Multiplying fractions word problem: laundry
About this video
Gina has 2/3 cup of detergent and uses half of it. The video finds half of 2/3 by multiplying 1/2 x 2/3 = 2/6 = 1/3, and checks answer choices, including the idea that 1/3 + 1/3 = 2/3.
You'll be able to
- write 'half of an amount' as multiplying by 1/2.
- multiply two fractions and simplify the answer.
- spot an expression that uses the wrong operation.
Key words
- simplify
- Rewrite a fraction with smaller numbers by dividing the top and bottom by the same number, like 2/6 = 1/3.
- equivalent fractions
- Fractions that look different but name the same amount, like 2/6 and 1/3.
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.
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