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

2 thoughts on “Find five<br />rational number between the following<br />:<br />1/4 and 1/2​”

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

   [tex] \dfrac{1}{2} = \dfrac{1 \times 2}{2 \times 2} [/tex]

   [tex] \dfrac{1}{2} = \dfrac{2}{4} [/tex]

   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

   [tex] \dfrac{1}{4} \times \dfrac{8}{8} [/tex]

   [tex] \dfrac{1}{4} = \dfrac{1 \times 8}{4 \times 8} [/tex]

   [tex] \dfrac{1}{4} = \dfrac{8}{32} [/tex]

   [tex] \dfrac{2}{4} \times \dfrac{8}{8} [/tex]

   [tex] \dfrac{2}{4} = \dfrac{2 \times 8}{4 \times 8} [/tex]

   [tex] \dfrac{2}{4} = \dfrac{16}{32} [/tex]

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

   [tex] \dfrac{9}{32} ,\dfrac{10}{32} , \dfrac{11}{32} , \dfrac{12}{32} , \dfrac{13}{32} , \dfrac{14}{32} , \dfrac{15}{32} [/tex]

   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

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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

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