By what percent will a fraction increase if its numerator is increased by 60% and its denominator is decreased by 20%?
100%
lets say the fraction is x/y x decreased by 20% and y decreased by 60%
so the next product is 0.8x/0.4y = 2 x/y = 200%-100% =100. so it increases by 100%
Ohhh, it's math time! Let's crunch some numbers.
If the numerator of a fraction is increased by 60% and the denominator is decreased by 20%, we can calculate the new fraction like this:
Let's say the original fraction is x/y.
After increasing the numerator by 60%, the new numerator will be 1.6x.
After decreasing the denominator by 20%, the new denominator will be 0.8y.
So the new fraction would be (1.6x)/(0.8y).
If we simplify that, we get 2x/y.
But wait, that's still the same fraction!
So, after all the changes, the fraction doesn't really increase or decrease at all. It remains the same. So, 0% increase!
Math can be quite tricky sometimes, but hey, at least we didn't need to pull out the circus tricks for this one!
To calculate the percentage increase in the fraction, follow these steps:
1. Start with the given fraction.
2. Increase the numerator by 60%.
3. Decrease the denominator by 20%.
4. Calculate the new fraction using the adjusted numerator and denominator.
5. Find the difference between the new fraction and the original fraction.
6. Divide the difference by the original fraction.
7. Multiply the result by 100 to convert it into a percentage.
Let's calculate it step by step.
Given fraction: numerator / denominator
1. Start with the given fraction:
Let's assume the given fraction is a/b.
2. Increase the numerator by 60%:
The new numerator will be a + (60% of a).
3. Decrease the denominator by 20%:
The new denominator will be b - (20% of b).
4. Calculate the new fraction:
The new fraction will be (a + (60% of a))/(b - (20% of b)).
5. Find the difference between the new fraction and the original fraction:
Difference = New fraction - Original fraction
6. Divide the difference by the original fraction:
Percentage increase = (Difference / Original fraction) * 100
7. Multiply the result by 100 to convert it into a percentage:
Finally, you will have the percentage increase in the fraction.
original fraction --- x/y
new fractions ------- 1.6x/.8y = 2x/y
it increased by 100%
e.g.
suppose the fraction was 5/8
new fraction = 1.6(5)/(.8(8))
= 8/6.4
= 80/64
= 10/8 ---> twice the 5/8