Page 71 - Math_Genius_V1.0_C7_Flipbook

D:\Surender Prajapati\CBSE_ICSE_Book_New\CBSE\Grade-7\Math_Genius-7\Open_File\03_Chapter\03_Chapter
\ 15-Nov-2024 Surender Prajapati Proof-6 Reader’s Sign _______________________ Date __________

Division of Rational Numbers

Division of a Rational Number by an Integer

Every integer can be written as a rational number by placing 1 in its denominator.

To divide a rational number by an integer, we can multiply the given rational number by the
reciprocal of the given integer.

 a a a 1
In general,   ÷ integer = b × reciprocalof integer = b × Integer

b
a Integer  a Integer b
Or Integer ÷= × reciprocal of  = ×

b 1  b 1 a

 −16   −16 
For example:   ÷=   × (reciprocalof8)
8


 21
 21
 − 16 2  1 − ( ) × 1 −2
2
=   × = =
 21  8 1 21 21
Division of a Rational Number by Another Rational Number

To divide one rational number by another rational number, we multiply the rational number by
the reciprocal of the other rational number.

a c c
In general, for any two rational numbers and such that ≠ 0 ,
b d d
×
a ÷ c = a c ) = ad
b d b × (reciprocal of d bc
×
−2  −  2 −2  −  2 −2  −  3 6 3
For example: ÷   = × reciprocal of   = ×   = =
7  3  7  3  7  2  14 7

Example 13: Divide the following.
3  −  8 40
(a) ÷− ( 6) (b)   ÷
4  3  21

Solution: We have,
−  
3 3 3  − 1   1
−
(a) ÷− ( 6) = × reciprocal of (–6) = ×    Reciprocal of (6) is   
4 4 4  6    6  
−3 −1
= =
24 8
−  8

−  8
(b)    3  ÷ 40 =    3  × Reciprocal of 40 





21

21
1 7
− 8 21 −7
= × =
3 40 5
1 5
69 Rational Numbers