The denominator of a rational number is less than its numerator than 5. If 5 is added to the numerator, the new number becomes Fin

Question

The denominator of a rational number is less than its numerator than 5. If 5 is added to the numerator,
the new number becomes
Find the original rational number
11/6. Find the original numars​

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Raelynn 5 months 2021-12-13T02:08:56+00:00 2 Answers 0 views 0

Answers ( )

    0
    2021-12-13T02:10:30+00:00

    Answer:

    1/9 and 4/8

    Step-by-step explanation:

    0
    2021-12-13T02:10:48+00:00

    ☯ The denominator of a rational number is less than its numerator than 5. So, \\ \\

    Let the numerator of rational number be x.

    Therefore, denominator of rational number is (x – 5). \\ \\

    :\implies\sf Fraction = \dfrac{x}{x - 5}\\ \\

    ⠀⠀⠀⠀━━━━━━━━━━━━━━━━━━━━━━━━━━

    \qquad\qquad\boxed{\bf{\mid{\overline{\underline{\purple{\bigstar\: According\: to \: Question :}}}}}\mid}\\ \\

    ☯ If 5 is added to the numerator, the new number becomes 11/6. \\ \\

    :\implies\sf \dfrac{x + 5}{x - 5} = \dfrac{11}{6}\\ \\

    :\implies\sf 6(x + 5) = 11(x - 5)\\ \\

    :\implies\sf 6x + 30 = 11x - 55\\ \\

    :\implies\sf 6x - 11x = - 55 - 30\\ \\

    :\implies\sf - 5x = - 85\\ \\

    :\implies\sf x = \cancel{ \dfrac{- 85}{- 5}}\\ \\

    :\implies{\boxed{\frak{\pink{x = 17}}}}\;\bigstar\\ \\

    ⠀⠀⠀⠀━━━━━━━━━━━━━━━━━━━━━━━━━━

    Therefore, \\ \\

    • Numerator, x = 17
    • Denominator, (x – 5) = 17 – 5 = 12 \\ \\

    \therefore Hence, The required rational number is 17/12.

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