Question 312086: help!! can you help me im trying to take a placement test to go back to school and one of the questions is 1/2+(2/3 / 3/4) -(4/5*5/6)= it may be simple but i have not gone to school for about 7 years and i dont know were to start
Answer by solver91311(24713)   (Show Source):
You can put this solution on YOUR website!
\ -\ \left(\frac{4}{5}\,\cdot\,\frac{5}{6}\right))
First let's deal with the multiplication that is going on in the second set of parentheses. Multiplying fractions requires you to multiply numerator (top number) times numerator and denominator (bottom number) times denominator. Whenever you have factors common to both numerator and denominator, you can eliminate them.
So for the multiplication in the second set of parentheses, notice that you have a 5 in the denominator of the first fraction and a 5 in the numerator of the second fraction. Change the 5s to 1s.
\ -\ \left(\frac{4}{1}\,\cdot\,\frac{1}{6}\right))
Also notice that 4 is equal to 2 times 2 and 6 is equal to 2 times 3, so:
\ -\ \left(\frac{2\,\cdot\,2}{1}\,\cdot\,\frac{1}{2\,\cdot\,3}\right))
Now we have a 2 in the numerator of the first fraction and a 2 in the denominator of the second fraction. Eliminate this common factor by changing the 2s to 1s.
\ -\ \left(\frac{1\,\cdot\,2}{1}\,\cdot\,\frac{1}{1\,\cdot\,3}\right))
Now we can perform the multiplication -- numerator times numerator and denominator times denominator:
\ -\ \left(\frac{2}{3}\right))
Next let's deal with the division problem in the first set of parentheses. To divide fractions, invert the divisor (the "divided by" number) and multiply. So:
\ -\ \left(\frac{2}{3}\right))
There are no common factors between the numerators and denominators this time, so we can only multiply numerator by numerator and denominator by denominator:
\ -\ \left(\frac{2}{3}\right))
Now we have three fractions that we must add. In order to add fractions, they must have the same denominator. First thing is to find the smallest number that can be evenly divided by 2, 3, and 9. In this case, that would be 18. Since 18 divided by 2 is 9, we are going to multiply the first fraction by  . That will make the denominator of the first fraction be 18 without changing the overall value of the fraction because we are actually multiplying it by  . Note: Anything divided by itself is 1, i.e.  no matter what  is.. Likewise, we want to multiply the second fraction by  and the third one by  :
\ -\ \left(\frac{2}{3}\,\cdot\,\frac{6}{6}\right))
Again, multiplication is numerator times numerator and denominator times denominator:
\ -\ \left(\frac{12}{18}\right))
Once we have all of the fractions with equal denominators, they can be added by adding the numerators.
Since 13 and 18 are co-prime, we cannot reduce this fraction any further.
John
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