Question

the numerator of a fraction is less than its denominator by 1 if the numerator becomes three times and the denominator is increased by 19. the new fraction becomes 1/7 find the fraction​

Answer 1

Step-by-step explanation:

Given :-

The numerator of a fraction is less than its denominator by 1 if the numerator becomes three times and the denominator is increased by 19. the new fraction becomes 1/7.

To find :-

Find the fraction ?

Solution :-

Let the denominator be X

Then the numerator = Denominator -1

=> The numerator = X-1

Then the fraction = (X-1)/X

If the numerator becomes three times then it will be 3(X-1)

Then the denominator is Increased by 19

=> (X+19)

Then new fraction = 3(X-1)/(X+19)

According to the given problem

The new fraction = 1/7

=> 3(X-1)/(X+19) = 1/7

On applying cross multiplication then

=> 3(X-1)×7 = (X+19)

=> 21(X-1) = X+19

=> 21X-21 = X+19

=> 21X-X = 19+21

=> 20X = 40

=> X = 40/20

=> X = 2

Denominator = 2

Numerator = 2-1 = 1

Fraction = 1/2

Answer:-

The required fraction for the given problem is 1/2

Check :-

The fraction = 1/2

Numerator = 1 = 2-1

=> Denominator -1

And

3 times the numerator = 3(1) = 3

Denominator+19 = 2+19 = 21

New fraction = 3/21 = 1/7

Verified the given relations in the given problem

Used formulae:-

Fraction = Numerator / Denominator

Answer 2

QUESTION:-

the numerator of a fraction is less than its denominator by 1 if the numerator becomes three times and the denominator is increased by 19. the new fraction becomes 1/7 find the fraction​ ?

Given:-

• the numerator of a fraction is less than its denominator by 1
• if the numerator becomes three times and the denominator is increased by 19. the new fraction becomes 1/7

TO FIND:-

The fraction

EXPLANATION:-

Let the denominator - x

then numerator- x-1

and the fraction we get - $\frac{x}{x-1}$

3 TIMES NUMERATOR - 3x

If denominator is increased by 19 ,denominator - x+19

A.T.Q,

$\frac{3(x-1)}{x+19}= \frac{1}{7} \\\\\frac{3x-3}{x+19}= \frac{1}{7} \\\\\\21x-21=x+19\\\\21x-x=19+21\\\\20x=40\\\\x=\frac{40}{20} \\\\x=2$

SO we took x as denominator ,

so denominator =x

denominator ==>2

and numerator is - x-1

numerator ==>2-1

numerator===>1

and fraction is $\frac{1}{2}$

FORMULA USED:-

$Fraction=\frac{Numerator }{Denominator }$