Numerator of a fraction is 4 less than its denominator. If we add 1 to the numerator
and subtract 2 from the denominator it becomes 4by5 . Find the original fraction
Answers
according to the question, numerator of a fraction is 4 less than its denominator and if we add 1 to the numerator
and subtract 2 from the denominator it becomes 4/5
let the denominator of the fraction be 'x'
therefore it's numerator will be = x - 4 (since numerator of the fraction is 4 less than it's denominator.
now, adding 1 to the numerator and subtracting 2 from the denominator.
➡ [(x - 4) + 1]/(x - 2) = 4/5
➡ (x - 3)/(x - 2) = 4/5
cross multiplying
➡ 5(x - 3) = 4(x - 2)
➡ 5x - 15 = 4x - 8
➡ 5x - 4x = -8 + 15
➡ x = 7
the value of x is 7
- denominator = x = 7
- numerator = x - 4 = 7 - 4 = 3
hence, the fraction is 3/7
Answer:
∴ Original Fraction = 3/7
Step-by-step explanation:
Assuming the denominator of the fraction as 'y'.
Now, according to the question:
Numerator of a fraction is 4 less than its denominator. If we add 1 to the numerator and subtract 2 from the denominator it becomes 4/5 .
To find:
The original fraction.
So, the numerator here is ( y - 4 ) as fraction is 4 less than the denominator.
Now,
Adding 2 & subtracting 1 from the denominator & numerator respectively.
⇒( y - 4 ) + 1/y - 2 = 4/5
⇒ y - 3/y - 2 = 4/5
Through cross multiplication, we have:
⇒ 5( y - 3 ) = 4( y - 2 )
⇒ 5y - 15 = 4y - 8
⇒ ( 5 - 4 )y = - 8 + 15
⇒ y = 7
Now ,
Value of denominator , y = 7
Value of numerator , ( y - 4 ) = 3