Mathematics has got to be the most interesting of all subjects. As I was telling the wonderful math faculty at Berkshire Community College, even arithmetic is fascinating. Addition and multiplication are commutative: 4+7=7+4 and 4×7=7×4. I recall MIT Professor Michael Artin saying:

When I ask my kids what’s 4×7, they answer “28.”

7×4? “28.”

4+7? “11.”

7+4? “You already asked us that.”

Commutativity of multiplication is true, but commutativity of addition is obvious. Later on those youngsters will find that for matrices, addition remains commutative but multiplication does not.

“Now if you could only make fractions interesting,” the math faculty responded.

## 2 thoughts on "Adding Fractions"

For a fun exercise, consider Egyptian fractions. The goal is to write any fraction a/b as a sum of reciprocals of distinct integers. Thus 3/4 = 1/2 + 1/4, and 3/5 = 1/2 + 1/10; note we’re not writing these as 1/4 + 1/4 + 1/4 or 1/5 + 1/5 + 1/5. Is it possible to do this for every a/b in the interval (0,1]? What about any positive rational?

Fractions are super fun with bar models/tape diagrams! You can visualize what the common denominator really is, and solve problems that seem like they would require algebra! I am hopeful that common core math will help students really understand fractions rather than encouraging them to memorize some algorithm they don’t understand. It is said that most math anxiety begins with fractions, but maybe we can change that.