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Division – About Division – pg.1/3

Posted in Math Theory by Lia on 11/18/2011

Division: pg. 1, 23

Contents:

pg.1…..Division  – about division

pg.2…..Division – exercises

pg.3…..Division – answers to exercises

 

About division

The result of division is called the quotient.

Division is the inverse of multiplication. 

a divided by b is equal with c or a over b is equal with c is written: a : b = c or a/b = c or {{a/b} = c}, where a is called the dividend, b is called the divisor and c is called the quotient.

Example:

8 divided by 2 is equal with 4 can be written: 8 : 2 = 4 or 8/2 = 4 or {{8/2} = 4}.

  • If the dividend has the same sign as the divisor, the quotient is a positive number.

Example:

{{{+ 6}/{+ 2}} = + 3; {}{}{}{{- 21}/{-3 }} = +7}

  • If the dividend has a different sign than the divisor, the quotient is a negative number.

Example:

{{{+ 10}/{- 5}} = - 2; {}{}{}{{-24}/{+ 6}} = -4}

 

Division  properties

 

  • Division is Distributive with respect to addition

tabular{11}{11}{{{(a + b + c)/d}  = {a/d} + {b/ d} + {c /d}}}

Example: {{(4 + 6 + 8)/2}  = {4/2} + {6/ 2} + {8/2} = 2 + 3 + 4 = 9}

or we can calculate in a different way to verify the result:

{{(4 + 6 + 8)/2}  = {{18}/2} = 9}

 

  • Identity element for division is 1. Any number divided by {{}{1}{}} has the result that number:  tabular{11}{11}{{{a/1} = a}}

Example: {{7/1} = 7}

 

  • Division inverse is the number itself. Any number divided to itself  has as result {{}{1}{}}:   tabular{11}{11}{{{a/a} = 1}}

Example: {{5/5} = 1}

 

  • Zero Number.

* Zero divided by any number has as result zero:  tabular{11}{11}{{{0/a} = 0}}

Example: {{0/5} = 0}

* Any number divided by zero is undefined:  tabular{11}{11}{{{a/0} = undefined}}

Example:{{5/0} = undefined}

 

  • The result of a division stays the same if we multiply or divide the dividend and divisor with the same number.

tabular{11}{11}{{{a/b} =  {{ac}/{bc}}}} in this case the divident and the divisor were multiplied with {{}{c}{}}

Example:

{{10/5} =  {{10*3}/{5*3}} = {{30}/{15}} = 2} in this case the dividend and the divisor were multiplied with {{}{3}{}}

{{12/4} =  {{12:2}/{4:2}} = {6/2} = 3} or can be written {{12/4} =  {{12/2}/{4/2}} = {6/2} = 3 }  in this case the dividend and the divisor were divided by {{}{2}{}}

 

Dividing numbers:

Example:

Division fig a

Division fig b

 

Division fig c and d

 

 

Division fig e and f

 

Division: pg. 1, 23

 


 

 

 

 

 

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