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.   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

18.   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
  19.   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

10.  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

11.  Calculate mentally.

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

12.  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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