A rational number is such that when you multiply it by 1/4 and add 2/5 to the product, you get 27/5. What is the number❓

August 16, 2021

By Elliana

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1. Answer:

   Ncert solutions

   Grade 8

   Mathematics

   Science

   Chapters in NCERT Solutions – Mathematics , Class 8

   Exercises in Linear Equations in One Variable

   Question 13

   Q13) A rational number is such that when you multiply it by \frac{5}{2}

   2

   5

   and add \frac{2}{3}

   3

   2

   to the product, you get -\frac{7}{12}−

   12

   7

   . What is the number?

   Solution

   Transcript

   Solution:

   Let the rational number be x.

   According to the question, \frac{5}{2}x+\frac{2}{3}=-\frac{7}{12}

   2

   5

   x+

   3

   2

   =−

   12

   7

   \Rightarrow\ \frac{5}{2}x+\frac{2}{3}-\frac{2}{3}=-\frac{7}{12}-\frac{2}{3}⇒

   2

   5

   x+

   3

   2

   −

   3

   2

   =−

   12

   7

   −

   3

   2

   [Subtracting \frac{2}{3}

   3

   2

   from both sides]

   \Rightarrow\ \frac{5x}{2}=\frac{-7-8}{12}⇒

   2

   5x

   =

   12

   −7−8

   \Rightarrow\ \frac{5x}{2}=\frac{-15}{12}⇒

   2

   5x

   =

   12

   −15

   \Rightarrow\ 5x\times12=-15\times2⇒ 5x×12=−15×2

   \Rightarrow60x=-30⇒60x=−30

   \Rightarrow\ \frac{60x}{60}=\frac{-30}{60}⇒

   60

   60x

   =

   60

   −30

   [Dividing both sides by 60]

   \Rightarrow\ x=\ \frac{-1}{2}⇒ x=

   2

   −1

   Hence, the rational number is \frac{-1}{2}

   2

   −1

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