Tutoring middle school math, you encounter mixed numerals. The tutor shows a way to add them.

An example of a mixed numeral is 2³⁄₄. There is a whole number part and a fraction part. Notice that the whole number part (in this case, 2), times the denominator (in this case, 4), plus the numerator (in this case, 3) gives 11. The denominator stays the same: 4. Then you have ¹¹⁄₄, which is the same value expressed as an improper fraction.

Imagine now, that we want to perform 3²⁄₅+ 4⁶⁄₇. Of course, we know that to add fractions, we need a common denominator. We have two choices: 1)add the mixed numerals or else 2)convert them to improper fractions and then add.

Choice 1: Add the mixed numerals

First, get common denominators for the fractions, then add them:

(2×7)/(5×7) + (6×5)/(7×5) = 44/35

Add the whole numbers together

3 + 4 = 7

So we have

7 44/35

We are done, except for one hang-up: we now have an improper fraction: ⁴⁴⁄₃₅. Dividing 44 by 35, we get 1 remainder 9. Therefore,

7 44/35 = 7+1  9/35 = 8 9/35

In my next post, I’ll follow up with the easier method, which is to convert the mixed numerals to improper fractions, then add.

Jack of Oracle Tutoring by Jack and Diane, Campbell River, BC.