Adding Fractions with Unlike Denominators

1. 1Predict FirstThe camera moves in on the misaligned cuts. Before anything is re-cut, predict the final answer!1/2 + 1/3 = ?
2. 2Re-cut into Equal PiecesRe-cut both bars into 6 equal pieces: each piece of the first bar splits into 3 small pieces, each piece of the second into 2. 1/2 becomes 3/6 and 1/3 becomes 2/6 — the same amounts, in smaller pieces.1/2 = 3/6; 1/3 = 2/6
3. 3Join the Two PartsWatch the second bar's shaded part slide up and dock onto the first bar's part. The addition itself happens on one bar: 3 pieces joined by 2 pieces, all the same size now.3/6 + 2/6 = ?
4. 4Count the Matching PiecesCount the joined pieces one by one: 5 pieces of 1/6. The denominator stays 6 — only the pieces were counted.3/6 + 2/6 = 5/6
5. 5The Written MethodOn paper the numbers fly in from the bars themselves: 3/6 from the first bar's label, 2/6 from the second's, and the counted answer joins them. The denominator never gets added.3/6 + 2/6 = 5/6
6. 6Why Adding Across FailsAdding straight across would give 2/5. Watch that bar shrink: it ends up SHORTER than the bigger fraction bar alone — the dashed line marks that bar's edge. A sum cannot be smaller than one of its parts, so adding across must be wrong.2/5 < the bigger part — impossible!
7. 7Check by Subtracting BackTake the second fraction's part back off the joined bar: it slides home, and what remains is 3/6 — exactly 1/2 again. The round trip lands where we started.5/6 − 2/6 = 3/6 ✓
8. 8The Rule1/2 + 1/3 = 5/6. Before re-cutting, the mismatched pieces could not be counted; after re-cutting, the matching pieces count at once. Subtraction works the same way.Common denominator first — then count

Change the numbers to test the engine with any sum & difference problem: