To solve the problem of determining how many liters of smoothies were sold, we need to follow these steps:
Step 1: Convert the mixed numbers into improper fractions or decimals for easier calculation.
1. The initial amount of smoothies prepared: [tex]\( 12 \frac{1}{2} \)[/tex]
- Converting this to a decimal: [tex]\( 12 \frac{1}{2} = 12 + \frac{1}{2} = 12 + 0.5 = 12.5 \)[/tex] liters
2. The remaining amount of smoothies: [tex]\( 2 \frac{5}{8} \)[/tex]
- Converting this to a decimal: [tex]\( 2 \frac{5}{8} = 2 + \frac{5}{8} = 2 + 0.625 = 2.625 \)[/tex] liters
Step 2: Subtract the remaining amount from the initial amount to find out how many liters were sold.
[tex]\[ 12.5 - 2.625 = 9.875 \][/tex]
Step 3: Convert the decimal result back to a mixed number for clarity:
To convert 9.875 to a mixed number:
- The integer part is [tex]\( 9 \)[/tex].
- The fractional part is [tex]\( 0.875 \)[/tex].
Step 4: Convert the fractional part back to a fraction:
[tex]\( 0.875 = \frac{875}{1000} \)[/tex]
Simplifying [tex]\(\frac{875}{1000}\)[/tex] by dividing both the numerator and the denominator by their greatest common divisor, which is 125:
[tex]\[ \frac{875 \div 125}{1000 \div 125} = \frac{7}{8} \][/tex]
So, [tex]\( 0.875 = \frac{7}{8} \)[/tex].
Therefore, [tex]\( 9.875 \)[/tex] can be expressed as [tex]\( 9 \frac{7}{8} \)[/tex].
Step 5: Match the result with the given options:
a) [tex]\( 9 \frac{7}{8} \)[/tex] (Correct answer)
b) [tex]\( 6 \frac{5}{8} \)[/tex]
c) [tex]\( 8 \frac{1}{2} \)[/tex]
d) 9
The correct answer is:
a) [tex]\( 9 \frac{7}{8} \)[/tex]
