Question

A red and blue are placed at the position 1/2 and 1/3 respectively on a number line . Shikha wants to place four yellow balls between these two balls represent rational numbers . find the positions of yellow balls​

Answer 1

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Answer 2

Given : A red and blue are placed at the position 1/2 and 1/3 respectively on a number line .

Shikha wants to place four yellow balls between these two balls

To Find : positions of yellow balls​

Solution:

Let say 4 Rational number inserted are A , B , C & D

1/3    A      B     C     D    1/2

1/2 - D = D - C =  C - B = B - A  = A  - 1/3  = k

1/2 - 1/3  = 5k

=> 1/6   = 5k

=> k = 1/30

A= 1/3 + k  = 1/3 + 1/30  =  11/30

B = A + k  = 11/30 + 1/30  = 12/30

C = B + k = 12/30 + 1/30 = 13/30

D = C + k  = 13/30 + 1  = 14/30

Positions of yellow Balls are

11/30 , 12/30  , 13/30 and 14/30

or

11/30 , 2/5 , 13/30 , 7/15

1/3    11/30      2/5     13/30     7/15     1/2

or another method

First get same denominator

1/2 = 3/6

1/3  = 2/6

to insert 4 rational number multiply numerator and denominator by 4+ 1 = 5

2/6 = 10/30

3/6= 15/30

4 rational numbers between  11/30 , 12/30 , 13/30 , 14/30

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