COMPARING FRACTIONS

PROBLEMS 2

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 1.  Same denominator.  Each pair of fractions is in the same ratio as
1.   which whole numbers?  Express that ratio with the lowest terms.

   1.  a)   3
8
  is to   5
8
  as  3 is to 5.      3.  b)   1
4
  is to   3
4
  as  1 is to 3.
 
   3.  c)   4
9
  is to   8
9
  as  1 is to 2.      3.  d)    6 
11
  is to    8 
11
  as  3 is to 4.

 2.  Cross-multiplying.  Each pair of fractions is in the same ratio as
2.   which whole numbers?  Express that ratio with the lowest terms.

   2.  a)   2
3
  is to   3
4
  as  8 is to 9.      2.  b)   5
8
  is to   7
9
  as  45 is to 56.
 
   2.  c)   1
6
  is to   1
2
  as  1 is to 3.      2.  d)   1
8
  is to   1
2
  as  1 is to 4.
 
   2.  e)   1
5
  is to    1 
25
  as  5 is to 1.      2.  f)   1
3
  is to    1 
12
  as  4 is to 1.

 3.  In the previous problem, why does cross-multiplying give the correct
5.   answer?

Cross-multiplying gives the numerators of the common denominator.

 4.  What ratio has

   4.   a)   2 to ½?   2 is four times ½.
   4.   b)   3
4
  to 2?     3
4
 is three eighths of 2.
   6.   c)   1¼ to 2?   1¼ is five eighths of 2.
   4.   d)   3½ to 4?   3½ is seven eighths of 4.
   6.   e)   2 3
4
  to 3?   Eleven twelfths.   f)   2¼ to 3?   Three quarters.
   5.  a)  Which is larger,   5
6
  or   6
7
 ?     6
7

6.   b)  Why does cross-multiplying give the right answer?

Cross-multiplying gives the numerators of the common denominator.

 6.  Which is larger,

   6.   a)   3
4
  or   5
7
?   3
4
     6.   b)   3
8
  or    4 
11
?    3 
 8 
     6.   c)    7 
10
  or   5
7
?   5
7
 
   6.   d)   2
3
  or    7 
11
?   2
3
     6.   e)   4
9
  or   3
7
?   4
9
     6.   f)    7 
12
  or   3
5
?   3
5

 7.  On a map, ½ inch represents 50 miles.  How many miles does 2¼
10. inches represent?  (Compare Example 5.)

225 miles.

 8.  More than or less than ½.  Pick out those numbers which are less
10.   than ½.

   5
8
     5 
12
     7 
16
     9 
16
     9 
20
    13
24
    14
30
    2
5
    3
5
    4
9
    5
9
     7 
15
     8 
15
    13
25
 5 
12
     7 
16
     9 
20
    14
30
    2
5
    4
9
     7 
15

 9.  Compare each number to ½, and decide which number is larger.

  8.   a)   5
8
  or    7 
14
?   5
8
  b)    7 
12
  or    9 
20
?    7 
12
    c)    7 
16
  or    6 
11
?    6 
11
  8.   d)    51 
100
  or    99 
200
?    51 
100
    e)   14
30
  or   26
50
?   26
50
    f)    499 
1000
  or   31
60
?   31
60

10.  Which is the largest number?

  9.   a)   1
2
    4
5
     5 
11
     7 
10
    4
5
        b)   3
8
   8 
15
    9 
15
   10
21
   9 
15
 
        c)    7 
11
    7 
12
   8 
17
    9 
20
   7 
11
        d)    7 
20
     7 
16
     8 
15
     8 
14
     9 
14
     9 
14
        e)   1
2
    1
3
    3
5
    3
8
     6 
11
    3
5

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