CLASS-7
RECIPROCAL OF FRACTION

Reciprocal of a Number

A number is called the reciprocal of another number if the product of the two numbers is 1. To find the reciprocal of a number, write the number as a proper or improper fraction and then interchange the numerator and denominator, retaining the negative sign, if any, in the numerator.

Example.1)

Find the reciprocal of  11

                                11          1

And.)  Reciprocal of 11 = (------) = ------

                                 1          11  

Example.2)

                                 5

Find the reciprocal of   3 --------

                                 7

Ans.)                               

                       5                        26

  reciprocal of  3 ------ = reciprocal of -------      

                       7                         7

                                                                                              26           7

    =   (-------) = -------   (Ans.)

             7           26

Example.3)

                                 3

Find the reciprocal of  - 2 ------

                                 5

Ans.)                                                                                                     3                          13

 reciprocal of - 2 ------ = reciprocal of - ------      

                       5                           5

                                                                                             13            5

  =  (- ------) = - ------   (Ans.)

            5            13

Example 4: If it takes 5/6 yards of fabric to make a dress, then how many yards will it take to make 8 dresses ?         

Ans.) To solve this problem, we will convert the whole number to an improper fraction. Then we will multiply the two fractions.

             5

          ------ x 8

             6

Solution: Number of yards required to make 8 dresses 

                                     2

Answer: It will take 6 ------ yards of fabric to make 8 dresses. (Ans.)

                            3

Example 5: Renee had a box of cupcakes, of which she gave 1/2 to her friend Juan. Juan gave 3/4 of his share to his friend Elena. What fractional part of the original box of cupcakes did Elena get?

Ans.) To solve this problem, we will multiply these two fractions. Solution: The fractional part of the original box of cupcakes that Elena got :

     1          3

  ------ x ------

     2          4

Answer: Elena got 3/8 of the original box of cupcakes.     (Ans.)

Example 6: A chocolate bar is 3/4 of an inch long. If it is divided into pieces that are 3/8 of an inch long, then how many pieces is that?

Ans.) To solve this problem, we will divide the first fraction by the second.

    3          3

 ------ ÷ ------

    4          8

Answer: 2 pieces    (Ans.)

                                                               3

Example 7: An electrician has a piece of wire that is 4 ----- 

                                                               8

                                                                      2

centimeters long. She divides the wire into pieces that are 1 ------ 

                                                                      3

centimeters long. How many pieces does she have?

Ans.) To solve this problem, we will divide the first mixed number by the second.

                                                   5

Answer: The electrician has 2 ------- pieces of wire.   (Ans.)

                                     8