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caroline has a pan of lasagna 3/4 full. Some friends come over and eat 2/3 of what was in the pan. How much lasagna did her friends eat?

caroline has a pan of lasagna 3/4 full. Some friends come over and eat 2/3 of what was in the pan. How much lasagna did her friends eat?

Daniel O. | Attorney and experienced teacher for LSAT Prep.Attorney and experienced teacher for LSA...
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The friends at 2/3 of 3/4.  "Of" is word problem for "multiply."  They ate (2/3)(3/4).  To multiply fractions, multiply the top across, and the bottom across:  (2/3)(3/4) = 6/12, which reduces to 1/2, since you can evenly divide both 6 and 12 by 6.  Your answer is 1/2 - they ate 1/2 a pan of lasagna.  1/4 is the amount remaining in the pan after the friends eat.

Daniel, you're absolutely correct. I think this is a prime example of why it's important to pay close attention to what the question asks. The first person that responded to the question did make accurate calculations, but ultimately provided the wrong answer since that's not the answer that the question called for.
Dattaprabhakar G. | Expert Tutor for Stat and Math at all levelsExpert Tutor for Stat and Math at all le...
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Carl:

What is 2/3 of 3/4? Answer is 1/2. So after the friends ate, 1/2 pan was full.  How much did the friends eat?

3/4 - 1/2 = 1/4.

Try it in decimals.  The pan was 0.75 full.  Two thirds of 0.75 (it is more convenient not to convert 2/3 in decimals, to get exact answers) 0.75 x 2/3 = 0.25 x 2 = 0.50.  The friends ate 0.75-0.50 = 0.25, which is 1/4.

Dattaaprabhakar (Dr.G.)