So, I was fiddling around the other day, actually helping out with some homework. Fractions came up. Yeah, fractions. Always a fun time, right? We landed on this one: trying to add one half and one third. Looked simple enough, but then you actually try to do it.
My first thought, maybe years ago, would’ve been, “Easy! 1 plus 1 is 2, and 2 plus 3 is 5. So, two fifths!” But hold on, that doesn’t make much sense when you think about it. A half is, well, half of something. A third is a smaller chunk. Adding them together should give you something bigger than a half, and two fifths is actually less than a half. So, that’s not it. That whole adding-straight-across thing is a trap, I guess.
Getting the Pieces the Same Size
The main problem is the bottom numbers, the 2 and the 3. They’re different. It’s like trying to add apples and oranges, or maybe like having pizza slices cut into halves and thirds – they just don’t line up right. You can’t just count them together directly. You need to cut them into the same size pieces first.
So, I started thinking, what’s a number that both 2 and 3 go into? You know, a common bottom number. Let’s see… 4? No, 3 doesn’t go into 4. 5? Nope. Ah, six! Yeah, 2 goes into 6 (three times), and 3 goes into 6 (two times). Six works. That’s the key, finding that common ground.
Okay, let’s recut the pieces:
- The one half (1/2): To make the bottom number 6, you multiply the 2 by 3. So you gotta do the same to the top number. 1 times 3 is 3. So, one half is the same as three sixths (3/6). Makes sense, right? Half of a pizza cut into 6 slices is 3 slices.
- The one third (1/3): To make the bottom number 6, you multiply the 3 by 2. Do the same to the top number. 1 times 2 is 2. So, one third is the same as two sixths (2/6). Yep, one third of that same pizza is 2 slices.
Putting It Together
Now we’re talking! We have pieces of the same size. We have three sixths and we have two sixths. Adding them is easy now. Just add the top numbers: 3 plus 2 equals 5.
So, 3/6 + 2/6 = 5/6.
And that’s it. One half plus one third is five sixths. It feels right, too. Five sixths is bigger than a half, which is what we expected. Funny how sometimes you gotta break things down into smaller, common pieces before you can build them back up. Took a minute to walk through it again, but we got there. Just needed to find that common bottom number.
