How do you add one third plus one sixth plus three eighteens?

Answer 1

two thirds. Here's how:

You need to have a common denominator to add or subtract fractions. Most people choose the Least Common Denominator (or Lowest Common Denominator), but any denominator which has all of the denominators as factors will get you the correct answer as an equivalent fraction. Now with this one, you could first simplify 3/18 to 1/6, then proceed, or you can just look at the denominators first.

Looking at the denominators you can just multiply them all together to get a common denominator of 324, or try to find a lower common denominator: 6 is a factor of 18, and 3 is a factor of 18, so 18 is the Lowest Common Denominator.

We need to convert the other fractions to equivalent fractions with 18 as the denominator. So for 1/3: 18 ÷ 3 = 6, so multiply the numerator and denominator by 6, to get 6/18; and for 1/6: 18 ÷ 6 = 3, so multiply numerator and denominator by 3, to get 3/18.

Now we have 6/18 + 3/18 + 3/18. Add the numerators: 6 + 3 + 3 = 12, and put this over 18: 12/18. Now simplify if you want: 6 is common to both 12 & 18, so you can cancel: 12/18 = (6 × 2)/(6 × 3) = 2/3.