UNIT FRACTIONS

PROBLEMS

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  11.  Let  1
4
 be the unit, and count up to 3 1
4
" 1
4
2
4
3
4
4
4
 or 1;   1 1
4
, 1 2
4
, 1 3
4
, 2;   2 1
4
, 2 2
4
, 2 3
4
, 3;   3 1
4
. "
  12.  Let  1
6
 be the unit, and count up to 2 1
6
" 1
6
2
6
3
6
4
6
5
6
, 1;   1 1
6
, 1 2
6
, 1 3
6
, 1 4
6
, 1 5
6
, 2;   2 1
6
" .
  13.  a)  In the fraction  7
8
 , what number is the unit?   1
8

13.  b)  How many of them are there?  7

14.  Every fraction is a sum of unit fractions.  Write the following as a
14.  sum of unit fractions.
  14. a)   3
8
 =  1
8
 +  1
8
 +  1
8
  14. b)   4
5
 =  1
5
 +  1
5
 +  1
5
 +  1
5
  14. c)   5
3
 =  1
3
 +  1
3
 +  1
3
 +  1
3
 +  1
3

15.  Add.

  15.  a)   2
7
 +  3
7
 =  5
7
  b)   1
5
 +  3
5
 =  4
5
  c)   5
8
 +  6
8
 =  11
 8
 = 1 3
8

16.  Write the missing numerator.  1 is equal to

  16.   a)   3
3
  b)   4
4
  c)   5
5
  d)   10
10
  e)   16
16
  f)   100
100

17.   How many times is each of these contained in 1?

     a)   1
2
   2   b)   1
4
   4   c)   1
8
   8   d)    1 
16
   16

18.   Calculate mentally.

  17.   a)  3 5
8
 +  2
8
 = 3 7
8
  b)  3 5
8
 minus 2
8
 = 3 3
8
  c)  3 5
8
 +  3
8
 = 4
 
  18.   d)  1 3
5
 +  2
5
 = 2   e)  7 1
4
 +  3
4
 = 8   f)  9 5
6
 +  1
6
 = 10

19.  In a recent survey, three fourths of the people responded Yes.
13.  20 people responded No.  How many responded Yes?

60.  Since three fourths responded Yes, one fourth remained. Those were the 20 who responded No. Three fourths is three times one fourth. 3 × 20 is 60.

  10.   a)  How many times is  1
3
contained in 2?  That is, 2 =  6
3
 
  18.   b)  How many times is  1
4
contained in 5?  20
 
  19.   c)  How many times is  1
6
contained in 8?  48
 
  19.   d)  How many times is  1
8
contained in 10?  80
 
  19.   e)  How many times is   1 
16
 contained in 20?  320

11.  The complement to 1.  Calculate mentally.

10.     a)  1 −  2
3
 =  1
3
  b)  1 −   5
12
 =   7 
12
  c)  1 −   1
10
 =   9 
10
10.     d)  1 −   7
20
 =  13
20
  e)  1 −   49
100
 =   51 
100

12.  Calculate mentally.

11.     a)  1  −  1
5
 =  4
5
  b)  9 −  1
5
 = 8 4
5
.    Compare part a).
11.     c)  1  −  3
4
 =  1
4
  d)   8 −  3
4
 = 7 1
4
.    Compare part c).

13.  Calculate mentally.

12.     a)  6 −  1
2
 = 5 1
2
  b)  8 −  1
3
 = 7 2
3
  c)  7 −  3
4
 = 6 1
4
 
12.     d)  3 −  5
8
 = 2 3
8
  e)  4 −  2
5
 = 3 3
5
  f)  2 −  2
7
 = 1 5
7

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