One serving of tortilla soup is one and two-thirds cups. A restaurant cooks 50 cups of soup. Is there enough to serve 25 people?
Let’s think about what we know. The restaurant has cooked 50 cups of soup, and each serving is one and two-thirds cups. We want to know if the restaurant can serve 25 people. To find out, we need to take the 50 cups that the restaurant cooked and divide that by the serving size, one and two-thirds. By dividing 50 by one and two-thirds, we’ll find out how many servings there are in 50 cups. But to do this, we’ll need to convert one and two-thirds into an improper fraction. One and two-thirds written as an improper fraction is five-thirds.
We know this because one whole written as a fraction with the denominator of three would be three over three and three over three plus two over three equals five over three. We now know that we need to divide 50 by five-thirds. But to divide with fractions, we multiply by the reciprocal. That means we’ll multiply by three-fifths. 50 times three-fifths can be simplified because five and 50 are both divisible by five. Now, we just need to multiply 10 by three, which gives us 30.
If the restaurant made 50 cups and there were one and two-thirds cup per serving, we could say that 50 cups makes 30 servings. Since 30 is greater than the 25 people we were wondering about, we can say, yes, this restaurant has enough soup to serve 25 people.
Before we move on, let’s think about one other way we could have solved this problem. We could have taken the 25 people and multiplied that by the number of cups in a serving, one and two-thirds. Again, we would need to use the improper fraction five-thirds to do this multiplication. From there, we would multiply the numerators together and the denominators together. Five times 25 is 125. One times three is three. This tells us to serve 25 people, you would need 125 over three cups.
But it’s probably better if we write this as a mixed number. If we do that, we get 41 and two-thirds cups. This is saying that in order to serve 25 people, you would need a minimum of 41 and two-thirds cups of soup. Since the restaurant has 50 cups of soup, that’s greater than the 41 and two-thirds cups required to serve 25 people. And again, we say, yes, this restaurant does have enough soup to serve 25 people.