Question

The product of two rational numbers is 2/5 , if one of them is -8/25, find the other.

Answer 1

$\sf \bf {\boxed {\mathbb {GIVEN:}}}$

Product of two rational numbers = $\frac{2}{5}$

One of the number = $\frac{-8}{25}$

$\sf \bf {\boxed {\mathbb {TO\:FIND:}}}$

The other number.

$\large\mathfrak{{\pmb{\underline{\orange{Solution}}{\orange{:}}}}}$

The other number is $\frac{ - 5}{4}$.

$\sf \bf {\boxed {\mathbb {STEP-BY-STEP\:\:EXPLANATION:}}}$

Let the other number be $x$.

As per the question, we have

$Product \: \: of \: \: the \: \: two \: \: rational \: \: numbers = \frac{2}{5}$

$➺ \: \frac{ - 8}{25} \times x = \frac{2}{5}$

$➺ \: x = \frac{2}{5} \times \frac{-25}{ 8}$

$➺ \: x = \frac{-50}{ 40}$

$➺ \: x = \frac{ - 5}{4}$

$\sf\purple{Therefore,\:the\:other\:number\:is\: \frac{ - 5}{4} .}$

$\sf \bf {\boxed {\mathbb {TO\:VERIFY :}}}$

$➺ \: \frac{ - 8}{25} \times \frac{ - 5}{4} = \frac{2}{5}$

$➺ \: \frac{40}{100} = \frac{2}{5}$

$➺ \: \frac{2}{5} = \frac{2}{5}$

➺ L. H. S. = R. H. S.

Hence verified.

$\red{\large\qquad \qquad \underline{ \pmb{{ \mathbb{ \maltese \: \: Mystique35☂}}}}}$

Answer 2

Answer:

x=-5/4

Step-by-step explanation:

Let the number be  x and y

     x.y=2/5    (The product of two rational numbers is 2/5)

if  one of the number is  -8/25

x.(-8/25)=2/5

(Here Substituted the value of one of the number yoy may substitute the value -8/25 in place of x

x=(2/5) *(-25/8)    

x=-5/4