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
[tex]\sf \bf {\boxed {\mathbb {GIVEN:}}}[/tex]
Product of two rational numbers = [tex]\frac{2}{5} [/tex]
One of the number = [tex]\frac{-8}{25} [/tex]
[tex]\sf \bf {\boxed {\mathbb {TO\:FIND:}}}[/tex]
The other number.
[tex]\large\mathfrak{{\pmb{\underline{\orange{Solution}}{\orange{:}}}}}[/tex]
The other number is [tex]\frac{ - 5}{4} [/tex].
[tex]\sf \bf {\boxed {\mathbb {STEP-BY-STEP\:\:EXPLANATION:}}}[/tex]
Let the other number be [tex]x[/tex].
As per the question, we have
[tex]Product \: \: of \: \: the \: \: two \: \: rational \: \: numbers = \frac{2}{5} \\[/tex]
[tex]➺ \: \frac{ - 8}{25} \times x = \frac{2}{5}\\ [/tex]
[tex]➺ \: x = \frac{2}{5} \times \frac{-25}{ 8}\\ [/tex]
[tex]➺ \: x = \frac{-50}{ 40} \\[/tex]
[tex]➺ \: x = \frac{ - 5}{4}\\ [/tex]
[tex]\sf\purple{Therefore,\:the\:other\:number\:is\: \frac{ - 5}{4} .}[/tex]
[tex]\sf \bf {\boxed {\mathbb {TO\:VERIFY :}}}[/tex]
[tex]➺ \: \frac{ - 8}{25} \times \frac{ - 5}{4} = \frac{2}{5} \\[/tex]
[tex]➺ \: \frac{40}{100} = \frac{2}{5}\\ [/tex]
[tex]➺ \: \frac{2}{5} = \frac{2}{5}\\ [/tex]
➺ L. H. S. = R. H. S.
Hence verified.
[tex]\red{\large\qquad \qquad \underline{ \pmb{{ \mathbb{ \maltese \: \: Mystique35☂}}}}}[/tex]
