When adding mixed numbers should you add the whole numbers first or the fractions?

Answer 1

I personally would convert them to improper fractions, add them and then convert the result back to a mixed number.

However, if you want to add the parts separately, it would be better to add the fractions first as this could result in a carry of a whole number to add into the addition of the whole numbers.

eg 2 1/3 + 3 5/6

Adding fractions and whole numbers separately:

Fractions: 1/3 + 5/6 = 2/6 + 5/6 = 7/6 = 1 + 1/6 = 1/6 + (carry to the whole numbers)

Whole numbers: 2 + 3 + (carry) = 2 + 3 + 1 = 6

→ 2 1/3 + 3 5/6 = 6 1/6

Done as improper fractions:

2 1/3 + 3 5/6 = (2x3+1)/3 + (3x6+5)/6 = 7/3 + 23/6 = 14/6 + 23/6 = 37/6 = (6x6+1)/6 = 6 1/6