Question

express the following rational number on the exponential from.​

Answer 1

Given:

The numerator of a fraction is 1 less than its denominator.

If the numerator is increased by 1 and denominator is increased by 5, the new fraction becomes 4/5.

To find:

Original Fraction?

Solution:

☯ Let Denominator of fraction be x.

Then, Numerator of fraction will be (x - 1).

⠀⠀⠀⠀

$\underline{\bigstar\:\boldsymbol{According\:to\:the\:question\::}}$

$:\implies\sf \dfrac{(x - 1) + 1}{x + 5} = \dfrac{4}{5}\\ \\ \\:\implies\sf \dfrac{x}{x + 5} = \dfrac{4}{5}$

$:\implies\sf 5(x) = 4(x + 5)\qquad\qquad\bigg\lgroup\bf Cross\: Multiplication \bigg\rgroup$

$:\implies\sf 5x = 4x + 20\\ \\ \\ :\implies\sf 5x - 4x = 20\\ \\ \\:\implies{\underline{\boxed{\frak{\purple{x = 20}}}}}\;\bigstar$

Therefore,

Denominator of fraction, x = 20

Numerator of fraction, (x - 1) = 20 - 1 = 19

⠀⠀⠀⠀

$\therefore\:{\underline{\sf{Hence,\:The\: original\:fraction\:is\: \bf{ \dfrac{19}{20}}.}}}$

⠀⠀⠀⠀━━━━━━━━━━━━━━━━━━━━━

$\qquad\qquad\boxed{\bf{\mid{\overline{\underline{\pink{\bigstar\: Verification :}}}}}\mid}$

Given that,

⠀⠀⠀⠀

If the numerator is increased by 1 and denominator is increased by 5, the new fraction becomes 4/5.

⠀⠀⠀⠀

$:\implies\sf \dfrac{19 + 1}{20 + 5} = \dfrac{4}{5}\\ \\ \\:\implies\sf \cancel{ \dfrac{20}{25}} = \dfrac{4}{5}\\ \\ \\:\implies\sf \dfrac{4}{5} = \dfrac{4}{5}$

$\qquad\qquad\qquad\dag\:{\underline{\underline{\sf{\purple{Hence\: Verified!}}}}}$