这个题怎么做---Sam bought $9 \frac{1}{2}$ liters of lemonade for a picnic. If each person drinks exactly $\frac{2}{5}$ of a liter of lemonade, what is the maximum number of people Sam can serve?
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Let's solve this step by step. Sam has 9 and one-half liters of lemonade total. Each person drinks exactly two-fifths of a liter. We need to find the maximum number of people Sam can serve. This is a division problem where we divide the total amount by the amount per person.
First, we need to convert the mixed number 9 and one-half to an improper fraction. We start with 9 and one-half equals 9 plus one-half. Converting 9 to halves gives us 18 halves plus 1 half, which equals 19 halves. So 9 and one-half equals 19 over 2.
Now we set up the division equation. We need to divide 19 over 2 by 2 over 5. This division asks the question: how many groups of 2 fifths can we make from 19 halves? Think of it as fitting smaller containers into a larger container to see how many will fit.
To divide fractions, we multiply by the reciprocal. The reciprocal of 2 over 5 is 5 over 2 - we flip the fraction. So 19 over 2 divided by 2 over 5 becomes 19 over 2 times 5 over 2. We multiply the numerators: 19 times 5 equals 95. We multiply the denominators: 2 times 2 equals 4. This gives us 95 over 4.
Now we convert 95 over 4 to a mixed number. 95 divided by 4 equals 23 with remainder 3, so 95 over 4 equals 23 and three-fourths. Since we can't serve a fraction of a person, the maximum number of people Sam can serve is 23. Let's verify: 23 times two-fifths equals 46 over 5, which is 9 and one-fifth liters. Since 9 and one-fifth is less than 9 and one-half, our answer is correct. Sam can serve 23 people.