Mastering Reverse Operations Practice Test Worksheets
Reverse operation questions (often called "I think of a number" problems) ask you to find an unknown starting number. Write an equation using n for that number, then undo the operations in reverse order, just as the worksheet answer keys show.
For students who can follow a calculation forward, but lose marks when they have to reverse the operations in the right order.
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What Do Reverse Operations Questions Look Like?
Reverse operation questions ask you to work backwards from a final answer to find an unknown starting number. The sample and full test answer keys use n for the original number, write the steps as an equation, and apply inverse operations to find n. Here is a worked example using the same method.
Simple Multi-Step Addition
Question:
Cynthia thinks of a number.
She adds 2.
She then adds 6.
The answer is 15.
What was her original number?
Worked Method
Step 1: Let n be the original number. Adding 2, then 6 gives the equation:
(n + 2) + 6 = 15
Step 2: Subtract 6 from both sides:
n + 2 = 9
Step 3: Subtract 2 from both sides:
n = 7
Answer: C (7)
Check: Substitute 7 into the original equation: (7 + 2) + 6 = 15.
Rules to Help You Solve Reverse Operations Questions
Let n stand for the original number and write an equation that follows the steps in the question. Use brackets to show which operations happen first, then undo the steps in reverse order. Keep these rules in mind:
🔄 Rule 1: Use the Inverse
Undo addition with subtraction and subtraction with addition. Undo multiplication with division and division with multiplication, using the same non-zero number. Apply the inverse to both sides of the equation to keep them equal.
Inverses: Addition ↔ Subtraction, Multiplication ↔ Division.
⏪ Rule 2: Reverse the Order
Read the equation from the outside in: undo the last operation first. In (n − 6) × 5 = 5, the subtraction is inside brackets and happens before the multiplication, so divide by 5 first.
Tip: Brackets preserve the order described in the question. (n − 6) × 5 is different from n − 6 × 5.
⚖️ Rule 3: Keep Both Sides Equal
Write the new equation after each inverse operation. Keep going until n is on its own, then substitute your answer into the original equation to check it.
Example: (n + 2) × 3 = 18. Divide both sides by 3 to get n + 2 = 6. Subtract 2 from both sides to get n = 4. Check: (4 + 2) × 3 = 18.
Two More Worked Examples
These examples follow the equation-based working in the test answer keys, including how to handle brackets and mixed operations.
Mixing Operations
Question:
Nisha thinks of a number.
She triples it.
She then adds 4.
The answer is 13.
What was her original number?
Worked Method
Step 1: Let n be the original number. Tripling it, then adding 4 gives:
(n × 3) + 4 = 13
Step 2: Subtract 4 from both sides:
n × 3 = 9
Step 3: Divide both sides by 3:
n = 3
Answer: B (3)
Check: (3 × 3) + 4 = 13. Adding 4 was the last operation, so it was the first one to undo.
Order of Operations Trap
Question:
Nisha thinks of a number.
She subtracts 6.
She then multiplies it by 5.
The answer is 5.
What was her original number?
Worked Method
Step 1: Let n be the original number. Subtracting 6, then multiplying the result by 5 gives:
(n − 6) × 5 = 5
Step 2: Divide both sides by 5:
n − 6 = 1
Step 3: Add 6 to both sides:
n = 7
Answer: B (7)
Check: (7 − 6) × 5 = 5.
Common mistake: Adding 6 to the right-hand side does not cancel the −6 inside (n − 6) × 5. Divide both sides by 5 first to isolate n − 6, then add 6 to both sides.
