 graola bars. You must share the bars equally with everyoe o the school bus. How may graola bars will each perso get, i each case? a) There are 30 people o the bus. b) There are 15 people o the bus. c) There are 12 people o the bus. d) There is o oe o the bus.

3 Master 1.24 Extra Practice 3 Lesso 1.3: Algebraic Expressios 1. Write a algebraic expressio for each statemet. a) Nie more tha a umber b) Eightee times a umber c) A umber divided by seve d) Twelve less tha a umber e) Six more tha eleve times a umber f) Eight times a umber is subtracted from 23 g) Thirtee subtracted from the product of three times a umber 2. Write each algebraic expressio i words. The evaluate each expressio for = 6. a) 4 b) + 8 c) 2 d) e) f) A perso ears $6/h shovellig sow. Fid the moey eared for each time. a) 4 h b) 9 h c) t hours 4. Which algebraic expressio ca be used to describe each phrase? Circle the correct aswer. a) A umber decreased by b) A umber divided by 2 a a a 2 c) Double a umber, the subtract 1. 2x 1 1 2x x 2 1 d) Five less tha four times a umber ( 5) e) Twelve added to twice a umber ( + 12) 12 2

4 Master 1.25 Extra Practice 4 Lesso 1.4: Relatioships i Patters 1. Let represet ay term umber. Write a relatio for the term for each umber patter. a) Term Number Term b) Term Number Term c) Term Number Term A equilateral triagle has three equal sides. Write a relatio for the perimeter of a equilateral triagle with side legth k. What is the perimeter of a equilateral triagle with side legth 15 cm? 3. The cost of soccer jerseys for the soccer team is $50 for the iitial set-up, plus $15 for each jersey ordered. a) Write a relatio for the total cost of j jerseys. b) Aother compay charges $80 for the iitial set-up, ad $12 per jersey. Write a relatio for the total cost of j jerseys for this compay. c) Which compay would charge less if you ordered 12 jerseys? 4. Suggest a real-life situatio that could be represeted by each relatio. a) + 7 is related to b) 4s + 5 is related to s c) d is related to d 5. There are studets i the cocert bad. Write a relatio for each statemet. a) the total umber of music stads, if each pair of studets shares oe stad b) the total umber of chairs, if there are 4 more chairs tha studets c) the total umber of sheets of music, if each studet has 7 sheets

5 Master 1.26 Extra Practice 5 Lesso 1.5: Patters ad Relatioships i Tables 1. Copy ad complete each table. Explai how the Output umber is related to the Iput umber. a) b) Iput Output 14 Iput Output 3 2. Describe a real-life situatio that could be represeted by each relatio above. 3. Use algebra. Write a relatio for each Iput/Output table. a) b) Iput Output Iput Output c) d) Iput Output Iput Output

6 Master 1.27 Extra Practice 6 Lesso 1.6: Graphig Relatios 1. Admissio to the Carival is $4. Each game played costs a additioal $2. a) Write a relatio to show how the total cost is related to the umber of games played. b) Create a table of values to show the total cost if you play 0, 2, 4, 6, 8, or 10 games. c) Graph the relatio. Describe the graph. d) Use the graph to aswer these questios: i) How much would it cost to play 5 games? ii) How may games could you play for $26? 2. Describe a real-life situatio that each graph below could represet. a) b) c) 3. Jey borrows $60 from her mother to get her hair highlighted. She promises to pay her mother $4 each week util her debt is paid off. a) Write a relatio to show how the amout Jey owes is related to the umber of weeks. b) Make a table for the amout owig after 2, 4, 6, 8, ad 10 weeks. c) Draw a graph to show the relatio. Describe the graph. d) Use the graph to aswer these questios. i) How much does Jey owe her mother after 12 weeks? ii) Whe will Jey fiish payig off her debt?

7 Master 1.28 Extra Practice 7 Lesso 1.7: Readig ad Writig Equatios 1. Follow the steps to write each equatio. Let represet the umber. a) Thik of a umber: Multiply the umber by 4: Add six: The result is 62. What is the equatio? b) Thik of a umber: Divide it by 5: Subtract 3: The result is 9. What is the equatio? 2. Write a setece for each equatio. a) + 11 = 15 b) 4 = 24 c) 6 = 5 d) = Write a equatio for each setece. a) Two more tha five times a umber is 17. b) Shaw s age 9 years from ow will be 23. c) The perimeter of a regular hexago with side legth s cetimetres is 42 cm. d) The cost of three boxes of popcor at $3 each, ad two driks at x dollars each is $ Match each equatio with the correct setece. a) + 3 = 6 A. A umber divided by three equals six. b) 3 = 6 B. The sum of a umber ad three is six. c) 3 = 6 C. The product of a umber ad three is six. d) = 6 D. Three more tha three times a umber is six.

