PROPER FRACTIONS, MIXED NUMBERS, IMPROPER FRACTIONS

PROBLEMS

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  11.  In this fraction   3
4
  what does the denominator signify and what does

11. the numerator?

The denominator signifies that number 1 has been divided into 4 equal parts. The numerator signifies that we are counting 3 of them.

  11.  Place  3
4
 on this number line. (How many time must you cut the line?)

The number line

Three fourths of 1.  Three cuts.

11.  To divide a line into four equal parts -- that is, into fourths -- cut it three times.

Why is that number called "three-fourths"?

Because 3 is three fourths of 4.

  12.  a)  Why is this number   1
3
  called "one-third"?

Because 1 is one third of 3.

  12.  b)   1
3
 is which part of 1?  One third.
  12.  c)  Place  1
3
 on this number line.

The number line

One third of 1

13.  What ratio has each number to 1?

 13.  a)   1
2
is one half of 1.                b)   1
4
is one quarter of 1.
 12.  c)   3
4
is three quarters of 1.                d)   1
3
is one third of 1.
 13.  e)   2
3
is two thirds of 1.                f)   5
8
is five eighths of 1.

14.  Read each number.

 14.  a)    7 
12
  Seven twelfths.   b)   11
 2
  Eleven halves.
 
 14.  c)   8
3
  Eight thirds.   d)   37
59
  37 over 59.
 
 14.  e)     9 
100
  9 hundredths.   f)      7   
1000
  7 thousandths.
 14.  g)        246     
1,000,000
  246 millionths.
 14.  h)  6 3
8
  Six and three eighths.   i)  7  5
16
  Seven and five sixteenths.

15.  Write the meaning of each mixed number.

14.     a)  1 1
2
  = 1 +  1
2
  b)  2 3
4
  = 2 +  3
4
    c)  3 5
8
  = 3 +  5
8

16.  From this list, pick out the proper fractions, and pick out the
16.  improper fractions.

2
5
    5
2
    7
9
    9
7
    7
7
    7
8
    8
5

Proper fractions:

2
5
   7
9
   7
8

Improper fractions:

5
2
    9
7
    7
7
    8
5

17.  What kind of fractions are less than 1?  Proper fraction.

1 8.  a)   What number is three fifths of 1?   3
5

18.  b)  Place that number on the number line.

The number line

Three fifths of 1

19.  What number is at the arrow?

One quarter of 1

1
4

Four fifths of 1

4
5

Two thirds of 1

2 2
3

10.  Cut the number line and place each number on it:

1
5
     2
5
     3
5
     4
5
    1 2
5
    2 1
5
    4 3
5

The number line

Those number on the number line

11.  Cut the number line and place each number on it.

a)   2
3
 
Two thirds of 1
 
b)   3
4
 
Three fourths of 1
 
c)   5
8
 
Five eighths of 1
 
d)  2 3
4
  Between 2 and 3
 
e)  3 3
8
  Between 3 and 4

12.  Answer with a mixed number or with a whole number plus a
12.  remainder
, whichever makes sense.

12.  a)  It takes three yards of material to make a skirt. How many skirts
12.  a)  can you make from 25 yards?

8 skirts. 1 yard will remain.

11.  b)  You are going on a journey of 25 miles, and you have gone a
11.  b)  third of the distance. How far have you gone?

8 1
3
 miles.

13.  Change each improper fraction to a mixed number or a whole
13.  number.  Do not write the division box.  Divide mentally.

12.   a)  7
5
 = 1 2
5
  b)   24
 3
 = 8     c)   23
 9
 = 2 5
9
  d)   31
 8
 = 3 7
8
 
12.   e)   10
10
 = 1     f)   12
12
 = 1     g)   71
 9
 = 7 8
9
  h)   53
 6
 = 8 5
6
 
12.   i)  63
 7
 = 9     j)   43
 6
 = 7 1
6
  k)   75
 8
 = 9 3
8
  l)   74
 9
 = 8 2
9

14.  Change each mixed number to an improper fraction.

11.     a)  1 2
3
 =  5
3
  b)  3 2
5
 =  17
 5
  c)  7 5
8
 =  61
 8
  d)  9 6
7
 =  69
 7
 
14.     e)  6 5
9
 =  59
 9
  f)  8 4
7
 =  60
 7
  g)  7 1
6
 =  43
 6
  h)  9 7
8
 =  79
 8

15.  Place on the number line.

  15.   a)   7
3
 
2 and 1/3
 
  15.   b)   15
 4 
 
 4 plus 1/4
 
  14.   c)   23
 5 
 
5 plus 3/5

16.  How much is a third of 7?

  7
3
 = 2 1
3

To take a third of a number, divide by 3.


Continue on to Section 2:  Comparing fractions.

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