## the denominator of a fraction exceeds its numerator by 5...

Simplificatation, evaluation, linear equations, linear graphs, linear inequalities, basic word problems, etc.
Motherof8
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### the denominator of a fraction exceeds its numerator by 5...

THe denominator of a fraction exceeds its numerator by 5. If the numerator is decreased by 3 and the denominator increased by 1, the resulting fraction is equal to 2/5. What was the original fraction?

THe answer in the book is 9/14. I worked it out plugging this answer in and it checks out, but how do you arrive at it? I put x -3/x+ 5+1 = 2/5. What do I do now?

maggiemagnet
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### Re: the denominator of a fraction exceeds its numerator by 5

THe denominator of a fraction exceeds its numerator by 5. If the numerator is decreased by 3 and the denominator increased by 1, the resulting fraction is equal to 2/5. What was the original fraction?

...I put x -3/x+ 5+1 = 2/5.
How did you get this equation?

Instead, try doing like they show here:

They give you the denominator in terms of the numerator, so pick a variable for the number in the numerator. Then make an expression for the denominator, which is "five more than the numerator". This is for the original fraction.

For the second fraction, use the variable for the numerator, and make an expression for "three less than the numerator". Use the expression for the denominator, and make an expression for "one more than the denominator". Use these new expressions for the second fraction.

Put this second fraction equal to "2/5". Then solve the equation.

If you get stuck, please come back and show what you've done. Thanks!

Martingale
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### Re: the denominator of a fraction exceeds its numerator by 5

THe denominator of a fraction exceeds its numerator by 5. If the numerator is decreased by 3 and the denominator increased by 1, the resulting fraction is equal to 2/5. What was the original fraction?

THe answer in the book is 9/14. I worked it out plugging this answer in and it checks out, but how do you arrive at it? I put x -3/x+ 5+1 = 2/5. What do I do now?
you should use parenthesis ...

x -3/x+ 5+1 = 2/5
(x-3)/(x+5+1)=2/5

$\frac{x-3}{x+5+1}=\frac{2}{5}$