Concept 3 of 8
Operator Substitution: Swap the Signs
Today's big idea
Swap the operator symbols as instructed, then solve with BODMAS on the new expression.
Rewrite first, then let BODMAS pick the order, not left to right.
How it works
👀 What's going on?
Some puzzles change what the signs mean before you start. A plus might really be a times, and a minus might really be a divide. The safest move is to rewrite the whole sum first, then work it out.
💡 Here's the trick
Look at the panel above. The upper row is the sum as printed, and the lower row is that same sum with the real signs put back. Work only on the lower row, because the printed row is a disguise.
🪄 How to do it
- 1.Copy the rule beside the panel above so you can see each swap.
- 2.Rewrite the sum, changing one sign at a time until all are done.
- 3.Solve the new sum with BODMAS, doing times and divide first.
✍️ Try it
If '+' means '÷' and '−' means '+', what is 20 + 5 − 3? Then, if '×' means '−', what is 9 × 4?
Rewritten, the first one reads 20 ÷ 5 + 3, and dividing before adding gives 7. The second one reads 9 − 4, which is 5.
⚠️ Watch out
You might be thinking you can just work across from left to right. Try 20 ÷ 5 + 3 × 2 that way and you land on 14. BODMAS says divide and times come first, so it is really 4 + 6, which is 10. Swap the signs first, then let BODMAS pick the order.
🌟 Why this matters
Calculators, spreadsheets and game scoring all follow BODMAS, so the order of a sum is never up to you. Reading a sum in the right order is a skill you will use for years.
Exam tip: Rewrite the whole line on your rough sheet before you touch a single number.
Watch me solve one
Quanta solves it
“Watch how I think through one of these — then you try.”
THE PROBLEM
“If ‘+’ means ‘×’ and ‘×’ means ‘+’, evaluate 6 + 2 × 1.”
- 1
Step 1 — REWRITE
Swap every symbol: 6 + 2 × 1 → 6 × 2 + 1. 🔀
- 2
Step 2 — apply BODMAS
6 × 2 + 1
- 3
Compute
6 × 2 = 12; 12 + 1 = 13.
- 4
Answer ✓
13
Now you try one — same steps, different story 👇
See it in action
⚡ Time to play!
Step 1: substitute the swapped symbols. Step 2: compute with BODMAS.
SWAP RULE · ROUND 1 OF 3
A = +, B = −, C = ×, D = ÷
Quick check
✅ VERIFICATION
If '×' means '+' and '÷' means '×', what is 12 ÷ 3 × 2?
⚡ Finish the activity above first to answer.
Keep going!
Up next: Analogy
Find the rule between A and B, then apply it to C.