Student can simplify numerical expressions using the correct order of operations (DMAS) and nested bracket hierarchy.
Introduce DMAS and Bracket hierarchy.
Before tackling complex brackets, we must recall the DMAS rule for basic operations. This rule tells us which calculation to perform first in an expression:
A visual showing the inside-out nature of nested brackets is critical.
![A polished process flowchart showing the order of resolving brackets from innermost to outermost: first ( ) Round brackets, then { } Curly brackets, and finally [ ] Square brackets, with a side panel listing the DMAS rule sequence: Division, Multiplication, Addition, Subtraction. Uses rounded card-style nodes, pastel gradient fills, elegant sans-serif typography, generous whitespace, subtle connecting arrows, light neutral background.](https://storage.googleapis.com/app-doodlingo.appspot.com/canonical/images/by-chapter/generic/unknown/general/unknown/brackets-and-the-dmas-rule-visual/brackets-and-the-dmas-rule-visual-illustration-4e7cd8cd.webp)
Always resolve brackets from the inside out, applying DMAS at each step.
Step-by-step unrolling of brackets.
Simplify the following numerical expression using the correct bracket hierarchy:
Applying DMAS inside a bracket.
Simplify the expression by applying the DMAS rule inside the brackets:
Faded practice for nested brackets.
Let's simplify the expression 20 - 3 - [7 - {2 + (4 - 3)}] step-by-step using the standard order of operations.
First, we must remove the innermost round brackets by solving (4 - 3). The expression then becomes 20 - 3 - [7 - {2 + }].
Next, we remove the curly brackets by adding the terms inside them. This simplifies our expression down to 20 - 3 - [7 - ].
Now, we evaluate the square brackets by solving the subtraction inside them. The expression is now reduced to 20 - 3 - .
Finally, we perform the remaining subtractions from left to right to get the final answer of 13.
Full complexity expression simplification.
Simplify:
Hint: Solve brackets from inside to outside: round brackets , then curly brackets , then square brackets .
Start with the innermost bracket.
Use your Step 1 answer inside the curly bracket.
Use your Step 2 answer inside the square bracket.
Subtract the square bracket value from 150.
Write the final simplified value.