what is the common denominator for 4/9 + 5/6+ 1/3

Question

I need to know how to work this problem and what the common denominator is: 4/9 + 5/6 +1/3 =

Answer 1

In order to work the problem, you need a common denominator (bottom number of a fraction).  You can always multiply the denominators to get a common denominator, but that may not be the least common denominator.  Using a larger number can result in needing to reduce a larger fraction to lowest terms.

Start with the largest denominator (9).  Multiply it by 2.  It equals 18.   Can the other 2 denominators divide evenly into 18?  Yes, they can.  That tells you that this is the common denominator.  If the answer was no, you would then multipy 9 by 3, 4, 5, etc., until one of the products could be used as the common denominator.

Next, you need to change each fraction to an equivalent (equal) fraction.  Put 18 as the denominator for all three fractions.  Divide the original denominator into 18 and multiply your answer by the numerator of the same fraction.  Do this process for each of the three fractions. 

Finally, add all three numerators.  The denominators do not get added.  The denominator in the answer will also be 18.  Your answer should be 29/18.  This is an improper fraction ( a fraction where the numerator is equal to or greater than the denominator).  Divide the denominator into the numerator (29 divided by 18).  Your answer will be 1 11/18.  Your remainder of 11 is put over the original denominator (18).  Hope this is helpful!

Answer 2

You need a least common denominator. Note it is a multiple of 9=2⁰3², 6=2¹3¹ and 3=2⁰3¹ (note that 2⁰=1 was inserted in two factorizations).

Just take the largest exponent of each prime to get 2¹3² = 18