Question

the numerator of a fraction is 1 less than the denominator. If raj adds 1 to the numerator and adds 2 to the denominator the fraction is 3/4 when in its simplest form .find original fraction

Answer 1

Answer:

5/6

Step-by-step explanation:

let the denominator be x then,

the fraction =

(x-1)/x

when raj adds 1 to numerator and 2 to the denominator the fraction becomes 3/4 thus,

((x-1)+1)/(x+2)=3/4

on solving we get,

4x=3x+6

thus

x=6

and required fraction =

6-1/6

=5/6

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Answer 2

Answer:

Correct Question :

The numerator of a fraction is 1 less than the denominator. If Sara adds 1 to the numerator and adds 2 to the denominator, the fraction is 3/4, when expressed in its simplest form. Find the original fraction.

Solution :

Let the numerator of the fraction be x and denominator be y

Fraction = \sf\dfrac{x}{y}yx

Given numerator is 1 less than the denominator

Fraction = \sf\dfrac{x-1}{x}xx−1

Sara added 1 to the numerator and 2 to the denominator.

Fraction = \sf\dfrac{x-1+1}{x+2}x+2x−1+1

The Fraction becomes 3/4

\longrightarrow \sf \: \dfrac{x - 1 + 1}{x + 2} = \dfrac{3}{4}⟶x+2x−1+1=43

\longrightarrow \sf \: \dfrac{x}{x + 2} = \dfrac{3}{4}⟶x+2x=43

\longrightarrow \sf \: 4 \times {x} = 3 \times (x + 2)⟶4×x=3×(x+2)

\longrightarrow \sf \: 4x= 3x+ 6⟶4x=3x+6

\longrightarrow \sf \: 4x - 3x = 6⟶4x−3x=6

\longrightarrow \sf \: x = 6⟶x=6

Hence,The value of x is 6 . Let's put it in our assumption \sf\dfrac{x-1}{x}xx−1

\longrightarrow\sf\dfrac{x - 1}{x}⟶xx−1

\longrightarrow\sf\dfrac{6 - 1}{6}⟶66−1

\longrightarrow\sf\dfrac{5}{6} \: \rightarrow\: Original \: Fraction⟶65→OriginalFraction

Hence,Original Fraction is 5/6