Equality Trap Spot the Mistake Practice Test Worksheets
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.
For students who can solve equations, but need practice spotting the one step that breaks equality.
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What Do Equality Trap Questions Look Like?
Students are given four equations using similar digit arrangements where three equations balance correctly and one is mathematically false. They must evaluate both sides of each equation independently using the order of operations to identify the incorrect statement. Here is a worked example.
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: Work out 4 × 5 before adding 77. Then compare the two totals.
Rules to Help You Solve Equality Trap Questions
As shown in the example above, each problem tests whether both sides of an equation evaluate to the same value. Use these key rules and strategies to test options quickly 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)
These questions use multiplication and addition without brackets, so multiply first, then add. Do this on each side of the equals sign.
Example: 7 × 7 + 45: do 7 × 7 = 49 first, then 49 + 45 = 94 — not 7 × (7 + 45).
🟢 Rule 3: Matching digits do not mean matching answers
The same digits can make different totals when they are grouped differently. Calculate both sides to check whether they are equal.
Tip: Compare the answers, not just the digits. Different digits can also give equal answers: 2 + 3 = 4 + 1.
🔴 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.
Two More Worked Examples
Practise checking equations when both sides look visually similar, then learn why equal sub-products do not guarantee that the full statements balance.
When Both Sides Look Similar
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 — checking the totals even when both sides have a similar layout.
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: A similar layout does not guarantee equal answers. Work out both sides.
Equal Products Do Not Make Whole Expressions Equal
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 8 × 7 in option A and 7 × 8 in option B and assume both equations must be correct. Swapping the numbers in a multiplication gives the same answer, but other numbers in these equations also change.
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: Check each equation separately. Option A gives 99 on both sides, so it is correct. Option B gives 83 on the left and 92 on the right, so it is incorrect. The fact that both options contain a multiplication worth 56 does not make both equations correct.
