Question

the the numerator of a fraction is less than its denominator by 4. if if denominator is decreased by 1 and the numerator is increased by 11 the new number becomes 7 by 3 find the original fraction please guys help me please please please​

Answer 1

Answer:

The original fraction = $\frac{3}{7}$

Step-by-step explanation:

Let's assume the denominator of the fraction is x

∴ The numerator is x - 4.

New denominator = x - 1

And New numerator = x - 4 + 11 = x + 7

According to the problem:

$\frac{x + 7}{x - 1} = \frac{7}{3}$

=> 3x + 21 = 7x - 7

=> - 4x = -28

∴ x = 7 = original denominator

Original numerator = x - 4 = 3

∴ The original fraction = $\frac{3}{7}$

Answer 2

GIVEN :-

• The numerator of a fraction is less than its denominator by 4.
• Denominator is decreased by 1 and the numerator is increased by 11 the new number becomes 7/3.

TO FIND :-

• The original Fraction.

SOLUTION :-

Let the denominator of the fraction be "x". Therefore the numerator of the fraction be "x - 4".

★ Original Fraction = (x - 4)/x

★══════════════════★

New numerator become x - 6 + 11 = "x + 7".

New denominator become = "x - 1".

★ New fraction = (x + 7)/(x - 1)

$\underline { \bigstar \: \textsf{According to the Question now :}}$

$: \implies \displaystyle \sf \: \frac{x + 7}{x - 1} = \frac{7}{3}$

$: \implies \displaystyle \sf \: 7(x - 1) = 3(x + 7)$

$: \implies \displaystyle \sf \: 7x - 7 = 3x + 21$

$: \implies \displaystyle \sf \: 7x - 3x = 21 + 7$

$: \implies \displaystyle \sf \: 4x = 28$

$: \implies \displaystyle \sf \: x = \frac{28}{4}$

$: \implies \underline{ \boxed{ \displaystyle \sf \: \textbf{ x = 7}}}$

★══════════════════★

★ Original Fraction = (x - 4)/x

★ Original fraction = (7 - 4)/7 = 3/7

Hence the required original fraction is 3/7.