Question

The product of two rational numbers is 28/81. if one of them is 14/9, then find the other

Answer 1

Given:

The product of two rational numbers is $\tt \frac{28}{81}$.

One of them is $\tt \frac{14}{9}$

To be found:

The other number.

So,

Let the other rational number be 'a'

According to the question:

$\bf \implies a\ \times \dfrac{14}{9} = \dfrac{28}{81}\\ \\ \\ \implies \bf a = \dfrac{28}{81} \div \dfrac{14}{9} \\\\ \\ \implies \bf a=\dfrac{28}{_9\cancel{81}} \times \dfrac{\not{9}^1}{14}\ \ \ \ \ \ \ \ \bigg[ \therefore (81 \div 9) = 9 \bigg] \\ \\ \\ \implies \bf a = \dfrac{^2\cancel{28}}{9} \times \dfrac{1}{_1 \cancel{14}} \ \ \ \ \ \ \ \ \bigg[ \therefore (28 \div 14) = 2 \bigg] \\ \\ \\ \implies \bf a=\dfrac{2}{9}$

Hence,

The other number is $\red{\boxed{\tt \dfrac{2}{9}}}$.

$\rule{200}2$

Verification:

Product of $\red{\boxed{\tt \dfrac{2}{9}}}$ and $\tt \frac{14}{9}$

$= \tt \dfrac{2}{9}\ \times \dfrac{14}{9} \\ \\ \\ = \tt \dfrac{2 \times 14}{9 \times 9} = \dfrac{28}{81}$

Hence, Verified

Answer 2

Step-by-step explanation:

${\red{\underline{\underline{\bold{Given:-}}}}}$

• The product of two rational numbers = $\frac{28}{81}$

• One of the number = $\frac{14}{9}$

${\blue{\underline{\underline{\bold{To\:Find:-}}}}}$

• The other number

${\green{\underline{\underline{\bold{Solution:-}}}}}$

Let the number be ' x '

According to the given question:-

$\frac{14}{9} \times x = \frac{28}{81} \\ \\ \implies x = \frac{28}{81} \times \frac{9}{14} \\ \\ \implies x = \frac{2}{9}$

Verification:-

$\frac{14}{9} \times x = \frac{28}{81} \\ \\ \implies \frac{14}{9} \times \frac{2}{9} = \frac{28}{81} \\ \\ \implies \frac{28}{81} = \frac{28}{81}$

L.H.S = R.H.S

Hence, verified

Therefore:-

$\boxed{The \:other\:number \:is \:\frac{2}{9}}$