8 Master 1.29 Extra Practice 8 Lesso 1.8: Solvig Equatios Usig Algebra Tiles 1. Write a equatio to represet each situatio. Solve each equatio usig algebra tiles. Verify each solutio. a) Samatha has 16 CDs. She has 4 more CDs tha Marlee. How may CDs does Marlee have? b) If Jui doubles the umber of comic books he has, he will have 14 comic books. How may comic books does Jui have? c) Five more tha three times a umber is 17. What is the umber? d) I the game of Yoder, a player scores x poits for a Pika ad 3 poits for a Grier. Samuel scored 20 poits. He had 4 Griers ad 2 Pikas. How may poits is oe Pika worth? 2. Describe a situatio that ca be represeted by the equatio = 15. Solve the equatio usig algebra tiles. 3. Solve each equatio. a) 4 + x = 15 b) a + 7 = 21 c) 3d = 15 d) 6f = For each equatio i questio 3, idetify a costat term, the umerical coefficiet, ad the variable. 5. Agelica is thikig of a umber. She multiplies it by 5 ad the adds 7. The result is 22. a) Write a equatio to represet this situatio. b) Solve the equatio to fid Agelica s umber.

9 Master 1.30 Extra Practice Sample Aswers Extra Practice 1 Master 1.22 Lesso A umber is divisible by 4 if the umber represeted by the last two digits is divisible by 4. So, the umbers divisible by 4 are 1724, 560, ad 748. A umber is divisible by 5 if the oes digit is 0 or 5. So the umbers divisible by 5 are 90, 395, 30, 560, ad I chose A umber is divisible by 8 if the umber represeted by the last 3 digits is divisible by 8. So, I chose a 3-digit umber, 160, that was a multiple of 8. I the picked the first 2 digits radomly. 3. To be divisible by 2, the umber must be eve. The oes digit is 6, so the umber is eve. The tes digit ca be ay digit. To be divisible by 4, the umber represeted by the last 2 digits must be divisible by 4. The multiples of 4 that have oes digit 6 are 16, 36, 56, 76, ad 96. So, the tes digit could be 1, 3, 5, 7, or 9. To be divisible by 8, the umber represeted by the last 3 digits must be divisible by 8. The hudreds digit is 3 ad the oes digit is 6. The multiples of 8 which have this form are 336 ad 376. So, the tes digit could be 3 or A umber is divisible by 4 if the umber represeted by the last two digits is divisible by 4. So, the umbers divisible by 4 are 80, 216, 132, 2160, ad A umber is divisible by 8 if the umber represeted by the last three digits is divisible by 8. So, the umbers divisible by 8 are 80, 216, ad A umber is divisible by 10 if the oes digit is 0. So, the umbers divisible by 10 are 80, 350, ad Adrew is correct, but Matthew is ot. Adrew s example works because 5 ad 8 do ot have a commo factor. But 4 ad 8 have 2 ad 4 as commo factors. Ay umber divisible by 4 is also divisible by 2, but ot all umbers divisible by 4 are also divisible by A umber with 0 i the oes place is a multiple of 10, ad 5 is a factor of 10. Extra Practice 2 Master 1.23 Lesso Noe of the umbers are divisible by 0 because o umber ca be divided by To be divisible by 6, the umber must be divisible by 2 ad by 3. So, it must be a eve umber, ad the sum of its digits must be a multiple of 3. The umbers divisible by 6 are 114, 216, 420, 636, 1026, ad To be divisible by 9, the sum of the digits must be a multiple of 9. So, the umbers divisible by 9 are 216, 675, 1026, ad The umbers i the regio where the loops overlap are multiples of 15.

