By what percent will a fraction change if its numerator is decreased by 50% and its denominator is decreased by 25%?
Let the original fraction be n/d
(0.5n)/(0.75d) = (0.5/0.75)(n/d) = (2/3)(n/d)
so the fraction will be decreased by 33.33%
To find the percent change in a fraction, we need to compare the difference between the original and new fractions to the original fraction, and then express that difference as a percentage.
Let's say the original fraction is p/q, where p is the numerator and q is the denominator.
If the numerator is decreased by 50%, it becomes 0.5 * p.
If the denominator is decreased by 25%, it becomes 0.75 * q.
So, the new fraction is (0.5 * p) / (0.75 * q), which can also be simplified to (0.5p/0.75q) * (4/4).
To compare this to the original fraction, we can express the original fraction as (p/q) * (4/4).
Now we have the original fraction and the new fraction in the same form, so we can compare the difference. The difference is (0.5p/0.75q) * (4/4) - (p/q) * (4/4).
Simplifying this, we get (0.5p - 0.75p) / (0.75q) * (4/4), which further simplifies to (-0.25p) / (0.75q) * (4/4) or (-p) / (3q) * (4/4).
To express this as a percentage, we multiply the difference by 100 to get (-p) / (3q) * (4/4) * 100.
Therefore, the percent change in the fraction can be calculated as -100p / 3q.