Dividing fractions and whole numbers word problems
Tracy is putting out decorative bowls of potpourri in each room of the hotel where she works. She wants to fill each bowl with 1/5 of a can of potpourri. If Tracy has 4 cans of potpourri, in how many rooms can she place a bowl of potpourri? So she has 4 cans, and she wants to divide this 4 cans into groups of 1/5 of a can. So if you have 4 of something and you're trying to divide it into groups of a certain amount, you would divide by that amount per group. So you want to divide 4 by 1/5. You want to divide 4 cans of potpourri into groups of 1/5. So let's visualize this. Let me draw one can of potpourri right over here. So one can of potpourri can clearly be cut up into 5/5. We have it right over here. 1, 2, 3, 4, 5. So 1 can of potpourri can fill 5 bowls if you put 1/5 in each bowl. Now, we have 4 cans. So let me paste these. So 2, 3, and 4. So how many total bowls of potpourri can Tracy fill? Well, she's got 4 cans. So this is going to be equal to-- let me do this is the right color-- this is going to be equal to, once again, she has 4 cans. And then for each of those cans, she can fill 5 bowls of potpourri because each bowl only requires a 1/5 of those cans. So this is going to be the same thing as 4 times 5. Or we can even write this as 4 times 5 over 1. 5 is the same thing as 5/1, which is the same thing as 4 times 5, which, of course, is equal to 20. She can fill 20 cans-- or I should say, with her 4 cans, she can fill 20 bowls of potpourri. Now, just as a review here, we've already seen that dividing by a number is equal to multiplying by its reciprocal. And we see that right over here. Dividing by 1/5 is the same thing as multiplying by the reciprocal of 1/5, which is 5/1. So she could fill up 20 bowls of potpourri.