Question

1. shelley pours \\(\frac{4}{5}\\) gallon of water into a bird bath. the next morning, she finds that \\(\frac{3}{4}\\) of the water is gone. what is the amount of water, in gallons, that is gone?\

a \\(\frac{7}{9}\\) gallon\
b \\(\frac{3}{5}\\) gallon\
c \\(\frac{1}{4}\\) gallon\
d \\(\frac{1}{5}\\) gallon

Explanation:

Step1: Identify the operation

To find the amount of water gone, we need to multiply the initial amount of water by the fraction of water that is gone. The initial amount is $\frac{4}{5}$ gallon and the fraction gone is $\frac{3}{4}$.

Step2: Perform the multiplication

Multiply $\frac{4}{5}$ by $\frac{3}{4}$. When multiplying fractions, we multiply the numerators together and the denominators together: $\frac{4}{5} \times \frac{3}{4} = \frac{4 \times 3}{5 \times 4}$.

Step3: Simplify the fraction

The 4 in the numerator and the 4 in the denominator cancel out, leaving us with $\frac{3}{5}$? Wait, no, wait. Wait, $\frac{4\times3}{5\times4}=\frac{12}{20}=\frac{3}{5}$? Wait, no, that's not right. Wait, 4 divided by 4 is 1, so it's $\frac{1\times3}{5\times1}=\frac{3}{5}$? Wait, no, the options don't have $\frac{3}{5}$. Wait, wait, maybe I made a mistake. Wait, the initial amount is $\frac{4}{5}$ gallon, and $\frac{3}{4}$ of it is gone. So $\frac{4}{5} \times \frac{3}{4}$. Let's do that again. 4 and 4 cancel, so it's $\frac{1}{5} \times 3 = \frac{3}{5}$? But the options are A. $\frac{7}{9}$, B. $\frac{3}{5}$, C. $\frac{1}{4}$, D. $\frac{1}{5}$. Wait, option B is $\frac{3}{5}$ gallon. So that's the answer.

Wait, let's check again. $\frac{4}{5} \times \frac{3}{4} = \frac{12}{20} = \frac{3}{5}$. Yes, so the amount of water gone is $\frac{3}{5}$ gallon, which is option B.

Answer:

B. $\frac{3}{5}$ gallon