Question

Find five
rational number between the following
:
1/4 and 1/2​

Answer 1

Given to find the five rational numbers between

1/2 and 1/4

SoLuTiOn :-

First we find the L.C.M of denominators 2 , 4

L.C.M of 2 , 4 is 4

So, multiply and divide with 2 for the number 1/2 In order to get the same denominator

$\dfrac{1}{2} = \dfrac{1 \times 2}{2 \times 2}$

$\dfrac{1}{2} = \dfrac{2}{4}$

Since ,

1/ 4 , 2/4 But we need 5 rational numbers So, again multiply and divide by 8 for the rational number 1/4 , 2/4

$\dfrac{1}{4} \times \dfrac{8}{8}$

$\dfrac{1}{4} = \dfrac{1 \times 8}{4 \times 8}$

$\dfrac{1}{4} = \dfrac{8}{32}$

$\dfrac{2}{4} \times \dfrac{8}{8}$

$\dfrac{2}{4} = \dfrac{2 \times 8}{4 \times 8}$

$\dfrac{2}{4} = \dfrac{16}{32}$

So, now we can find the rational numbers between 8/32 and 16/32

$\dfrac{9}{32} ,\dfrac{10}{32} , \dfrac{11}{32} , \dfrac{12}{32} , \dfrac{13}{32} , \dfrac{14}{32} , \dfrac{15}{32}$

So, the rational numbers between 1/4 and 1/2 are 9/32, 10/32, 11/32, 12/32 , 13/32

Note :-

• There are infinity number of rational numbers between two rational numbers
• We can multiply and divide with anynumber inorder to get same denominators

Answer 2

Answer:

1×6 2×6

-----=6/24 --------=12/24

4×6 4×6

6 7 8 9 10 11

-- , ---- , --- ,----, ----, ----

24 24 24 24 24 24