14. In a fraction, twice the numerator is 2 more than the denominator. If 3 is added to the
numerator and to the denominator, the new fraction is2/3
Find the original fraction.
Answers
Step-by-step explanation:
Many of these other answers seem a bit confusing. I’ll try to simplify this a bit.
Let’s use x as the numerator, and I’ll explain everything else in terms of x.
From what you are describing, the equation would be (x+3)/(2x+1)=2/3.
I got here firstly by creating the “original fraction, which consists of a numerator x, and a denominator 2x - 2 (two less than twice the numerator). I then added 3 to both the numerator and denominator, and then I simplified them. I then equated this all to 2/3, the fraction you wanted them to equal.
Now, let’s solve this out. We can cross multiply:
(x+3) * 3 = (2x+1) * 2
Now, let’s distribute the 3 and 2:
3x + 9 = 4x + 2
3x + 7 = 4x
-3x -3x
7 = 1x
x=7
Therefore, the original fraction is 7/12.
7/12 add 3 to both the numerator and denominator becomes 10/15, which is 2/3.
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