Question 693943: Evaluate x over y or x/y for x = 2/3 and y = 5/6
Found 2 solutions by stanbon, RedemptiveMath:
Answer by stanbon(75887)   (Show Source):
You can put this solution on YOUR website! x/y for x = 2/3 and y = 5/6
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x/y = (2/3)/(5/6)
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Multiply numerator and denominator by (6/5) to get:
x/y = (2/3)(6/5) = 4/5
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cheers,
Stan H.
Answer by RedemptiveMath(80) (Show Source):
You can put this solution on YOUR website! Dividing fractions may look confusing if we use the backslash (/) or Vinculum (horizontal bar meaning division) symbol, but if we use the basic "÷", it may clear things up a lot.
So, we have our first fraction, 2/3, that represents x. We have our second fraction, 5/6, that represents y. The problem wants us to divide x by y, or x/y. This would look confusing if we did it like this: (2/3)/(5/6). However, if we do it like this, it may help us: 2/3 ÷ 5/6. By laws of division, we would "keep, flip and multiply." Or, we would change the second fraction into its reciprocal and multiply the first fraction and reciprocal fraction together. We would get:
2/3 ÷ 5/6
2/3 ÷ 6/5 (keep the first; flip the second)
2/3 * 6/5 (multiply both fractions)
12/15.
We get 12/15 as an answer, but this is not simplified. This fraction can be reduced. What number can we divide into the numerator, 12, and the denominator, 15, to reduce it to lowest terms? 3 would work:
12/15
(12÷3)/(15÷3)
4/5.
Our answer should be 4/5. To check ourselves, we can do this operation in a calculator. Take 2 divided by 3 to get our first fraction of 2/3. Then multiply by the numerator of the reciprocal fraction, or 6. Finally divide by 5. This should come out to be a decimal of 0.8, which this is equal to 4/5 in decimal form. If you have a scientific calculator on a computer, you can simply divide 2/3 and 5/6 without having to take the reciprocal. You have to make sure to put both fractions in parentheses and a division sign between them in order to get the required answer. The calculator should still read 0.8 or 4/5.
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