the numerator of a fraction is 4 less that it’s denominator. if 1 is added to both its numerator and denominator, it becomes ⁴/¹².

2 thoughts on “the numerator of a fraction is 4 less that it’s denominator. if 1 is added to both its numerator and denominator, it becomes ⁴/¹².”

1. Question : –

   The numerator of a fraction is 4 less than it’s denominator. If 1 is added to both it’s numerator and Denominator. Then, it becomes 4/12. Find the fraction.

   _____________________________

   ★ Let the Denominator of the fraction be x respectively.

   [tex]Then, \: it’s Numerator = (x \: – \: 4).[/tex]

   [tex]According \: to \: the \: Question \rightarrow[/tex]

   • If 1 is added to both it’s numerator and Denominator. Then, it becomes 4/12.

   [tex]⟹ \: \frac{(x – 4) + 1}{x + 1} = \frac{4}{12} [/tex]

   [tex]⟹ \: \frac{x – 3}{x + 1} = \frac{4}{12} [/tex]

   [tex]⟹12(x – 3) = 4(x + 1)[/tex]

   [tex]⟹12x – 36 = 4 x + 4[/tex]

   [tex]⟹12x – 4x = 4 + 36[/tex]

   [tex]⟹8x = 40[/tex]

   [tex]⟹x = \frac{40}{8} [/tex]

   [tex] \color{red}⟹x = 5[/tex]

   so,

   Numerator of fraction, (x – 4) = (5 – 4) = 1

   Denominator of fraction, x = 5

   ★ hence the required fraction is 1/5...

   Reply

2. Question : –

   The numerator of a fraction is 4 less than it’s denominator. If 1 is added to both it’s numerator and Denominator. Then, it becomes 4/12. Find the fraction.

   _____________________________

   ★ Let the Denominator of the fraction be x respectively.

   According to the Question ⟹

   If 1 is added to both it’s numerator and Denominator. Then, it becomes 4/12.

   ⟹ (x – 4) + 1 {x + 1} = 4/12

   ⟹ {x – 3} {x + 1} = 4/12

   ⟹12(x – 3) = 4(x + 1)

   ⟹12x – 36 = 4 x + 4

   ⟹12x – 4x = 4 + 36

   ⟹8x = 40

   ⟹x = 40/8

   ⟹x = 5

   So ,

   ⟹ Numerator of fraction , (x – 4) = (5 – 4) = 1

   ⟹ Denominator of fraction , x = 5

   ★ Hence the required fraction is 1/5…

   Reply