Question

the numerator of a fraction is 4 less than denominator if the numerator is decreased by 2 and denominator increased by 1 then the denominator is eight times the numerator find the fraction this question of 20 points only intelligent can tell

Answer 1

let the denominator is x.
so,numerator=x-4

fraction=x-4/x

given,
8 (x-4-2)=x + 1

8 (x- 6)=x + 1

8x-48=x + 1

8x-x= 1 +48

7x=49

x=49/7

x=7.


fraction=x-4/x.

=7-4/7

= 3/7.

I hope it helps you.

Answer 2

ANSWER TO YOUR QUESTION:

STEP 1:
"numerator of a fraction is 4 less than denominator"from that statement we can bring out that  the denominator is  "x-4"
 and numerator can also be given as " x"

STEP 2:

so the fraction can be written as::

x-4 / x---------------------------EQUATION 1

STEP 3:

" if the numerator is decreased by 2 and denominator increased by 1 then the denominator is eight times the numerator"

BY THIS WE CAN WRITE 

 8 (x-4-2) / x+1
( as in the question the numerator is subtracted by 2 and denominator is increased( +) by 1 and it is said that the DENOMINATOR IS 8TIMES  THE NUMERATOR so to make it equal multiply the numerator by "8")

WE GET 
 8 (x-4-2) / x+1 --------------------EQUATION 2:

8( x-4-2) = x+ 1  ( by cross multiplication)

8( x-6) =  x+ 1 ( as -4-2 = -6,,,, (-)(-)=(+))

8  x-  48   =   x + 1

( now bring all the 'x' terms to one side and all the numericals to one side for calculation)

8 x -x  = 1 +48

now we get

7 x  = 49 

now by cross multiplying and bringing 7 to the denominator  we get "x " value

x   = 49 / 7 

i.e...... (x= 7)-------------EQUATION 3



STEP 4:



FROM EQUATION ONE OBTAINED IN STEP 2:

SUBSTITUTE EQUATION 3 IN 2


WE GET


=7-  4   /  7

= 3  /  7.------by the series of the step's as per the question the final fraction to be obtained is finally here !!!


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