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CCSS Math: 5.NF.B.6

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.