Question

The product of two rational number is -40/3 . if one of the numbers is -5/2 ,find the other​

Answer 1

$\huge{\boxed{\sf{\red{G}\orange{i}\green{v}\blue{e}\purple{n}:}}}$

The product of two rational number is $\frac{-40}{3}$

One of the numbers is $\frac{-5}{2}$

$\huge{\boxed{\sf{\red{To}\ \orange{be}\ \green{found}\blue{:}\purple{-}}}}$

The other number

So,

Let the number be 'a'

Now,

According to the question,

The product of two numbers is $\frac{-40}{3}$.

So,

$\implies \bf a \times \dfrac{-5}{2} = \dfrac{-40}{3} \\ \\ \\ \implies \bf a = \dfrac{-40}{3} \div \dfrac{-5}{2} \\ \\ \\ \big[ Taking\ \frac{-5}{2}\ to\ RHS \big] \\ \\ \\ \implies \bf a = \dfrac{-40}{3} \times \dfrac{-2}{5} \\ \\ \\ \big[40\ can\ be\ divided\ by\ 5 \big] \\ \\ \\ \implies a = \dfrac{-8}{3} \times \dfrac{-2}{1} \\ \\ \\ \implies \bf a = \dfrac{16}{3}$

Hence,

The other number = a = $\boxed{\sf{\frac{16}{3}}}$

$\huge{\boxed{\sf{Check:-}}}$

$\bf a \times \dfrac{-5}{2} = or \neq \dfrac{-40}{3}$

Putting the value of a

$\bf = \dfrac{16}{3} \times \dfrac{-5}{2} \\ \\ \\ \big[16 \div 2 = 8\big] \\ \\ \\ = \bf \dfrac{8}{3} \times \dfrac{-5}{1} \\ \\ \\ = \bf \dfrac{-40}{3}$

Hence verified.

Answer 2

Answer:

-16/3

Step-by-step explanation:

The product of two rational number is -40/3

One of the number is -5/2

Then, other one is Y

⇒ -5/2×Y=-40/3

⇒Y=-40/4×-2/5

⇒Y=-16/3