What distinguishes this approach--which my students and I called “The System"--is that it involves combining numbers rather than adding or subtracting them, as illustrated here: ...

For example: When you're adding and subtracting fractions with different denominators, ... Divide fractions by integers. count. 17 of 17. What are fractions? count. 1 of 17. Language: ...

When you're adding and subtracting fractions with different denominators, you need to change one, and sometimes both, of the fractions so that they have the same denominator. Let's look at an example: ...