A fraction is equivalent to 5/9. When 3 is subtracted from numerator, its value is 1/2. Find the value of the fraction if the denominator is increased by 6.
(5 n - 3) / (9 n) = 1 / 2 ... 2(5 n - 3) = 9 n ... n = 6
original fraction ... 30 / 54
30 / (54 + 6) = 30 / 60 = 1 / 2
Thank you
Well, well, well, it seems we have a fraction mystery on our hands! Let's put on our detective hats and solve this case!
We have a fraction that is equivalent to 5/9, and when we subtract 3 from the numerator (top number), it becomes 1/2. Now, we need to find the value of the fraction when the denominator is increased by 6.
First, let's find the original value of the fraction before any changes. To do that, we can set up an equation using the information we have:
(5 - 3) / 9 = 1/2
Simplify it a bit:
2/9 = 1/2
Next, we'll find the new numerator by adding 3:
2 + 3 = 5
Now, let's increase the denominator by 6:
9 + 6 = 15
So, after all these calculations, the value of the fraction with the increased denominator is 5/15.
Voila! We've solved the fraction mystery!
To solve this problem, we need to find the numerator and the denominator of the fraction. Since we are given that the fraction is equivalent to 5/9, we can set up the following equation to represent the given information:
x/ (9) = 5/9
where x is the numerator of the fraction.
Now, we are told that when 3 is subtracted from the numerator, the value of the fraction becomes 1/2. We can set up another equation to represent this information:
(x - 3)/ (9) = 1/2
To find the value of the fraction when the denominator is increased by 6, we need to modify the equations accordingly. Let's define y as the increased denominator.
First, let's increase the denominator by 6. The new denominator is 9 + 6 = 15.
Now, we can modify the original equation accordingly:
x/ (15) = 5/9
Next, let's modify the equation when the numerator is decreased by 3:
(x - 3)/ (15) = 1/2
To solve these equations, we can use cross multiplication.
For the first equation:
9x = 5 * 15
9x = 75
x = 75/9
x ≈ 8.333
For the second equation:
2 * (x - 3) = 1 * 15
2x - 6 = 15
2x = 15 + 6
2x = 21
x = 21/2
x = 10.5
Since we are interested in the value of the fraction when the denominator is increased by 6, we need to use the value of x obtained from the first equation:
Fraction = x/ (15)
Fraction ≈ 8.333/ (15)
To get the precise decimal value of this fraction, we can divide 8.333 by 15:
Fraction ≈ 0.55553
Therefore, the value of the fraction when the denominator is increased by 6 is approximately 0.55553.