Equality Trap Spot the Mistake
Each question gives you four equations — three are correct, one is wrong. Your job is to find it. This page teaches you the technique so you can spot errors quickly and confidently.
The Rules Every Equality Trap Question Uses
Every question follows the same pattern: two sides of an equation, both using the same digits. Once you understand the structure, you can check each option efficiently without guessing.
🔵 Rule 1: Evaluate both sides independently
Never assume the equation is true just because it looks balanced. Calculate the left-hand side (LHS) and the right-hand side (RHS) separately.
Example: 3 × 4 + 57 vs 34 + 5 × 7 → LHS: 12 + 57 = 69; RHS: 34 + 35 = 69 ✓
🟠 Rule 2: Follow order of operations (BODMAS)
Multiplication comes before addition. Always calculate any × first, then add. A common error is to work left to right without applying priority.
Example: 7 × 7 + 45: do 7 × 7 = 49 first, then 49 + 45 = 94 — not 7 × (7 + 45).
🟢 Rule 3: The digits are the same on both sides
In a valid equation, the same four digits appear on both sides — just rearranged. If one side uses different digits entirely, that is not automatically wrong, but it is a useful check.
Tip: Scan for digit mismatches first — it can help you eliminate options quickly before you calculate.
🔴 Rule 4: Only one option is wrong
Three of the four equations balance perfectly. The task is to find the single one that doesn't. Once you find the error, stop — you don't need to verify every option.
Strategy: Start with the option that looks most suspicious or that you can calculate fastest. If it's wrong, you're done.
3 Worked Examples
One straightforward, one multi-step, and one classic mistake to avoid.
1. A Clear Arithmetic Error
Question: Identify the incorrect calculation.
A. 9 × 5 + 62 = 95 + 6 × 2
B. 7 × 7 + 45 = 77 + 4 × 5
C. 3 × 4 + 57 = 34 + 5 × 7
D. 6 × 4 + 75 = 64 + 7 × 5
Worked Method
What it's testing: Rule 1 and Rule 2 — calculating both sides using correct order of operations.
Check option B (it looks plausible but has a subtle error):
LHS: 7 × 7 + 45 = 49 + 45 = 94
RHS: 77 + 4 × 5 = 77 + 20 = 97
94 ≠ 97, so option B is wrong. No need to check further.
Tip: Always apply multiplication before addition. 4 × 5 = 20, not 4 × (5) skipped. The error here is on the RHS where the digits suggest a similar structure — but the products don't balance.
2. When LHS and RHS Look Symmetric
Question: Identify the incorrect calculation.
A. 6 × 9 + 25 = 69 + 2 × 5
B. 2 × 8 + 39 = 28 + 3 × 9
C. 7 × 9 + 54 = 79 + 5 × 4
D. 5 × 9 + 26 = 59 + 2 × 6
Worked Method
What it's testing: Rules 1–3 — the equations look symmetrically structured, which encourages students to assume they all balance.
Check option C:
LHS: 7 × 9 + 54 = 63 + 54 = 117
RHS: 79 + 5 × 4 = 79 + 20 = 99
117 ≠ 99, so option C is wrong.
Compare with option A: LHS: 6 × 9 + 25 = 54 + 25 = 79; RHS: 69 + 2 × 5 = 69 + 10 = 79 ✓
Tip: The symmetric layout (a × b + cd = ab + c × d) works only when the cross-products match. When the multiplier changes, the balance breaks — that's where the trap is set.
3. The Digit-Flip Trap
Question: Identify the incorrect calculation.
A. 8 × 7 + 43 = 87 + 4 × 3
B. 7 × 8 + 27 = 78 + 2 × 7
C. 5 × 5 + 66 = 55 + 6 × 6
D. 7 × 2 + 94 = 72 + 9 × 4
Worked Method
What students do wrong: They see that options A and B are near-mirrors of each other (8 × 7 vs 7 × 8) and assume both must be correct since multiplication is commutative.
Check option B:
LHS: 7 × 8 + 27 = 56 + 27 = 83
RHS: 78 + 2 × 7 = 78 + 14 = 92
83 ≠ 92, so option B is wrong.
Check option A to confirm it's valid: LHS: 8 × 7 + 43 = 56 + 43 = 99; RHS: 87 + 4 × 3 = 87 + 12 = 99 ✓
The rule: Commutative multiplication (a × b = b × a) does not mean the whole equation stays balanced — the other terms change too. Check each one independently, regardless of how similar they look.
Before You Buy
Want to check the level and layout first? Download the free 3-question sample. It uses the same question style, printable format, and answer-key approach as the full pack.
Download Free Sample PDFGet the Full Practice Pack
The full pack contains 90 questions across 3 sets of 30 — with a complete answer key for every question. Download, print and practise straight away.
Checkout and downloads are securely handled on Etsy.com