SOLUTION: The numerator of a fraction is one more than the denominator. If the numerator and the denominator are both increased by 2, the new fraction will be one fourth less than the origi
Algebra.Com
Question 205861: The numerator of a fraction is one more than the denominator. If the numerator and the denominator are both increased by 2, the new fraction will be one fourth less than the original fraction. What is the original fraction?
Here's what I tried...
n+1/n original fraction
n+1+2/n+2 = n+1/n - 1/4 (n+1/n)
Don't know if I have it set up correctly. Need help. THanks!
Answer by ankor@dixie-net.com(22740) (Show Source): You can put this solution on YOUR website!
The numerator of a fraction is one more than the denominator.
If the numerator and the denominator are both increased by 2, the new fraction
will be one fourth less than the original fraction.
What is the original fraction?
:
Looks like you are on the right track, here's how I would do it
:
Let x = the denominator
"The numerator of a fraction is one more than the denominator." therefore:
(x+1) = the numerator
;
" If the numerator and the denominator are both increased by 2, the new fraction will be one fourth less than the original fraction."
= -
:
= -
Multiply equation by 4x(x+2)
4x(x+2)* = 4x(x+2)* - 4x(x+2)*
Cancel the denominators:
4x(x+3) = 4(x+2)(x+1) - x(x+2)
:
4x^2 + 12x = 4(x^2 + 3x + 2) - x^2 - 2x
:
4x^2 + 12x = 4x^2 + 12x + 8 - x^2 - 2x
Arrange as a quadratic equation on the left
4x^2 - 4x^2 + x^2 + 12x - 12x + 2x - 8 = 0
:
x^2 + 2x - 8 = 0
Factors to:
(x+4)(x-2) = 0
Positive solution
x = 2 is the denominator
then
2 + 1 = 3 is the numerator
:
What is the original fraction?
:
:
Check solution in the statement:
if the numerator and the denominator are both increased by 2, the new fraction will be one fourth less than the original fraction."
= -
= -
RELATED QUESTIONS
The denominator of a fraction is one more than twice the numerator. If both numerator and (answered by josgarithmetic,MathTherapy)
The numerator of a fraction is 1 less than the denominator. If the numerator and the... (answered by ankor@dixie-net.com)
The denominator of a fraction is 3 more than twice the numerator. If both the
numerator... (answered by josgarithmetic)
The denominator of a fraction is 4 more than the numerator if both the numerator and... (answered by ankor@dixie-net.com)
The denominator of a fraction is 9 more than its numerator. If the numerator and the... (answered by MathLover1)
The denominator of a fraction is four more than twice the numerator. If both numerator... (answered by solver91311,stanbon)
The denominator of a fraction is two more than twice the numerator. If both numerator and (answered by Fombitz)
the denominator of a fraction is 2 more than the numerator.
if both numerator and... (answered by mananth,josgarithmetic)
The denominator of a fraction is five more than twice the numerator. If both numerator... (answered by Fombitz,MathTherapy)
The denominator of a fraction is two more than the numerator. If both numerator and... (answered by josgarithmetic,MathTherapy)