Question

11. The numerator of a fraction is 1 less than the denominator. If
numerator is decreased by 2 and denominator is increased by 3, the
fraction becomes 1/4. Find the fraction.

Answer 1

Answer:

Fraction = 4/5

Step-by-step explanation:

Question

The numerator of a fraction is 1 less than the denominator. If numerator is decreased by 2 and denominator is increased by 3, the fraction becomes 1/4. Find the fraction.

Answer

• 》Let the denominator be x

• 》Numerator = x -1 (Given in the Question)

In the Question it is given that when the numerator is decreased by 2 and denominator is increased by 3, the

fraction becomes 1/4.

Equation

• 》[(x -1) - 2 )] / (x + 3) = 1/4

• 》Do cross multiplication

• 》4(x - 1 - 2 ) = (x + 3) × 1

• 》4 ( x - 3) = (x + 3)

• 》(4 × x) - (4 × 3) = x + 3

• 》4x - 12 = x + 3

• 》4x - x = 12 + 3

• 》 3x = 15

• 》x = 15/3

• x = 5

So we got the x as 5

∴Denominator = x = 5

∴ Numerator = x - 1 = 5 - 1 = 4

∴ Fraction = 4/5

Answer 2

$\footnotesize{ Let, \: the \: fraction \: be \: \frac{x - 1 }{x}. }$

$\footnotesize{\frac{ x - 1 - 2}{ x + 3 }= \frac{1}{4} }$

$\footnotesize{\implies \frac{ x - 3}{ x + 3 }= \frac{1}{4} }$

$\footnotesize{\implies 4x - 12 = x + 3 }$

$\footnotesize{\implies 4x - x = 12 + 3 }$

$\footnotesize{\implies 3x = 15 }$

$\footnotesize{\implies x = \frac{15}{3} }$

$\footnotesize{\implies x = 5 }$

$\footnotesize{Fraction = \frac{x - 1}{x} }$

$\footnotesize{\implies Fraction = \frac{5 - 1}{5} }$

$\footnotesize{\implies Fraction = \frac{4}{5} }$