The onion diagram

To keep the order of the steps under control in a complicated expression, a visual aid is handy.

Example — The "onion" diagram

The onion diagram (or tree diagram) highlights the operations that can be carried out at each step, using different colours for each level: $(3-2)\cdot 4 - \bigl[2\cdot 3 + 24 : (7-3)\bigr]$ At the first step, all the innermost brackets are solved simultaneously ($3-2$, $2\cdot 3$, $7-3$); only afterwards do we move on to the next level.

Each colour identifies a group of operations that can be carried out in the same step.

Links

Topics: Numbers and operations
Concepts: Numerical expression · Order of operations
Skills: Calculating