suppose a large pizza is divided into 3 equal size pieces and a small pizza is divided into 4 equal size pieces and you get 1 piece from each pizza. Does 1/3 + 1/4 represent the amount you received? Explain why or why not.

The large pizza is clearly not the same size as the small pizza. So we cannot combine these unlike terms so to speak. It would be like saying 1 apple + 1 orange = 2 apples or 2 oranges, which is of course incorrect. Therefore, 1/3 + 1/4 isn't particularly meaningful here.

But what if the pizzas were the same exact size? The next section covers this aspect.

Keep in mind that the next section is optional and not something you'd write on your homework. It's simply meant to show how fractions work.

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Let's call the two pizzas A and B, and we'll assume they are the same size.

Pizza A gets divided into 3 equal slices. If you took one slice, then you get 1/3 of it.
Pizza B gets divided into 4 equal slices. Grabbing one slice means you get 1/4 of it.

Assuming the pizzas are the same size, then 1/3 + 1/4 does represent how much of a whole single pizza you have grabbed when getting both slices.

Think of it like this: 1/3 = 4/12 since we can multiply top and bottom by 4, and the fraction will be equivalent. What's going on is that each of the three original slices from pizza A is divided further into 4 smaller pieces. That gives 3*4 = 12 smaller slices. Grabbing 4 slices out of 12 leads to 4/12 = 1/3 of pizza A.

Through similar logic, 1/4 = 3/12 is the amount you get from pizza B.

Then we add the fractions like so:

1/3 + 1/4 = 4/12 + 3/12 = (4+3)/12 = 7/12

This says you have 7 tiny slices overall. The denominators must be the same when adding fractions.

Check out the diagrams below. Figure 1 uses the pizza/cake/pie model to represent the fractions being added; while figure 2 uses the fraction tape method. Feel free to use whichever is your favorite.

Once again, this only works when the two pizza sizes are the same. Otherwise, the answer is simply "no 1/3+1/4 doesn't represent the total fractional amount received".