a fraction has denominator 4 more than its numerator. If 6 is added to the numerator and 6 is subtracted from the denominator the fraction is
[tex] \frac{11}{3} [/tex]
Find the fraction.
Fast answer please
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a fraction has denominator 4 more than its numerator. If 6 is added to the numerator and 6 is subtracted from the denominator the fraction is
[tex] \frac{11}{3} [/tex]
Find the fraction.
Fast answer please
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Answer
Let the numerator be x.
Let the denominator be x + 4.
Numerator of the fraction :
According to the question,
[tex]{\sf \dashrightarrow \dfrac{x + 6}{(x + 4) - 6} = \dfrac{11}{3}}[/tex]
Cross multiply the numbers.
[tex]{\sf \dashrightarrow 3 (x + 6) = 11 (x + 4 - 6)}[/tex]
[tex]{\sf \dashrightarrow 3x + 18 = 11x + 44 - 66}[/tex]
[tex]{\sf \dashrightarrow 3x - 11x = 44 - 66 - 18}[/tex]
[tex]{\sf \dashrightarrow -8x = -22 - 18}[/tex]
[tex]{\sf \dashrightarrow -8x = -40}[/tex]
[tex]{\sf \dashrightarrow x = \dfrac{-40}{-8}}[/tex]
[tex]{\sf \dashrightarrow x = 5}[/tex]
Now, we can find the denominator of the fraction.
Denominator of the fraction :
[tex]{\sf \dashrightarrow x + 4}[/tex]
[tex]{\sf \dashrightarrow 5 + 4 = 9}[/tex]
So, the fraction is,
[tex]{\sf \dashrightarrow \dfrac{5}{9}}[/tex]
Hence, the fraction is [tex]\sf \dfrac{5}{9}[/tex]
Verification
[tex]{\sf \dashrightarrow \dfrac{x + 6}{(x + 4) - 6} = \dfrac{11}{3}}[/tex]
[tex]{\sf \dashrightarrow \dfrac{5 + 6}{(5 + 4) - 6} = \dfrac{11}{3}}[/tex]
[tex]{\sf \dashrightarrow \dfrac{11}{9 - 6} = \dfrac{11}{3}}[/tex]
[tex]{\sf \dashrightarrow \dfrac{11}{3} = \dfrac{11}{3}}[/tex]
[tex]{\sf \dashrightarrow LHS = RHS}[/tex]