1/2 + 1/4. Step 1: The parts are different sizes — halves and quarters cannot be counted together yet. Step 2: 4 is a multiple of 2, so the denominators are related. Relating factor: 2 × 2 = 4. Rewrite 1/2 = 2/4. The amount did not change — only the size of the parts. Step 3: Now both fractions name quarters. Add the numerators, keep the denominator: 2/4 + 1/4 = 3/4. Model: a bar split in quarters with 2 quarters + 1 quarter shaded, beside a 0–2 number line marked in quarters: jump 2/4 from 0, then jump 1/4 more, land on 3/4. The denominator names the size of the parts — we never add denominators, because we are counting parts, not changing their size.

1/6 + 1/3 → 1/3 = 2/6, so 1/6 + 2/6 = 3/6 = 1/2