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Answers
Answer:
The numerator of a fraction is 4 less than it's denominator. If 1 is added to both it's numerator and Denominator. Then, it becomes 4/12. Find the fraction.
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❍ Let the Denominator of the fraction be x respectively.
Then, it's Numerator = (x – 4).
⠀
\underline{\bigstar\:\boldsymbol{According\;to \;the \;given\; Question \;:}}
★AccordingtothegivenQuestion:
⠀
If 1 is added to both it's numerator and Denominator. Then, it becomes 4/12.
⠀
Therefore,
⠀
\begin{gathered}:\implies\sf \dfrac{(x - 4) + 1}{x + 1} = \dfrac{4}{12}\\\\\\:\implies\sf \dfrac{x - 3}{x + 1} = \dfrac{4}{12} \\\\\\:\implies\sf 12(x - 3) = 4(x + 1)\\\\\\:\implies\sf 12x - 36 = 4x + 4\\\\\\:\implies\sf 12x - 4x = 4 + 36\\\\\\:\implies\sf 8x = 40\\\\\\:\implies\sf x = \cancel\dfrac{40}{8}\\\\\\:\implies{\underline{\boxed{\frak{\pink{x = 5}}}}}\;\bigstar\end{gathered}
:⟹
x+1
(x−4)+1
=
12
4
:⟹
x+1
x−3
=
12
4
:⟹12(x−3)=4(x+1)
:⟹12x−36=4x+4
:⟹12x−4x=4+36
:⟹8x=40
:⟹x=
8
40
:⟹
x=5
★
⠀
Hence,
⠀
Numerator of fraction, (x – 4) = (5 – 4) = 1
Denominator of fraction, x = 5
⠀
\therefore{\underline{\sf{Hence, \;the\; required\; fraction\;is\;\bf{\dfrac{1}{5}}.}}}∴
Hence,therequiredfractionis
5
1
.
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V E R I F I C A T I O N :
If 1 is added to both it's numerator and Denominator. Then, it becomes 4/12. Let's verify :
\begin{gathered}\dashrightarrow\sf \dfrac{1}{5} = \dfrac{4}{12} \\\\\\\dashrightarrow\sf \dfrac{1 + 1}{5 + 1} = \cancel\dfrac{4}{12} \\\\\\\dashrightarrow\sf \cancel\dfrac{2}{6} = \cancel\dfrac{2}{6} \\\\\\\dashrightarrow\underline{\boxed{\frak{ \dfrac{1}{3} = \dfrac{1}{3}}}}\end{gathered}
⇢
5
1
=
12
4
⇢
5+1
1+1
=
12
4
⇢
6
2
=
6
2
⇢
3
1
=
3
1
\qquad\quad\therefore{\underline{\textsf{\textbf{Hence, Verified!}}}}∴
Hence, Verified!