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### Course: Arithmetic (all content) > Unit 5

Lesson 23: Multiplying fractions word problems# Multiplying fractions word problem: laundry

Learn how to solve word problems involving multiplication of fractions. Watch examples of real-life scenarios where fractions are multiplied, and practice applying the concept to solve similar problems. Created by Sal Khan.

## Want to join the conversation?

- I don't think this is correct because 2/3 = 4/6 and 1/2 = 3/6 so 4/6 subtract 3/6 = 1/6(9 votes)
- Notice that Gina used half of the detergent, not half a cup of detergent.

She started with 2∕3 cup and used 1∕2 of it,

i.e. she used (1∕2)(2∕3) = 1∕3 cup.

Thereby she'd be left with 2∕3 − 1∕3 = 1∕3 cup.(25 votes)

- Why multiply? Shouldn't he subtract? To get what's left he should subtract.(3 votes)
- There are 2/3 cups of detergent and she uses 1/2 of it. She uses 1/2 of the detergent that she has, not 1/2 half of a cup. Usually, when you're trying to find a proportion of something, you're multiplying. The key word for multiplying is "of".(8 votes)

- How do u know when a word problem is multiplying fractions or dividing fractions(5 votes)
- you do this and that you equal your head(4 votes)

- This isn't a homework question so can anyone figure out the answer to this question?

1/3 gallon milk poured into 5 equal sized cups. What fraction of a gallon of milk is in each cup.(2 votes)- 1/15 gallons of milk is in each of the five cups, because 1/3 divided by 5 is equal to 1/15.(3 votes)

- Sal said, "She used a third of her detergent and has a third left". She actually used a 1/2

of her detergent.(0 votes)- Sal said she used a third CUP of her detergent, which is equal to a half of her detergent before she used it.

As in, a half of 2/3 cups is 1/3 cup.(5 votes)

- How come in the video, they multiplied for some reason?? Shouldn't you subtract? That was confusing. Can someone explain the whole thing to me??(2 votes)
- Subtracting will do no good in this kind of problem. I can't really explain, but I can sense it... It seems rather obvious to me... Although, ( I don't want to offend anybody, side note), some people might be oblivious to that.(1 vote)

- Why didn't he just subtract I know it's a multiplication problem but it literally asked how much detergent she was left with.. after she used some that's just subtracting E.G "I had had 1 liter Cola or 4/4 of a cola I drank 2/4 how much is left I mean please someone explain logically thank a you.(0 votes)
- The truck is that she used half of the 2/3 that she had. If you subtract 1/2 from 2/3 you are assuming that she used a half of a full bottle's worth, not half of the 2/3.

When you multiply 1/2 x 2/3 you get 1/3, which is the actual amount Gina used. You can subtract 1/3 from 2/3 to get 1/3 which is the amount Gina has left. (Though that subtraction step sort of got glossed over in the video because we know that, being a half, the other half is going to be the same.)(4 votes)

- If the problem was mary drank 2/3 of a water bottle that had the original amount of 7/8 how much water was left? Then would the same technique be used?(0 votes)
- If you are told that james eats 1/3 of pizza and friend easts 2/4 pizza and told that ten slices are left. How may slices originally?(1 vote)
- Sal chose the fourth option but, as they said how much detergent will be left, we can to choose the first option because it makes more sense. Why did sal choose the fourth option instead of the first one??(1 vote)
- In the first option, they're saying 2/3 MINUS 1/2. We are trying to find the answer for 2/3 TIMES 1/2. Hope this helps.(1 vote)

## Video transcript

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.