Question

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

With steps explained.

Answer 1

x=-5/4

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

Answer 2

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

Product of two rational numbers =
`(2)/(5)`

One of the number =
`(-8)/(25)`

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

The other number.

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

The other number is
`( - 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 = (2)/(5) \\`

`➺ \: ( - 8)/(25) * x = (2)/(5)\\`

`➺ \: x = (2)/(5) * (-25)/( 8)\\`

`➺ \: x = (-50)/( 40) \\`

`➺ \: x = ( - 5)/(4)\\`

`\sf\purple{Therefore,\:the\:other\:number\:is\: ( - 5)/(4) .}`

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

`➺ \: ( - 8)/(25) * ( - 5)/(4) = (2)/(5) \\`

`➺ \: (40)/(100) = (2)/(5)\\`

`➺ \: (2)/(5) = (2)/(5)\\`

➺ L. H. S. = R. H. S.

Hence verified.

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