7th Grade Math

R8 Selected Answers and Solutions

Selected Answers and Solutions

55 ^12 ÷^7 21 =^ ^12 ÷^ ^152 Rename 7 ^12 as ^152.

= _^1 2

1

·^2

1

_^

15

Divide 2 and 2 by their GCF, 2.

Then multiply.

= _ 151

7. 1 15 9. 56 slices 11. 167 13. 1 31 15. - 12 17. ^23


8. 12 portions 21. 154 23. -^2 3
   2525 3 ^45 ÷^1 ^13 =^ ^195 ÷ ^43 Rename each mixed number.
   = ^195 × ^34 Multiply.
   = ^5720 Simplify.
   = 2 ^1720


9. 
   
   
   
   • 7 54 29. 36 servings 31a. 3 ^3435 31b. 1 _^4099
   
   
   
   


10. 2 _^12

Sample answer: The model on the left shows that

_^58 of a rectangle with 8 sections is 5 sections. _^14 of

8 sections is 2 sections. The model on the right shows

those 5 sections divided into 2 _^12 groups of 2 sections.

35. 3 _^14

Sample answer: The model on the left shows that

2 _^16 of a rectangle with 6 sections is 13 sections. _^23 of

6 sections is 4 sections. The model on the right shows

those thirteen sections being divided into 3 _^14 groups

of four sections.

37. 7 31 39. - 1
    4141 12 ^12 ÷^ ^34 =^ ^252 ÷ ^34
    = ^252 × ^43
    = ^251 × × 32
    = ^503 or 16 ^23 times larger
    43a. 2 ^38 times as many 43b. 7 4 5 times as many


38. 6:30 p.m.; Sample answer: 105 ÷ 35 = 3. The
    storm will travel 105 miles in 3 sets of half hours, or
    1 ^12 hours. Adding 1 ^12 hours to 5:00 p.m. will make
    it 6:30 p.m. 47. _^103 49. Yes; sample answer: If the

fi rst proper fraction is larger than the second

proper fraction, then the resulting quotient will be

a whole number or mixed number. 51. H 53. _ 161

Pages 179–180 Lesson 3-4A

1. 69 3. ( ^23 ) 9 5. - 12 c^8
   77
   ^47
   43
   = 47 -^3 The common base is 4.
   = 44 Subtract the exponents.


2. 2 t^3 11. 510 13. ( _^15 ) 5 15. 78 17. n^3 19. 18 j^4 k^13


3. 14 h^11 23. 24 x^12 25. 42 p^16 27. 85 29. c^3 31. x


4. 10 n^5 35. 45 or 1,024 fi sh

3737 a.

_^1012

106

= 1012 -^6

The common base is 10. Division is

used to find how many times

greater one number is than another.

= 106 Subtract the exponents.

One trillion is 10^6 times as great as one million.

b.^10

18

_

109

= 1018 -^9

The common base is 10. Division is

used to find how many times

greater one number is than another.

= 109 Subtract the exponents.

One quintillion is 10^9 times as great as one billion.

39. Equal; sample answer: Using the quotient
    of powers,^4
    200
    _
    4199
    = 4200 -^199 , or 4^1 , which is 4. 41. A


40. 42 x^9 ft^2 45. 6 32 47. 4 49. - 9 ^23 51. 8 ft


41. 0.38, _ 167 , 44%

Pages 183–184 Lesson 3-4B

1. _^1
   52
   33 t-^10 =^ _t^110 Definition of a negative exponent


2. 3 -^4 7. 7 -^2 9. h^2 11. r 13. 10 -^6 15. _^1
   53


3. ^1
   (-3)^3
   19. ^1
   104
   21. ^1
   a^10
   23. ^1
   q^4
   25. _^1
   x^2


4. 5 -^5 29. k-^2 31. 9 -^2 or 3-^4 33. 2 -^4 or 4-^2


5. g-^2 or ^1
   g^2
   37. 15 v-^5 or ^15
   v^5
   39. k-^1 or _k^1


6. 9 c-^4 or ^9
   c^4
   4343 Penicillin molecules have a greater mass
   because -18 is greater than -23.
   ^10 -^18
   10 -^23
   = 10 -^18 - (-23)

The common base is 10. Division is

used to find how many times

greater one number is than another.

= 105 Subtract the exponents.

The mass of a penicillin molecule is 10^5 times

greater than the mass of an insulin molecule.

45. 10 -^2 47. 10 -^5 49. 8 -^8 , 8^0 , 8^3 ; A negative
    exponent means _^18 to the 8th power. This is a very
    small number between 0 and 1. 8^0 is 1 and 8^3 is 8
    multiplied by itself 3 times. 51. Sample answer:
    A base of 10 raised to a negative exponent represents
    a number between 0 and 1. 53. H 55. B


46. x^6 59. 2 n^7 61. 2 _ 103 T/mo

R01_R42_EM_SelAns_895130.indd R8 1/18/10 9:50 AM