Certainly! Let's break down and understand the problem step by step:
### Step 1: Initial Amount of Milk
The cafe started the day with [tex]\(\frac{15}{16}\)[/tex] of a crate of milk. We can express this as:
[tex]\[
\text{Milk Initial} = \frac{15}{16}
\][/tex]
### Step 2: Amount of Milk Used
During the day, the cafe used [tex]\(\frac{1}{5}\)[/tex] of the milk it initially had. So, we need to calculate how much milk was used:
[tex]\[
\text{Milk Used} = \frac{1}{5} \times \left(\frac{15}{16}\right) = \frac{15}{16} \times \frac{1}{5} = \frac{15 \times 1}{16 \times 5} = \frac{15}{80}
\][/tex]
### Step 3: Simplify the Fraction for Milk Used
We simplify the fraction [tex]\(\frac{15}{80}\)[/tex] by finding its greatest common divisor (GCD). The GCD of 15 and 80 is 5, so we divide both the numerator and the denominator by 5:
[tex]\[
\frac{15}{80} = \frac{15 \div 5}{80 \div 5} = \frac{3}{16}
\][/tex]
Thus, the milk used during the day is [tex]\(\frac{3}{16}\)[/tex].
### Step 4: Calculate the Remaining Milk
To find out how much milk remains at the end of the day, we subtract the amount of milk used from the initial amount of milk:
[tex]\[
\text{Milk Remaining} = \frac{15}{16} - \frac{3}{16}
\][/tex]
Since the fractions have the same denominator, we can directly subtract the numerators:
[tex]\[
\text{Milk Remaining} = \frac{15 - 3}{16} = \frac{12}{16}
\][/tex]
### Step 5: Simplify the Fraction for Milk Remaining
Again, we simplify the fraction [tex]\(\frac{12}{16}\)[/tex] by finding its greatest common divisor (GCD). The GCD of 12 and 16 is 4, so we divide both the numerator and the denominator by 4:
[tex]\[
\frac{12}{16} = \frac{12 \div 4}{16 \div 4} = \frac{3}{4}
\][/tex]
Thus, the remaining milk at the end of the day is [tex]\(\frac{3}{4}\)[/tex].
### Final Summary
- The initial amount of milk was [tex]\(\frac{15}{16}\)[/tex] (or 0.9375 in decimal form).
- The amount of milk used during the day was [tex]\(\frac{3}{16}\)[/tex] (or 0.2 in decimal form).
- The remaining amount of milk at the end of the day was [tex]\(\frac{3}{4}\)[/tex] (or 0.75 in decimal form).
So, at the end of the day, the cafe has [tex]\(\frac{3}{4}\)[/tex] (0.75) of a crate of milk left.
