Basic Mathematics for College Students

Chapter 1 Summary and Review 121

For the division shown on the previous page, the result checks.

Quotient divisor remainder

14

8,317  Dividend

( 361  23 )  8,303 14

  



To checkthe result of a division, we multiply
the divisor by the quotient and add the
remainder. The result should be the dividend.

Properties of Division

Any whole number divided by 1 is equal to
that number.

Any nonzero whole number divided by itself
is equal to 1.

Division with Zero

Zero divided by any nonzero number is equal
to 0.

Division by 0 is undefined.

and

and

and

is undefined and is undefined

2,190

0

7

0

0

23

 0

0

7

 0

103

103

 1

9

9

 1

58

1

 58

4

1

 4

There are divisibility teststo help us decide
whether one number is divisible by another.
They are listed on page 61.

Is 21,507 divisible by 3?

21,507 is divisible by 3, because the sum of its digits is divisible by 3.

2  1  5  0  7  15 and 15  3  5

There is a shortcut for dividing a dividend by a
divisor when both end with zeros.We simply
remove the ending zeros in the divisor and
remove the same number of ending zeros in the
dividend.

Divide:

Remove two zeros from the dividend and the divisor, and divide.

 

64,0001,600 640  16

To estimate quotients,we use a method that
approximates both the dividend and the
divisor so that they divide easily.

Estimate the quotient for by finding

The dividend is approximately

The divisor is approximately



154,908 46 150,000 50



154,908 46 150,00050.

Application problems that involve forming
equal-sized groupscan be solved by division.

Some key wordsand phrasesthat are often
used to indicate division:

split equally distributed equally

shared equally how many does each

how many left (remainder) per

how much extra (remainder) among

BRACES An orthodontist offers his patients a plan to pay the $5,400

cost of braces in 36 equal payments. What is the amount of each

payment?

The phrase 36 equal paymentsindicates division:

 5,400 36

The amount of

each payment

REVIEW EXERCISES

Divide, if possible.

63. 
    
    
    
    64. 
        
    
    
    
    


64. 
    
    
    
    66. 
        
    
    
    
    


65. 
    
    
    
    68. 
        
    
    
    
    


66. 
    
    
    
    70. 
        
    
    
    
    


67. 
    

    (^127) 5,347 72.1,482,0003,900

    
    

165

0

0

10

1,269 54 21  405

1,443 39 68 20,876

595

35

72

4

73. Write the related multiplication statement for


74. Use a check to determine whether the following
    division is correct.


75. Is 364,545 divisible by 2, 3, 4, 5, 6, 9,or 10?

45 R 6

7  320

160  4 40.