Multiplying fractions word problem: laundry

Gina had 2/3 cups of laundry detergent. She used half of the detergent on Friday to wash all of her sheets. How much detergent does she have left? So we're essentially going to take half of 2/3, or 1/2 times 2/3. So let's see which of these choices match up. So we should be taking 1/2 times 2/3. Well, here they're taking 2/3 minus 1/2, so this isn't going to be right. Here they're going to be taking-- let's see, 1/3, because 2/3 times 1/2, this is exactly what we want to do. We want to take half of 2/3. And we multiply the numerators, 2 times 1 is 2. Multiply the denominators, 3 times 2 is 6. You have 2/6. You could say the 2/6 has either been used up or 2/6 is left. And 2/6 is the exact same thing as 1/3. Divide the numerator and the denominator by 2, so this looks right. And so here 1/6 cup, well, we know it's not 1/6 cup. We know it's 1/3 cup. So here, 1/3 cup, because 2/3 is equal to 1/3 plus 1/3, that's right. So half of 2/3 must be 1/3. This is exactly right as well. These are both completely reasonable ways to getting to the right answer that Gina has 1/3-- she used 1/3 of a cup of laundry detergent, and she has 1/3 left.