Question

The Numerator of a fraction is 6 less than the denominator. if 3 is added to the numerator, the fraction becomes equal to 2/3. find the original fraction......

please anyone will help me in doing this question....please..​

Answer 1

Given:-

• The Numerator of a fraction is 6 less than the denominator.

• if 3 is added to the numerator, the fraction becomes equal to 2/3.

To Find:-

• The Original Number.

Now,

Let the Denominator be "x"

→ Numerator = x - 6

Atq

→ Numerator = x - 6 + 3 → x - 3

→ Denominator = x

→ $\rm{\dfrac{ x - 3 } { x } = \dfrac{ 2 }{3}}$

• Cross Multiplication method

→ 3 ( x - 3 ) = 2 ( x )

→ 3x - 9 = 2x

→ 3x - 2x = 9

→ x = 9

Hence, The Value of x is 9

Therefore,

→ Denominator = 9

→ Numerator = x - 6 → 9 - 6 → 3.

Hence, The Original fraction is $\rm{\dfrac{ 3 }{9}}$

Answer 2

ɢɪᴠᴇɴ:-

• The Numerator of a fraction is 6 less than the denominator.
• If 3 is added to the numerator, the fraction becomes equal to 2/3.

ᴛᴏ ғɪɴᴅ:-

• The original fraction?

ᴇxᴘʟᴀɴᴀᴛɪᴏɴ:-

Let the denominator of the fraction be x.

Then,

Numerator = x - 6

New numerator formed = x - 6 + 3 = x - 3

According to question,

$\sf\pink{↬}$ $\dfrac{x-3}{x}$ =$\dfrac{2}{3}$

[By Cross Multiplication method]

$\sf\green{↬}$ 3(x - 3) = 2x

$\sf\red{↬}$3x - 9 = 2x

$\sf\purple{↬}$ 3x - 2x = 9

$\green{ \underline{ \boxed{ \sf{x=9}}}}$

Hence,

The denominator of the fraction is 9.

Numerator of the fraction = 9 - 6 = 3.

So, the original fraction = 3/9.

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