Question

The numerator of a fraction is 2 less than the denominator. If 3 is added to both numerator and denominator, the fraction becomes / .Find the fraction. linear equations in one variable class 8

Answer 1

ɢɪᴠᴇɴ :-

• Numerator of a fraction is 2 less than the denominator.

• If 3 is added to both numerator and denominator, fraction becomes 3/4

ᴛᴏ ꜰɪɴᴅ :-

• The fraction

ꜱᴏʟᴜᴛɪᴏɴ :-

Let the denominator be 'x'.

Numerator = ( x - 2)

Now,

According to question :-

If 3 is added to both then, we get 3/4

$\begin{lgathered}:\implies \tt\: \frac{(x - 2) + 3}{x + 3} = \frac{3}{4} \\ \\ :\implies \tt\: \frac{x + 1}{x + 3} = \frac{3}{4} \\ \\ \implies \tt\: 4(x + 1) = 3(x + 3) \\ \\ :\implies \tt \: 4x + 4 = 3x + 9 \\ \\ :\implies \tt \: 4x - 3x = 9 - 4 \\ \\ :\implies \tt \: x = 5\end{lgathered}$

Hence,x = 5

So,

Numerator = ( x - 2) = ( 5 - 2) = 3

Denominator = x = 5

$\boxed{ \bold{ \underline{ Original\;\;\ Fraction} = \frac{3}{5}}}$

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Answer 2

Complete Question :-

• The numerator of a fraction is 2 less than the denominator. If 3 is added to both the numerator and the denominator, the fraction becomes ¾.Find the fraction.

Given :-

• The numerator of a fraction is 2 less than the denominator. If 3 is added to both the numerator and the denominator, the fraction becomes ¾.

To Find :-

Required Fraction = ?

Solution :-

Let Denominator be x and Numerator be x - 2

• According to Question :-

→ x - 2 + 3/x + 3 = 3/4

→ x + 1/x + 3 = 3/4

By cross multiplication we get :

→ 3(x + 3) = 4(x + 1)

→ 3x + 9 = 4x + 4

Combin like terms :

→ 9 - 4 = 4x - 3x

→ 5 = x

→ x = 5

Therefore,

• Numerator = x - 2 = 5 - 2 = 3

• Denomintaor = x = 5

Hence,the required fraction is 3/5.