Answer:
18 servings, because you can make the recipe 6 times.
Explanation:
I'll assume that the recipe requires 1/4 lb of onion, and not 1/4 of an onion. Otherwise you can't solve it. (I think there's a "lb" missing after "1/4" in the question.
An easy way to do this one is just to think about it: if you make the recipe once, then you've used 1/4 lb of onion, right?
And if you make it again, then you've used another fourth of a pound, so you've used up 1/2 lb of onion.
You could keep going like that for a total of 6 times to use up all the available onions.
Or you could think, "If I make the recipe twice, that uses 1/2 lb of onion. How many half-pounds are in one and a half pounds? Oh, that's just 3. So if I made it twice to use half a pound, then I have to do that 3 times to use up the whole 1.5 lbs. Okay, so doubling the recipe 3 times is making it 2 x 3 = 6 times."
But the answer isn't "6," because then you remember that each recipe makes 3 servings, and the question asks how many servings. So that's 6 x 3, of course, or 18. 18 servings.
Or if you're comfortable with fractions (or even if you're not), you can just figure out how many quarter-pounds are in 1.5 pounds. You can reason it out by realizing that there must be 4 quarter-pounds in 1 pound, then 2 quarter-pounds in a half-pound. So making the recipe 6 times would use up 6 quarter-pounds of onions, which is the same as the 1.5 lbs of onions he has.
Or if you want to do it with an equation, you just have to divide 1 1/2 by 1/4, which is the same thing, right? Figuring out how many fourths are in one and a half.
1 1/2 ÷ 1/4 = ?
Remember that when you divide by a fraction you get to invert it and multiply, so the problem becomes:
1 1/2 x 4/1 = 3/2 x 4 = 12/2 = 6
But again, that just means you can make the recipe 6 times.
Then you have to remember that each recipe makes 3 servings, so you've made: 6 x 3 = 18 servings.