Subtract Fractions Within Whole by Changing One

Let's solve ten twelfths minus three fourths, which could also be said as taking three fourths away from ten 12s. As usual with fractions, we want common denominators. Fourths and 12s are not the same. So we look at our fourths, which is a bigger chunk than a 12. Can fourth become 12? Well, with our tiles, I would line these up and see if I have an equivalent fraction. And it sure looks like one fourth is the same as three 12s. And if I give just a little bit of space, you can see that the next one fourth, same situation. And the next one for same situation. If we were doing this with calculations, we would say that three fourths is worth the same as how many 12s. Well, the equivalent fraction rule says any number times one whole equals itself. Four times what is 12? Of course, three, and don't forget. That same three of these little pieces that made the one fourth is the same three that we have as our multiplier. The box is worth a whole. That's why the numerator is three. Four times three is 12 and above. In the numerator, three times three is 9. I can go back to my original equation and I can make a replacement because three fourths is equivalent with 9 12. I have every right. If I'd like to make that substitution, I sure can. I can take the one fourth, give me three 12s. I could take the next one fourth, do the same thing. Get another three 12s. And as you would expect, the final of the three fourths gets me another set of three twelfths. Now, you might think we've got more tiles than we need. And that's true. We could do this without making the substitution the way I did, and I'll show you that in just a moment. So now for subtraction, we could say that the difference between ten, 12, and 9, 12, is one 12. And that will be a correct final answer. Another way we could do this, especially if you are running a little bit low on tiles, we could actually cover as if we're doing the takeaway. So one fourth. We're removing three 12s. Another fourth, we are removing the three 12s. And yep. One fourth removing the three 12. Again, the answer is 9, 12. Sorry, ten, 12, -9, 12. The answer there would give us one 12th. And the last way you could do this is literally take away 9 12s. One, two, three, four, 5, 6, 7, 8, and 9. If I had ten 12s and I take away 9 12s, I would still get the same answer as the other ways and that of course would be one 12th.