10 is divisible by 1 ad itself. 132 is eve so it is divisible by = 66 The sum of the digits of 132 is 6, so 132 is divisible by 3 but ot by = is divisible by 4 because 32 is a multiple of = is divisible by 2 ad by 3, so it is also divisible by = 22 Lookig at the quotiets, I ca see that 132 is divisible by = 12 The factors of 132 are 1, 2, 3, 4, 6, 11, 12, 22, 33, 44, 66, , 1134, ad 9999; I wrote 4 digits each time so that the sum of the digits was a multiple of a) Yes, is eve. b) No, the sum of the digits is ot divisible by 3. c) Yes, the umber represeted by the last 2 digits is divisible by 4. d) No, the oes digit is ot 0 or 5. e) No, the umber is ot divisible by 3. f) Yes, the umber represeted by the last 3 digits is divisible by 8. g) No, the sum of the digits is ot a multiple of 9. h) No, the oes digit is ot 0. i) No, o umber is divisible by a) 2 graola bars b) 4 graola bars c) 5 graola bars d) I caot share graola bars equally amog o oe. Extra Practice 3 Master 1.24 Lesso a) + 9 b) 18 c) 7 d) 12 e) f) 23 8 g) a) 4 times a umber; 4 6 = 24 b) 8 more tha a umber; = 14 c) A umber divided by 2; 6 2 = 3 d) 7 more tha 3 times a umber; = 25 e) 15 less tha 10 times a umber; = 45 f) 8 times a umber subtracted from 50; = 2 3. a) $24 b) $54 c) $6t 4. a) 6 b) a 2 c) 2x 1 d) 4 5 e) Extra Practice 4 Master 1.25 Lesso a) + 6 related to b) 7 related to c) related to 2. 3k related to k A equilateral triagle with side legth 15 cm has perimeter 45 cm. 3. a) j related to j b) j related to j c) For 12 jerseys, the first compay would charge: $50 + $15 12 = $230 The secod compay would charge: $80 + $12 12 = $224. It would cost less to buy from the secod compay. 4. a) My age related to my sister s age, if I am 7 years older b) The total cost of a video club membership if the cost to joi is $5, plus $4 for each video reted c) The cost of takig the class to the museum if there is a flat fee of $20, plus $4 per studet 5. a) 2 b) + 4 c) 7

11 Extra Practice 5 Master 1.26 Lesso a) b) Iput Output Each Output umber is the Iput umber subtracted from 14. Iput Output Each Output umber is three times the Iput umber. 2. a) The umber of days before Valetie s Day related to days, if Valetie s Day is two weeks today b) The perimeter of a equilateral triagle related to its side legth, 3. a) 9 related to b) related to c) 5 1 related to d) 7 related to Extra Practice 6 Master 1.27 Lesso a) Let p represet the umber of games played. The relatio is 4 + 2p related to p. b) Number of Total Cost c) Games Played ($) p 4 + 2p The poits lie o a straight lie goig up to the right. As the umber of games played icreases by 2, the total cost icreases by $4. d) i) $14 ii) 11 games 2. a) The umber of eyes i the class related to the umber of studets b) The umber of boxes of cookies I have left related to the umber I ve sold if I started with 14 boxes c) The umber of books related to the umber of boxes, if each box holds 6 books ad there are 2 books ot i a box 3. a) Let the umber of weeks be. The relatio is 60 4 related to.

12 b) Amout c) Number of Owig Weeks ($) Name Date The poits lie o a straight lie goig dow to the right. As the umber of weeks icreases by 2, the amout owig decreases by $8. d) i) $12 ii) After 15 weeks Extra Practice 7 Master 1.28 Lesso a) ; 4; 4 + 6; = 62 b), 5 ; 5 3; 5 3 = 9 2. a) Eleve more tha a umber is fiftee. b) Four times a umber is 24. c) A umber divided by six is five. d) Four more tha three times a umber is ietee. 3. a) Let represet the umber. The equatio is = 17. b) Let a represet Shaw s age ow. The equatio is a + 9 = 23. c) The equatio is 6s = 42. d) The equatio is 2x + 9 = a) B b) C c) A d) D Extra Practice 8 Master 1.29 Lesso a) Let m represet the umber of CDs Marlee has. Samatha has 4 more CDs tha Marlee, so she has m + 4 CDs. Samatha has 16 CDs, so the equatio is m + 4 = 16. The solutio is m = 12 Marlee has 12 CDs. Verify: = 16 b) Let c represet the umber of comic books Jui has. Double the umber of comic books is 2c. The equatio is 2c = 14. The solutio is c = 7. Jui has 7 comic books. Verify: 2 7 = 14 c) Let represet the umber. Five more tha three times the umber is The equatio is = 17. The solutio is = 4. The umber is 4. Verify: = = 17 d) 4 Griers are worth 12 poits. 2 Pikas are 2x. Samuel scored 20 poits altogether. The equatio is 2x + 12 = 20. The solutio is x = 4. A Pika is worth 4 poits. Verify: 2 x = = 20

13 2. Joaie is collectig cas of food to take to the food bak. She has 3 cas. Joaie the asks each of her frieds to brig 2 cas of food over to her house. How may frieds brought over 2 cas of food if Joaie eded up with 15 cas of food? The solutio is = 6. Six frieds brought 2 cas of food to Joaie s house. 3. a) x = 11 b) a = 14 c) d = 5 d) f = 3 4. a) Costat term: 4 or 15; Numerical coefficiet: 1; Variable: x b) Costat term: 7 or 21; Numerical coefficiet: 1; Variable: a c) Costat term: 15; Numerical coefficiet: 3; Variable: d d) Costat term: 18; Numerical coefficiet: 6; Variable: f 5. a) = 22 b) = 3; Agelica s umber is 3.