consider a proper fraction such that the numerator is 2 less than the

1.	consider a proper fraction such that the numerator is 2 less than the denominator. if the numerator and denominator are each increased by 1, then the ratio of the numerator and denominator of the new fraction is 4:5. determine the original fraction
Answer» Answer:- LET the fraction be x/y. Given: Numerator is 2 less than the denominator. ⟶ Numerator = denominator - 2 ⟶ x = y - 2 -- equation (1) And, If numerator and denominator are increased by 1 , the RATIO of numerator and denominator is 4 : 5. According to the above condition, $\longrightarrow \sf \: \dfrac{x + 1}{y + 1} = \dfrac{4}{5}$ Substitute the VALUE of x from equation (1). $\longrightarrow \sf \: \frac{y - 2 + 1}{y + 1} = \frac{4}{5} \\ \\ \longrightarrow \sf \:5(y - 1) = 4(y + 1) \\ \\ \longrightarrow \sf \:5y - 5 = 4y + 4 \\ \\ \longrightarrow \sf \:5y - 4y = 4 + 5 \\ \\ \longrightarrow \boxed{ \sf \:y = 9}$ Substitute the value of y in equation (1) ⟶ x = y - 2 ⟶ x = 9 - 2 ⟶ x = 7 ∴ The original fraction x/y is 7/9

consider a proper fraction such that the numerator is 2 less than the denominator. if the numerator and denominator are each increased by 1, then the ratio of the numerator and denominator of the new fraction is 4:5. determine the original fraction

Answer»

Answer:-

LET the fraction be x/y.

Given:

Numerator is 2 less than the denominator.

⟶ Numerator = denominator - 2

⟶ x = y - 2 -- equation (1)

And,

If numerator and denominator are increased by 1 , the RATIO of numerator and denominator is 4 : 5.

According to the above condition,

$\longrightarrow \sf \: \dfrac{x + 1}{y + 1} = \dfrac{4}{5}$

Substitute the VALUE of x from equation (1).

$\longrightarrow \sf \: \frac{y - 2 + 1}{y + 1} = \frac{4}{5} \\ \\ \longrightarrow \sf \:5(y - 1) = 4(y + 1) \\ \\ \longrightarrow \sf \:5y - 5 = 4y + 4 \\ \\ \longrightarrow \sf \:5y - 4y = 4 + 5 \\ \\ \longrightarrow \boxed{ \sf \:y = 9}$

Substitute the value of y in equation (1)

⟶ x = y - 2

⟶ x = 9 - 2

⟶ x = 7

∴ The original fraction x/y is 7/9