the denominator of the fraction is 5 more than its numerator. if 2is subtracted from both the numerator and the denominator the fraction becomes4/5 find the fraction
Share
the denominator of the fraction is 5 more than its numerator. if 2is subtracted from both the numerator and the denominator the fraction becomes4/5 find the fraction
Sign Up to our social questions and Answers Engine to ask questions, answer people’s questions, and connect with other people.
Login to our social questions & Answers Engine to ask questions answer people’s questions & connect with other people.
Answer :-
[tex] \large \bold{Given \: That}[/tex]
The denominator of the fraction is 5 more than its numerator. if 2is subtracted from both the numerator and the denominator the fraction becomes 4/5.
[tex] \large \bold{To \: Find}[/tex]
Find the fraction.
[tex] \large \bold{Solution}[/tex]
Let the Numerator be 'x'.
and, Denominator be '5x'.
According to question.
[tex] = > \: \: \frac{x \: - \: 2}{5x \: - \: 2} \: \: = \: \: \frac{4}{5} \\ \\ = > \: \: 5 \: (x \: - \: 2) \: \: = \: \: 4 \: (5x \: - \: 2) \\ \\ = > 5x \: - \: 10 \: \: = \: \: 20x \: - \: 8 \\ \\ = > \: \: - 10 \: + \: 8 \: \: = \: \: 20x \: - \: 5x \\ \\ = > - 2 \: \: = \: \: 15x \\ \\ = > \: \: x \: \: = \: \: \frac{ - 2}{15} [/tex]
Thanks My Answer
Answer:
[tex]\sf{The \: fraction \: is \: \: \dfrac{22}{27}}[/tex]
Step-by-step explanation:
Let,
The numerator of the fraction = x
The denominator of the fraction = x + 5
★ If 2 is subtracted from both the numerator and the denominator
The numerator of the fraction = x - 2
The denominator of the fraction = x + 5 - 2
⇒ x + 5 - 2
⇒ x + 3
.°. The denominator of the fraction = x + 3
⇒ [tex]\sf{\dfrac{x \: - \: 2}{x \: + \: 3} \: = \: \dfrac{4}{5}}[/tex]
⇒ 5 (x - 2) = 4 (x + 3)
⇒ 5x - 10 = 4x + 12
⇒ 5x - 4x = 12 + 10
⇒ 1x = 22
⇒ x = 22
The numerator of the fraction = 22
The denominator of the fraction = x + 5
⇒ 22 + 5
⇒ 27
The denominator of the fraction = 27
Therefore,
[tex]\sf{The \: fraction \: is \: \: \dfrac{22}{27}}[/tex]