Question

The product of two numbers is 5/9. If one of the number is -35/24. Find the another​

Answer 1

Answer :-

• The other rational number is -8/21.

To find :-

• The other rational number.

Step-by-step explanation :-

One of the rational numbers is -35/24.

Let :-

• The other rational number be "x".

It is given that :-

• The product of the two numbers, that is, the product of -35/24 and x is 5/9.

---------------------------------------

Therefore :-

$\longmapsto \sf \dfrac{-35}{\:\:\:24} \times x = \dfrac{5}{9}$

Transposing -35/24 from LHS to RHS, changing it's sign,

$\longmapsto \sf x = \dfrac{5}{9} \div \dfrac{-35}{\:\:\:24}$

The reciprocal of -35/24 is 24/-35, so let's multiply 5/9 with 24/-35,

$\sf \longmapsto x = \dfrac{5}{9} \times \dfrac{\:\:\:\:24}{-35}$

Reducing the numbers,

$\sf \longmapsto x = \dfrac{1}{3} \times \dfrac{\:\:\:\:8}{-7}$

On multiplying,

$\sf \longmapsto x = \dfrac{\:\:\:\:\:8}{-21}$

Multiplying the numerator and denominator of 8/-21 with (-1),

$\longmapsto \underline{\boxed{\sf x = \dfrac{-8}{\:\:21}}}$

---------------------------------------

• Hence, the other rational number is -8/21.

Answer 2

${\large{\underline{\underline{\pmb{\frak{Let's\ understand\ the\ concept:-}}}}}}$

☀️ As per the given information, we know that product of two numbers is 5/9 and one of those numbers is -35/24. In order to find the another number firstly we have to assume that number as a variable. After that, we can form an equation according to the question.

❍ Then, by solving the equation we have formed according to the given condition of the question we can easily find the another number.

${\large{\underline{\underline{\pmb{\frak{Given:-}}}}}}$

• The product of two numbers is 5/9.

• One of the number is -35/24.

${\large{\underline{\underline{\pmb{\frak{To\;find:-}}}}}}$

• Find the another​

${\large{\underline{\underline{\pmb{\frak{solution:-}}}}}}$

~Let the another number be ' x '

$\underline{\bigstar\:\textsf{According\;to\;question \: :}}$

$\sf :\; \implies \dfrac{-35}{24} \times \; x = \dfrac{5}{9}$

$\sf : \; \implies x = \dfrac{5}{9} \; \div \; \dfrac{-35}{24}$

$\sf : \; \implies x = \dfrac{5}{9} \; \times \; \dfrac{24}{-35}$

$\sf \maltese \;\; \bigg\{ Cancelling \; \; numbers \; \bigg\}$

$\sf : \; \implies x = \dfrac{1}{3} \; \times \; \dfrac{8}{-7}$

$\boxed{\bf{ \;\; \leadsto \; x = \dfrac{-8}{21} }}$

____________

Henceforth,

• The required number is -8/21