Write 8/12 in simplest form. Step 1: Look for a factor that 8 and 12 share. Both can be divided by 2 - and by 4. Step 2: Divide both numbers by 2 first: 8 / 2 = 4, 12 / 2 = 6, so 8/12 = 4/6. The amount did not change. Step 3: 4 and 6 still share a factor of 2. Divide again: 4 / 2 = 2, 6 / 2 = 3, so 2/3. Step 4: 2 and 3 share no factor except 1, so 2/3 is the simplest form. Model both ways, side by side: a bar in twelfths with 8 shaded, regrouped into sixths (4 shaded), then into thirds (2 shaded) - same shading every time - AND the 0-2 number line where 8/12, 4/6 and 2/3 are one single point. Say it plainly: simplifying is partitioning in reverse - the parts get bigger and fewer, in the same balance.

Write 6/9 in simplest form. -> Divide both by 3: 2/3