PROPERTIES OF DIVISION

PROBLEMS

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29.   Say that the quotient of two numbers is 10:

Dividend ÷ Divisor = 10.

a)   If you multiply the Dividend by 5, and do not change the Divisor, what will be the new quotient?

50

b)   If you multiply the Divisor by 5, and do not change the Dividend, what will be the new quotient?

2

c)   If you multiply both the Divisor and the Dividend by 5, what will be the quotient?

10

30.   What property of division allows us to write the following:

 4.
.005
  =   4500
   5

If we multiply the dividend and divisor by the same number
-- 1000, in this case -- the quotient will not change.

31.   To divide, the divisor must be a whole number.

a)    12
.3
 =  120
  3
 =  40   b)    24
.4
 =  240
  4
 =  60
 
c)    45
.5
 =   450
  5
 =  90   d)    42
.7
 =   420
  7
 =  60  
 
e)    12
.03
 =   1200
   3
 =  400   f)    24
.04
 =   2400
   4
 =  600  
g)      45 
.005
 =   45,000
    5
 =  9,000   h)      32 
.008
 =   32,000
    8
 =  4,000
i)    1.
.07
 =   140
 7
 =  20   j)     3.5
.005
 =   3500
    5
 =  700
 
k)    .27 
.009
 =   270
 9
 =  30   l)     3.6
.006
 =   3600
    6
 =  600

32.   The order of multiplying and dividing does not matter.

a)    9 × 12
    3
 =  9 × 4 = 36   b)    8 × 12
    4
 =  2 × 12 = 24
 
c)    6 × 22
    2
 =  6 × 11 = 66   d    25 × 25
     5
 =  5× 25 = 125

33.  Show three ways of doing this problem:
1)    9 × 12
    3
 =  9 × 4 = 36   2)    9 × 12
    3
 =  3 × 12 = 36
3)    9 × 12
    3
 =  108
  3
 =  90 + 18
     3
 =  30 + 6 = 36

34.   Find a multiple of the divisor in the dividend.

81
 =  9 × 9
   3
 =  3 × 9 = 27.
144
6  
 =  12 × 12
     6
 =  2 × 12 = 24
 
500
125
 =  2 × 250
  125
 =  2 × 2 = 4.
 
1000
125 
 =  4 × 250
   125
 =  4 × 2 = 8

35.   A stack of CD's is 8 inches high.  Each CD is .25 inches thick.
18.   How many CD's are there?

 8 
.25
 =   800
 25
 =   8 × 100
  25
 =   8 × 4 = 32

36.   Write the first five multiples of

36.   a)  12.    12, 24, 36, 48, 60.

336.   b)  18.    18, 36, 54, 72, 90.

36.   c)  75.    75, 150, 225, 300, 375.

36.   d)  If you divide $6,000 equally among 12 people, how much will
21.   d)  each one get?   $500

36.   e)  How many 18's are there in 540?   30

36.   f)  How many times could you subtract 75 from 3,000?   40

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