Concept 6 of 9
Brackets: Solve the Inside First
Today's big idea
Solve the innermost brackets first, then work outward.
Size does not decide the order, the pair with nothing inside it goes first.
How it works
👀 What's going on?
A long sum can hide brackets inside brackets, like a set of nesting dolls. Open the wrong one first and every step after it goes wrong.
💡 Here's the trick
Look at the brackets above. Round brackets ( ) sit inside square ones [ ], which sit inside curly ones { }. You always clear the innermost pair first, swap in its value, then move outward.
🪄 How to do it
- 1.Find the innermost pair in the brackets above and solve it.
- 2.Swap that pair for its value, so a new pair becomes innermost.
- 3.Repeat outward until no brackets are left.
✍️ Try it
What is 6 × [20 − (7 + 5)]? Then: what is {40 ÷ (13 − 5)} + 9?
The inner (7 + 5) is 12, so 20 − 12 = 8, and 6 × 8 = 48. In the second, (13 − 5) is 8, then 40 ÷ 8 = 5, so the total is 14.
⚠️ Watch out
You might be thinking the curly brackets come first because they look biggest. Size is not the clue. The pair with nothing else inside it goes first, and that is almost always a round pair.
🌟 Why this matters
When you follow a recipe you finish the sauce before you build the dish. Brackets work the same way, smallest job first, then the bigger one.
Exam tip: Rewrite the whole sum after each bracket you clear, so nothing gets lost.
Watch me solve one
Quanta solves it
“Watch how I think through one of these — then you try.”
THE PROBLEM
“Solve: 841 − [51 + {128 − (190 − 147)}]”
- 1
Innermost first ( )
(190 − 147) = 43. 🪆
- 2
Next layer { }
128 − 43 = 85. Replace inside.
- 3
Square brackets [ ]
51 + 85 = 136.
- 4
Finally outside ✓
841 − 136 = 705
Now you try one — same steps, different story 👇
See it in action
⚡ Time to play!
Tap the INNERMOST bracket first, then work your way outward.
NESTED · ROUND 1 OF 3
120 − [40 − (15 + 8)]
Quick check
✅ VERIFICATION
Solve: 200 − [40 + {60 − (25 + 15)}]
⚡ Finish the activity above first to answer.
Keep going!
Up next: Orders
2⁴ = 2 × 2 × 2 × 2 = 16. Solve before × or ÷.