Add Fractions Within Whole by Changing Both

In this problem we're going to add two thirds plus one fourth. You can see there by my blue one whole shape that this sum is going to be less than one whole. Well, thirds and fourths, we'd love them to have common denominators. Obviously, they're not. So what we need to do is change the denominator to make equivalent fractions so that the denominators match. Well, thirds and fourths, if I skip count by three, three, 6, jumps right over fourths. So that tells me that thirds cannot become an equivalent fraction with a denominator of four. So we have to find a denominator in which both one, two thirds rather, and one fourth can become. Well, a simple multiplication three times four is 12. We'll get us there. That might not necessarily be the least common denominator, but that is a guaranteed common denominator. So first thing we'll do is we'll take our thirds and we'll turn them into 12. Again, three times four is 12 so that guarantees us that thirds can be rewritten as something out of 12. And that guarantees us that fourth can be rewritten as something out of 12. Here it is, visually. Now, what would that look like mathematical calculation? Well, we're going to use that equivalent fraction rule any number times one whole equals itself. In this case, thirds needs to become 12s. And the multiplier four fourths, and that gives us 8 12s. One, two, three, four, 5, 6, 7, 8, 12. Another cool thing here is if you look at the multiplier of four, that tells you what one of the thirds is worth four of the 12. And the other third is worth four of the 12. So the multiplier does have kind of a secret meaning there. Instead of two thirds, we're going to call this 8 12. And then over here for the one fourth, you can see the same situation with the equivalent fraction rule, any number times one whole equals itself. And we see that one fourth does equal three 12s. Again, a quick substitution. And here in the pink tiles, you can see we now have 8 12 plus three 12s giving us a final sum of 1112.