Question

The numerator of a fraction is 6 less than the denominator. If 3 is added to the
the fraction is equal to 2/
3. Find the orignal fraction

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Answer 1

Answer:

9/15

Step-by-step explanation:

Let the denominator =x

Let the numerator = x-6

According to the question:-

x-6+3/x = 2/3

=>x-3/x= 2/3

=>2(x) = 3(x-3)

=>2x  = 3x -9

=>9 = 3x-2x

=>9 =x

Denominator = 9

Numerator = x-6=9-6=3

Original fraction = 3/9

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Answer 2

✪AnSwEr

${\tt{\red{\underline{\large{Given}}}}}$

• Word problem
• Related to fraction

${\sf{\green{\underline{\large{To\:find}}}}}$

• Original fraction

${\sf{\pink{\underline{\Large{Explanation}}}}}$

☞Let denominator of fraction be X

Then, numerator be (x-6)

According to the question

• 3 is added to the fraction than it is equal to 2/3

Therefore The equation will be

$\tt\frac{x-6}{x}+3=\frac{2}{3}$

$\implies\tt\frac{x-6}{x}+3=\frac{2}{3}$

$\implies\tt\frac{x-6+3x}{x}=\frac{2}{3}$

$\implies\tt\frac{4x-6}{x}=\frac{2}{3}$

=>3(4x-6) = 2x

=>12X-12=2x

=>10x=12

$\therefore\sf{X}=\frac{12}{10}$

$\therefore\sf{X}=\cancel{\frac{12}{10}}$

$\therefore\sf{X}=\frac{6}{5}$

Original fraction be

Numerator

(x-6)

$\rightarrow\frac{6}{5}-6$

$\rightarrow\frac{6-30}{5}$

$\rightarrow\frac{-24}{5}$

Now original fraction be

$\tt\large{\dfrac{\frac{-24}{5}}{\frac{6}{5}}}$

----->-4/1

Hence, fraction will be -4/1