Question

the product of two rational numbers is -3 1by5 . if one of the numbers is 2 1 by 4 find the other​

Answer 1

Question :-

The product of two rational numbers is $\sf{-3 \dfrac{1}{5}}$. If one of the numbers is $\sf{2\dfrac{1}{4}}$. Find the other.

Answer :-

Given :- Product of two numbers = $\sf{-3 \dfrac{1}{5}}$ ;

One number = $\sf{2\dfrac{1}{4}}$.

To Find :- Other number.

Solution :-

Let the other number be x.

According To Question :-

$\rightarrow{\sf{2 \dfrac{1}{4} \times x = -3 \dfrac{1}{5}}}$

$\rightarrow{\sf{\dfrac{9}{4} \times x = \dfrac{-14}{5}}}$

$\rightarrow{\sf{x = \dfrac{-14}{5}\times \dfrac{4}{9}}}$

$\rightarrow{\boxed{\sf{x = \dfrac{-56}{45}}}}$

Verification :-

$\rightarrow{\sf{\dfrac{9}{4} \times \dfrac{-56}{45}}}$

$\rightarrow{\sf{\dfrac{-504}{180}}}$

$\rightarrow{\sf{\dfrac{-14}{5} = R.H.S.}}$

Hence, Verified !!

$\boxed{\boxed{\sf{So,\ the\ other\ number\ is\ \dfrac{-56}{45}.}}}$

Answer 2

☞ The product of two rational numbers is -3 $\frac{1}{5}$.

Let the number be M.

If one of the numbers is 2 $\frac{1}{4}$.

A.T.Q.

=> -3 $\frac{1}{5}$ = 2 $\frac{1}{4}$ × M

=> $\dfrac{5\:\times\:(-3)\:+\:1}{5}$ = $\dfrac{4\:\times\:2\:+\:1}{4}$ × M

=> $\dfrac{-14}{5}$ = $\dfrac{9}{4}$ × M

=> $\dfrac{9}{4}$ × M = $\dfrac{-14}{5}$

=> M = $\dfrac{-14}{5}$ × $\dfrac{4}{9}$

=> M = $\dfrac{-56}{45}$

_____________________________

Other number is $\dfrac{-56}{45}$

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