THE MEANING OF MULTIPLYING FRACTIONS

PROBLEMS

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1.  Explain the meaning of each of the following; then "multiply."

  1.   a)   1
3
 × 12  A third of 12.  4.   b)   1
7
 × 56  One seventh of 56.  8.
    1. c)   1
5
 × 35  One fifth of 35.  7.   d)   1
8
 × 72  One eighth of 72.  9.
  1.   e)  2
5
 × 40  Two fifths of 40.  16.
  1.   f)   3
4
 × 20  Three fourths of 20.  15.
  1.   g)   2
3
 × 21  Two thirds of 21.  14.
  1.   h)   5
9
 × 9  Five ninths of 9.  5.
  1.   i)   3 
20
 × 100  Three twentieths of 100.  15.
  1.  j)  11
50
 × 100  Eleven fiftieths of 100.  22.
  1.  k)   8 
25
 × 100  Eight twenty-fifths of 100.  32.
  1.  l)   7 
10
 × 100  Seven tenths of 100.  70.

2.  How much is

  2.  a)  Two thirds of 10?  6 2
3
  b)  Three fourths of 9?  6 3
4
  2.  c)  Seven tenths of 3?  2  1 
10
  d)  Five eighths of 9?  5 5
8
  2.  e)  One sixth of 7?  1 1
6
  f)  One third of 2?   2
3
  2.  g)  Five ninths of 7?  3 8
9
  h)  Seven eighths of 11?  9 5
8

3.  You are going on a journey of 25 miles, and you have gone two

   thirds of the distance.  How far have you gone?   16 2
3
 miles.

4.  A recipe calls for 4 cups of flour and 5 cups of milk.  Proportionally, 4.  how much milk should you use if

4.  a)  you use 2 cups of flour?

   2 cups are half of 4 cups. Therefore, half of 5 cups of milk is 2½ cups of milk

4.  b)  you use 3 cups of flour?

3 cups are three fourths of 4 cups.
Therefore, three fourths of 5 cups of milk = 3 3
4
 cups of milk.

4.  c)   you use 3½ cups of flour?

3½ cups are seven eighths of 4 cups.
Therefore, seven eighths of 5 cups of milk = 4 3
8
 cups of milk.

5.  Express each fraction as a percent.  (Multiply times 100%.)

  3.   a)   1
6
 = 16 2
3
%   b)   5
6
 = 83 1
3
%
  3.   c)   1
9
 = 11 1
9
%   d)   8
9
 = 88 8
9
%

6.  Multiplying by a mixed number.  Calculate mentally.

6.  a)  If bananas cost 50¢ a pound, and you buy 2½ pounds, how much
4. a)   do you pay?  $1.25

6.  b)  If cheese is $3.20 a pound, and you buy 1¼ pounds, how much
4. a)    do you pay?  $4.00

7.  Calculate mentally.

  5.   a)  2½ × 10  = 25   b)  1½ × 12  = 18
 
  5.   c)  2¼ × 16  = 36   d)  3½ × 80  = 280
  5.   e)  4 1
3
 × 6  = 26   f)  4 2
3
 × 6  = 28
 
   5.  g)  4 1
4
 × 40  = 170   h) 5 3
4
 × 40  = 230

8.  Calculate mentally.

8.  a)  What is the price of 8 items at $52 each?  $416

8.  b)  A yard of material cost $5.25.  What is the price of 12 yards?  $63

8.  c)  John needs 24 feet of lumber at $1.50 a foot.  How much must he
6.  c)  pay?   $36

9.  Multiplying by numbers ending in 5.  Calculate mentally.

9.  a)  15 × 12  = 180         b)  15 × 18  = 270         c)  15 × 240  = 3600

9  d)  35 × 6  = 210           e)  25 × 16  = 400          f)  45 × 22  = 990


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