THE MEANING OF MULTIPLYING FRACTIONS

PROBLEMS

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

 1.   a) 13 × 12  A third of 12.  4. b) 17 × 56  One seventh of 56.  8.
 1. c) 15 × 35  One fifth of 35.  7. d) 18 × 72  One eighth of 72.  9.
 1.   e) 25 × 40  Two fifths of 40.  16.
 1.   f) 34 × 20  Three fourths of 20.  15.
 1.   g) 23 × 21  Two thirds of 21.  14.
 1.   h) 59 × 9  Five ninths of 9.  5.
 1.   i) 3 20 × 100  Three twentieths of 100.  15.
 1.   j) 1150 × 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 23 b)  Three fourths of 9 ?  6 34
 2.  c)  Seven tenths of 3 ?  2 1 10 d)  Five eighths of 9 ?  5 58
 2.  e)  One sixth of 7 ?  1 16 f)  One third of 2 ? 23
 2.  g)  Five ninths of 7 ?  3 89 h)  Seven eighths of 11?  9 58

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 23 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 34 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 38 cups of milk.

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

 3.   a) 16 = 16 23 % b) 56 = 83 13 %
 3.   c) 19 = 11 19 % d) 89 = 88 89 %

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 13 × 6  = 26 f)  4 23 × 6  = 28 5.  g)  4 14 × 40  = 170 h) 5 34 × 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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