7th Grade Math

R6 Selected Answers and Solutions

Selected Answers and Solutions

Pages 136–138 Lesson 3-1C

1. 
   

   
   

   
   
   3. < 5. Elliot; 3 out of 4 has an average of 0.75;
      7 out of 11 has an average of 0.64. 7. 0.02, 0.1, ^18 , ^23
   
   

   
   

   
   


2. < 11. =
   1313 The LCM of 7 and 8 is 56.
   4 7 = 4 7 × ×^88 = ^3256 and^5 8 = ^58 × ×^77 =^35 56
   Since^32 56 < ^3556 ,^4 7 <^5 8.


3. 
   

   
   

   
   
   17. 
       

       
       

       
       
       19. < 21. Jim;^10 16 > 154 23. 108 ,
           0.805, 0.81 25. -1.4, -1.25, - 1 251 27. 3.47, 3 74 , 3 ^35
       
       

       
       

       
       
   
   

   
   

   
   


4. 
   

   
   

   
   
   31. = 33. >
       3535 Write the fractions as decimals and then
       compare the decimals.
       1 127 gallons 1 ^58 gallons
       7 ÷ 12 = 0.58 −3 5 ÷ 8 = 0.625
       Since 1.58 − 3 < 1.625, then 1 127 gallons < 1 5 8 gallons.
   
   

   
   

   
   


5. 6 c, 6 ^13 c, 6.5 c 39. ^15 g, 1.5 g, 5 g 41a. 3 cubes:
   18 86 in., rod: 12 87 in. 41b. Yes; 69 81 < 69 ^68.


6. Sample answer: ^6332 is closest to 2 because the
   difference of 3263 and 2 is the least. 45. C 47. C


7. A
   Pages 141–143 Lesson 3-2A
   1.^4 5
   33 - ^34 +^ (- _^34 )^ =
   
   
   • 3 + (-3)
     _ 4 Add the numerators.
   
   
   
   

= - _^64 Simplify.

= - 1 _^12

5. -^3 5 7. ^1950
   99 ^45 +^ ^35 =^
   ^4 +^3
   5 Add the numerators.
   = ^75 Simplify.
   = 1 _^25


6. 
   
   
   
   • 21 13. - 1 ^23 15. ^35 17. ^37 19. 125
     2121 2817 -^ ^1128 =^ 286 or 143
     23a. 10033 23b. 10067 25. 81 27. 2 29. 1 _^17
   
   
   
   

3131

_^13

16 -

_^5

16 =

_^8

16 or

_^1

2 in.

33. Sample answer: 1811 and 185 ; 1811 - 185 = 186 ,
    which simplifi es to ^13. 35. To add and subtract
    fractions with the same denominator, add or
    subtract the numerators. Write the result using the
    common denominator. 37. I 39. 4 41. > 43. <


34. _ 83 47. _1,000^19

Pages 148–151 Lesson 3-2C

1. 97 3. ^58

55 _^16 + _^38

= _ 61 × ×^44 + _^38 × ×^33 Rename using the LCD, 24.

= _ 244 + _ 249 Add the fractions.

= _^1324 Simplify.

7. 
   
   
   
   • 1 4 9. Addition; ^1116 in.; Sample answer: To fi nd
     how much smaller the total height of the photo is
     now, add 165 and ^38. 11. _ 107
   
   
   
   

1313 ^56 -^ (- ^23 )^ =^56 ^ - (-^ ^2 3 ××^2 2 )^ Rename using the LCD, 6.

= ^56 - (^) (- ^46 ) Subtract.
= ^56 + ^46 Add the numerators.
= ^96 Simplify.
= 1 ^36 or 1 _^12 Simplify.

15. 
    
    
    
    • 32 17. 1 2413 19. 94 21. - 4526 23. Addition;
      1 ^1120 ft; Sample answer: To fi nd the smallest width to
      make the shelf, add ^45 and 43. 25. Subtraction;^38 lb;
      Sample answer: To fi nd how much more turkey
      Makayla bought, subtract 41 from 8 ^5. 27. 2823 29. 127
    
    
    
    


16. 1 ^14 33. 2 32 35. 152
    3737 ^12 + ^34
    = 21 × ×^22 + ^34 × ×^11 Rename using the LCD, 4.
    = 42 + ^34 Add the fractions.
    = 45 or 1 _ 41 Simplify.


17. 121
    4141 Find the total amount of time used by the
    second and third students. Find the difference
    between the available ^23 hour and the time used by
    the two students. This will show the amount of
    time remaining for the fi nal student.
    _^2
    3 - (^

_^1

6 +

_^1

4 )^ =

_^2

3 - (^

_^1 ×^2

6 × 2 +

_^1 ×^3

4 × 3 )^

= ^23 - (^) ( 122 + 123 )
= 32 - 125
= 128 - 125
= 123 or _^14 hr

43. LaTasha; ^18 mile; LaTasha’s position on the track is
    ^1
    4 of a mile from the start. Colin’s position on the
    track is 85 - 21 , or 81 , of a mile from the start. So,
    LaTasha is farther ahead on the track by ^14 -^18 or ^18
    of a mile. 45. Sample answer:^1 4 + 61 + _ 121


44. fi lling the ^34 -measuring cup once; Filling the
    ^2
    3 -measuring cup twice gives her

_^1

3 cup more fl our

than she needs. Filling the _^34 -measuring cup twice

R01_R42_EM_SelAns_895130.indd R6 1/18/10 9:50 AM