Question

the product of two rational numbers is -8/9 if one of the number is -10/3 find the other one

Answer 1

★GIVEN★

The product of two rational numbers is -8/9 if one of the number is -10/3.

★To Find★

Find the other one.

★SOLUTION★

Let the other rational number be x.

According to the question,

=> -10/3 × x = -8/9

=> x = -8/9 ÷ -10/3

=> x = -8/9 × 3/-10

=> x = 4/15

★VERIFICATION★

=> -10/3 × 4/15 = -8/9

=> -8/9 = -8/9

=> LHS = RHS

The other rational no is 4/15.

Answer 2

☯ Let the other rational number be "x".

⠀⠀⠀━━━━━━━━━━━━━━━━━━━━━━━━━

$\qquad{\underline{\boxed{\frak{\pink{According \;to\;the\:Question,}}}}}\;\bigstar$

• Product of two rational numbers is -8/9.
• One rational number is -10/3.

⠀

$:\implies\sf \dfrac{-10}{3} \times (x) = \dfrac{-8}{9}$

$:\implies\sf x = \dfrac{\dfrac{-8}{9}} {\dfrac{-10}{3}}$

$:\implies\sf x = \dfrac{-8}{9} \times \dfrac{-10}{3}$

$:\implies{\boxed{\frak{\pink{x = \dfrac{4}{15}}}}}\;\bigstar$

⠀

$\therefore\;{\underline{\sf{Hence,\;the\;two\;numbers\;are\;\dfrac{4}{15}\;and\; \dfrac{-8}{9}.}}}$

⠀⠀⠀━━━━━━━━━━━━━━━━━━━━━━━━━

$\qquad\qquad\boxed{\underline{\underline{\purple{\bigstar \: \sf\:Verification}}}}$

$:\implies\sf \dfrac{-10}{3} \times \dfrac{4}{15} = \dfrac{-8}{9}$

$:\implies{\boxed{\frak{ \dfrac{-8}{9} = \dfrac{-8}{9}}}}\;\bigstar$