One Part Unlocks the Split

Imagine eighty-four golden counters landing on a table. You must split them between two teams in the ratio three to four. It sounds like a guessing game... but one tiny unit unlocks the whole split. The clue is that a ratio counts equal-sized parts, not the actual number of counters. On screen, the counters sweep into seven tidy groups, ready to prove it.

Look at three amber boxes beside four blue boxes. Count every box: three plus four makes seven equal parts altogether. The colours show who receives each part. All seven boxes are identical, because every ratio part must have the same value. Now the total, eighty-four, sits above the seven boxes. Divide eighty-four by seven. Each equal part is worth twelve counters. Every box fills with twelve, so the model matches the whole total exactly. Here is the trap. Do NOT divide eighty-four by three, or by four. Those numbers tell you how many parts each team gets. Add them first to find all seven parts.

Let's work through an example. A school shares eighty-four art tokens between the Amber team and the Blue team in the ratio three to four. How many tokens does each team receive? First, draw three amber parts and four blue parts. Add the ratio numbers: three plus four equals seven. So eighty-four tokens are being shared across seven equal parts. Next, find one part. Eighty-four divided by seven equals twelve. Watch one small label, twelve, copy into every part. That is the key step - one ratio part is worth twelve tokens. Now scale each side. Amber has three parts, so three times twelve equals thirty-six. Blue has four parts, so four times twelve equals forty-eight. Check: thirty-six plus forty-eight equals eighty-four. The shares use every token, so the answer is Amber thirty-six and Blue forty-eight.

Remember: add the ratio parts, divide the total by that sum, then multiply for each share. Find ONE part first, and the split becomes clear. You have got this!