Answer:
The fraction decreases by 80 percent.
Step-by-step explanation:
1. Let the numerator be denoted by n and denominator be denoted by d. The fraction, f, becomes \frac{n}{d}.
2. The change in fraction is to be found out when the numerator is decreased by 40% and its denominator is decreased by 25%.
3. The new fraction, f1, consists of the modified numerator and modified denominator.
4. Hence, modified numerator and denominator are computed as explained. First, the new numerator is computed followed by the computation of new denominator.
5. Here, calculations are simple and involve equations in two variables. The expressions for both numerator and denominator are formed below.
6. The two variables are n1 and n, for numerator and the value of n1 is found in terms of n.
The new numerator, n1, is obtained when original numerator, n, is decreased by 40%, which is computed as shown.
n1 = n - (\frac{40}{100} \times n)
n1 = n - (\frac{2}{5} \times n)
n1 = n \times ( 1 - \frac{2}{5})
n1 = n \times \frac{3}{5}
n1 = \frac{3n}{5}
7. Similarly, the two variables for denominator are d1 and d, and the value of d1 is found in terms of d.
The new denominator, d1, is obtained when original denominator, d, is decreased by 25%, which is computed as shown.
d1 = d - (\frac{25}{100} \times d)
d1 = d - (\frac{1}{4} \times d)
d1 = d \times ( 1 - \frac{1}{4})
d1 = d \times \frac{3}{4}
d1 = \frac{3d}{4}
The new fraction, f1, is given by new numerator divided by new denominator.
f1 = \frac{new numerator}{new denominator}
f1 = \frac{3n}{5} \times \frac{4}{3d}
f1 = \frac{n}{5} \times \frac{4}{d}
f1 = \frac{4n}{5d}
f1 = \frac{4}{5} \times \frac{n}{d}
f1 = \frac{4}{5} \times f
percent decrease = \frac{4}{5} \ times 100 = \frac{400}{5} = 80
8. Hence, if the numerator is decreased by 40% and the denominator is decreased by 25%, the original fraction is decreased by 80 percent.
