Question

The numerator of a fraction is 2 less than the denominator. If 5 is added to both the numerator and the denominator, the fraction becomes 3/4 Find the fraction,​

Answer 1

Step-by-step explanation:

Given: Numerator of a fraction is 2 less than the denominator To find: The fraction Assumption: Let the denominator be x Numerator = x – 2 Therefore, the fraction (x - 2)/x If one is added to the numerator and denominator, fraction becomes (x - 2 +1)/(x + 1) = (x - 1)/(x + 1) Sum of the fractions = (x - 2)/x + (x - 1)/(x + 1) Sum of the fractions = 19/15 Therefore, Cross-multiplying we get, 30x2 – 30x – 30 = 19x2 + 19x 30x2 – 19x2 – 30x – 19x – 30 = 0 11x2 – 49x – 30 = 0 Now we need to factorise such that, on multiplication we get 330 and on substraction we get 49. So, equation becomes, 11x2 – (55x – 6x) – 30 = 0 11x2 – 55x + 6x – 30 = 0 11x(x – 5) + 6(x – 5) = 0 (11x + 6)(x – 5) = 0 So, 11x + 5 = 0 or x – 5 = 0 ← Prev Question Next Question → Related questions 0 votes 1 answer The numerator of a fraction is 3 less than the denominator. If 2 is added to both the numerator and the denominator, original fraction is 29/20. asked May 1 in Quadratic Equations by Fara (32.1k points) quadratic equations class-10 0 votes 1 answer The numerator of a fraction is 3 less than denominator. If 2 is added to both 29 numerator as well as denominator, asked Oct 14, 2020 in Quadratic Equations by Anika01 (57.1k points) quadratic equations class-10 0 votes 1 answer The numerator of a fraction is 3 less than its denominator. If 1 is added to the denominator, asked Jul 15 in Quadratic Equations by Ankush01 (14.3k points) quadratic equations class-10 0 votes 1 answer The denominator of a fraction exceeds its numerator by 3. If 3 is added to both numerator and denominator, asked Oct 14, 2020 in Quadratic Equations by Anika01 (57.1k points) quadratic equations class-10 0 votes 1 answer The denominator of a fraction exceeds its numerator by 3. If one is added to both numerator and denominator, asked Oct 14, 2020 in Quadratic Equations by Anika01 (57.1k points) quadratic equations class-10 Read more on Sarthaks.com - https://www.sarthaks.com/940151/the-numerator-fraction-less-than-the-denominator-added-to-both-numerator-and-denominator

Answer 2

Given :

The numerator of a fraction is 2 less than the denominator. If 5 is added to both the numerator and the denominator, the fraction becomes 3/4 Find the fraction

Solution :

Let us assume :

The numerator to be x

According to the question

The numerator is 2 less than the denominator which means

The denominator is x + 2

We know that :

$\underline{\blue{\boxed{ \green{ \frak{Fraction_{(Original)} = \frac{Numerator}{Denominator}}}}}}$

Hence, putting the assumed values we get

$\dashrightarrow \frak{Fraction_{(Original)} = \frac{x}{x + 2} }$

5 is added to both numerator and denominator

Therefore our new fraction is :

$\dashrightarrow \frak{Fraction_{(New)} = \frac{x + 5}{x + 7} }$

After this the new fraction becomes 3/4

Hence, the equation is :

$\dashrightarrow \frak{ \frac{x + 5}{x + 7} = \frac{3}{4} }$

By cross multiplying we get,

$\dashrightarrow \frak{4(x + 5) = 3(x + 7)}$

$\dashrightarrow \frak{4x + 20= 3x + 21}$

Transposing them to the other side we get

$\dashrightarrow \frak{4x - 3x = 21 - 20}$

$\: \: \: \: \: \: \: \: \: \star \: \red{\underline{ \orange{ \boxed{ \pink{\frak{x = 1}}}}}}$

___________________________

Putting the value of x in the original fraction we get

$\twoheadrightarrow \frak{Fraction_{(Original)} = \frac{1}{1 + 2} }$

$\twoheadrightarrow \frak{Fraction_{(Original)} = \frac{1}{3} }$

Henceforth, the original fraction is 1/3