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​

Answer 1

Step-by-step explanation:

x-6/x

x-6+3/x+3=2/3

3x-18=2x+6

x=24

the original number is 24-6/24

18/24

or 3/4

Mark my answer as braniest answer

Answer 2

${\fbox{\huge\sf{\pink{An}\purple{sW}\green{eR}}}}$

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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