Question

3
Q#4: The numerator of a
fraction is
7 less than the
denominator. If 3 is added
to the
numerator and 9
is substracted from the
denominator. The
new fraction
is Equal
to
3/2. Find
the origional fraction.

​

Answer 1

Let denominator be= x

Numerator= x-7

Adding the numbers in both--------------

Denominator= x+9

Numerator=x-7+3=>x-4

According to the question:

(x-4/x+9)=3/2

2(x-4)=3(x+9)

2x-8=3x+27

x=-27-8

x=(-35)

Answer 2

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$\color{red}\large\underline{\underline{Question:}}$

The numerator of a fraction is 7 less than the denominator. If 3 is added to the numerator and 9 is substracted from the denominator. The new fraction is Equal to 3/2. Find the origional fraction.

$\color{blue}\large\underline{\underline{Answer:}}$

Let the denominator of the fraction be 'x'.

So the original fraction is

$\frac{x - 7}{x}$

• Let us assume the given situation.

$\frac{x - 7 + 3}{x - 9} = \frac{3}{2}$

$\frac{x - 4}{x - 9} = \frac{3}{2}$

• By Cross Multiplication,

$2(x - 4) = 3(x - 9)$

$2x - 8 = 3x - 27$

$2x - 3x = - 27 + 8$

$- x = - 19$

$x = 19$

Put the value of x in the fraction to find the original fraction.

Original fraction =

$\frac{x - 7}{x} = \frac{19 - 7}{19} = \frac{12}{19}$

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