The parts method is reliable — but two misreadings sneak past people constantly. Both come from confusing what the numbers in a ratio actually stand for.
Trap One: "a : B" Is Not "a Out of B"
If the ratio is 3 : 2, the first share is not 3/2 of the whole — and it's not 3/2 at all, since that's more than one. The denominator of the fraction is the total parts, which is 3 + 2 = 5. So the first share is 3/5 of the whole and the second is 2/5. The toy puts the slip right next to the truth so you can see the missing parts.
Trap Two: Given One Share, Not One Part
Sometimes a question hands you a share and asks for the rest. "In the ratio 3 : 2, the first share is 18 — find the other." The slip is to treat 18 as the value of one part and multiply it up. But 18 is 3 parts, so first undo that: 18 ÷ 3 = 6 per part. Now the other share is 2 × 6 = 12, and the whole is 5 × 6 = 30. This is the "unitary" move — always get back to one part before you scale.
Your Shares Must Add Back
Both traps get caught by the same safety net from rung 1: the shares have to add back to the whole. If you'd said "18 is one part, so the whole is 5 × 18 = 90", that's a giant red flag — the first share alone was only 18. Whenever an answer feels too big or too small, add the shares and see if they rebuild the total.