7th Grade Math

Selected Answers and Solutions R3

Selected Answers and Solutions

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answer: The total amount earned forms the

sequence 6.5, 13, 19.5, 26, .... Since each term is 6.5

more than the previous term, the sequence is

arithmetic. 41. F 43. each term is multiplied by 3;

162, 486, 1,458

Pages 55–56 Lesson 1-3B

1. 36
   33 17 ×^17 =^289


2. 3 7. 11 9. 24 in. by 24 in. 11. 1 13. 121


3. 400 17. 1,156 19. 4 21. 10 23. 16 25. 25


4. 40 ft
   2929 18 ×^18 = 324, so the length of the side of the
   chessboard including the border is 18 inches.
   Subtract an inch for the border on both sides of the
   region containing the small squares. The length of
   one side of that region is 16 inches.
   31a. Yes; Sample answer: A pen that measures
   10 feet by 10 feet has the same perimeter, but its
   area is 100 square feet, which is greater than 84
   square feet. 31b. Sample answer: the square that
   measures 10 feet on each side; Sample answer: The
   perimeter is the same, and the area is 100 square
   feet, or 16 square feet greater than that of the
   original pen. 33. √  25 · √ 4 ; Sample answer: √ 25
   is 5 and √4 is 2. So, 5  × 2 = 10. The √ 25 · 4 = √  100
   and the √ 100 = 10. So, 10 = 10. 35. D 37. C
   Pages 58–60 Lesson 1-3B


5. 6
   33 90 is between the perfect squares 81 and 100.
   Find the square root of each number.
   81 < 90 < 100
   √ 81  < √  90 < √  100
   9 < √  90 < 10
   So, √ 90 is between 9 and 10. Since 90 is closer to
   81 than to 100, the best whole number estimate
   zis 9.


6. 10 ft 7. 3 9. 6
   1111 89 is between 81 or 92 and 100, or 102.89 is 8
   away from 81 and 11 away from 100. So it is closer
   to 81. Therefore, √ 89 to the nearest whole number
   is 9.


7. 12 15. 8.2 in. 17. about 1.5 19. 30 21. 40


8. 4 25. 11 27. 8
   2929 Estimate the square root of 1,008.
   1,008 is between the perfect squares 961 and 1,024.
   Find the square root of each number.
   961 < 1,008 < 1,024
   √  961 < √ 1,008 < √ 1,024
   31 < √ 1,008 < 32
   So, √1,008 is between 31 and 32. Since 1,008 is
   closer to 1,024 than to 961, the best whole number
   estimate is 32. The approximate length of the
   postage stamp is 32 millimeters.

b. Use the relationship 1 mm = 10 cm.

1 mm = 0.1 cm

32 × 1 mm = 32 × 0.1 cm

32 mm = 3.2 cm

31. √ 81 ; Sample answer: It is not rational. Sample
    answer: 17, 18, 19 33. Sample answer: 71 is
    between the perfect squares 64 and 81. Since 71 is
    closer to 64 than 81, √ 71 is closer to √ 64 , or 8.


32. 0.7 37. 1.7 39. It cannot be written as a
    fraction. 41. G 43. 6 45. 9 47. 5

Pages 64–67 Chapter Study Guide and Review

1. false, equivalent expressions 3. false, factors


2. false, square 7. false, two 9. 243 11. 324


3. 18 15. 36 17. $5.75h + $8.95; $62


4. 68; Sample answer: Rewrite 14 + (38 + 16) as
   14 + (16 + 38) using the Commutative Property of
   Addition. Rewrite 14 + (16 + 38) as (14 + 16) + 38
   using the Associative Property of Addition. Find
   14 + 16, or 30, mentally. Then fi nd 30 + 38, or 68,
   mentally.


5. 
   
   
   
   23. 21 25. Each
       term is found by
       adding 0.8 to the
       previous term; 6.6,
       7.4, 8.2 27. $4.50n
   
   
   24. 9 31. 80 ft
   
   
   
   


6. 10 35. 9 37. 7


7. 
   

9 10111213

132

41.

12345

12

Chapter 2 Integers

Page 74 Chapter 2 Are You Ready?

1. 6 3. 17 5. 24 7. 7 9. (1, 1) 11. (8, 1)


2. (1, 5) 15. (7, 6)

Pages 79–80 Lesson 2-1B

1. 
   
   
   
   • 11 3. 16 5. - 15
   
   
   
   


2. 
   
   
   
   • 10 - 8 - 6 - 4 - 20 2 4 6 810
     99 1 + ⎪^7 ⎥^ =^1 +^7
     = 8
   
   
   
   


3. 9 13. - 53 15. - 2 17. 12 19. - 7


4. 
   
   
   
   • 3 - 2 - 10 1
   
   
   
   


5. 
   
   
   
   • 10 - 8 - 6 - 4 - 2 0 2 4 6 8 10
   
   
   
   


6. 10 27. 2 29. 14 31. 25

R01_R42_EM_SelAns_895130.indd R3 1/18/10 9:50 AM