Your answer doesn't match the answer key? Start here.
When your answer doesn't match the answer key, keep your working. First check that you are comparing the same question, the same value and the requested answer format. Then test your result against the original problem. A different-looking answer can be equivalent; a matching number can still leave part of the task unanswered. The aim is to locate the disagreement before deciding what to change.
When your answer doesn't match the answer key
Start with identity, not arithmetic. Check the page, exercise number, part letter and book edition. A worksheet may reuse question numbers on its reverse side, and a key may list only selected questions. Compare the actual instruction as well as the number beside it. A correct answer to part b is not a correction of your work on part a.
Now compare every symbol you copied. In our original example, 3(x − 2) = 18 has solution x = 8, because 3(8 − 2) = 18. The visually similar 3x − 2 = 18 has solution x = 20/3. These are different tasks. If a bracket disappeared when you copied the question, no amount of comparing final values will settle the intended problem.
Write a small comparison note: “My question says …; the key is for …”. Include a diagram label, a minus sign or a rounding instruction if it differs. Keep this note beside your original attempt. You may find that the mismatch belongs to the copied input rather than the method you used.
If both statements are identical, continue. If you cannot confirm the key's version, flag that uncertainty and ask for the matching question. Do not quietly rewrite the task until its answer resembles the printed result.
A different form can represent the same value
Suppose your answer is 5/4 and the key says 1.25. Dividing 5 by 4 shows that both represent the same value. Likewise, 9/50, 0.18 and 18% describe the same proportion when they refer to the same whole. Compare meaning before comparing typography. A fraction bar and a decimal point do not automatically signal different mathematics.
The requested form still matters. If the task says “give a fraction in simplest form”, 1.25 does not meet that presentation instruction even though its value is correct. Convert it to 5/4 and preserve the working that produced the value. If the task asks for a percentage, write 18%, rather than leave a bare 0.18 and make the reader infer your representation.
Expressions need a broader check. Expanding (x + 2)(x − 2) gives x² − 4, so those two expressions agree for every real x. Trying one value can reveal a disagreement, but a single successful substitution does not prove an identity. For example, x and x² both equal 1 at x = 1, while they differ at x = 2.
Keep conditions when simplifying. The expression (x² − 4)/(x − 2) equals x + 2 only where the original denominator is nonzero, so x = 2 remains excluded. An answer that looks simpler may have dropped that restriction. Record both the equivalent form and the conditions under which the equivalence holds.
Separate precision from a calculation error
Rounding creates answers that look different without implying different exact calculations. For 36/7, the decimal begins 5.142857…. To one decimal place it is 5.1; to two decimal places it is 5.14. Read the question before choosing between those written results. Keep 36/7 as the exact value in your working until the requested rounding step.
Decimal places and significant figures are different instructions. Two decimal places retain two digits after the decimal point. Two significant figures retain two significant digits from the first nonzero digit. For 0.04736, those instructions produce 0.05 and 0.047 respectively. Write the instruction beside the number so you can check the rule you actually applied.
Also distinguish an exact value from a rounded approximation. The equality 36/7 = 5.14 is not exact; use 36/7 ≈ 5.14 when presenting the approximation. If a later calculation needs the quotient, use the exact fraction or the unrounded stored value, rather than repeatedly calculating from a shortened display.
AQA's mathematics marking guidance discusses equivalent forms and rounding within its own assessment rules. That is a reminder to inspect the actual instructions and marking context, not a universal promise about what every teacher or homework system accepts.
Check that both answers describe the same quantity
A value without its quantity can hide a mismatch. A rectangle with sides 12 cm and 8 cm has area 96 cm² and perimeter 40 cm. Both calculations use the same two lengths, but they answer different questions. If the prompt asks how much surface is covered, an edge-length answer does not become relevant because it came from the same diagram.
Read the unit as part of the answer. Centimetres measure length; square centimetres measure area. If one answer is 0.6 m and another is 60 cm, converting to a common unit reveals agreement. If one is 60 cm², the difference is about the quantity, not merely the placement of a decimal point.
Draw a quick distinction between the region being covered and the boundary being measured. The geometry homework guide develops these task and diagram checks. Here, use that distinction to identify which result the answer key is reporting before you compare numerical values.
For a word problem, finish with a sentence that names what your result means. “Eight tickets remain” and “eight tickets were sold” can both contain the number eight while making different claims. Compare the sentence with the command word and the stated starting amount. A unit check helps only when the quantity itself is the right one.
Try the next step with your own homework.
Bring your question and attempt into Lirno. Ask for a hint, discuss the reasoning, then try the next step yourself.
Test the result against the original problem
Once the question, form and units match, test the proposed answer independently. For an equation, put each candidate into the original equation and evaluate both sides. OpenStax explains this solution check. Use the original line, rather than a later line that could already contain your mistake.
Our original practice task is 5(x − 2) = 30. Candidate x = 8 gives 5(8 − 2) = 30. Candidate x = 4 gives 5(4 − 2) = 10, which does not equal 30. That comparison identifies which candidate satisfies this equation; it does not tell you why someone obtained the other value. To find the cause, inspect their first transition that differs from valid working.
A size estimate provides a second kind of evidence. In 19.8 × 4.1, both factors are slightly above 19 and 4, so a result near 80 is plausible; the exact product is 81.18. An answer of 8.118 deserves a decimal-placement check. An estimate can reject an implausible scale, but it cannot establish every final digit.
For the underlying transformations, use the algebra guide. Keep the diagnostic question specific: did you miscopy an input, apply an operation incorrectly or write the correct value in a different form? A useful check narrows the repair instead of replacing your entire attempt.
A matching value may still be an incomplete answer
Agreement on one number does not settle every task. If the instruction is “solve x² = 49 over the real numbers”, the complete solution set is x = −7 or x = 7. Both square to 49. Writing only 7 omits a solution even though that value passes substitution. If x instead represents a physical length in the stated model, a positive-length condition can exclude −7.
Look for instructions such as find all, justify, prove, give an interval or explain your choice. A short key may show only a result while your assignment requires working or a reason. Do not infer that the shortest printed entry is the entire required response. Match your final answer with every part of the instruction you were given.
Checking also has limits. One tested example cannot prove a general statement; a close decimal cannot establish exact equality; a calculator output cannot decide whether a copied condition belongs to the problem. State what your test establishes and what it leaves open. That is especially useful when two methods arrive at different-looking expressions.
If your candidate survives the appropriate checks but still differs from the key, prepare a question for your teacher: include the exact task, your steps, the key's entry and the check you performed. Ask whether the difference is equivalent form, a missing condition, a different question version or an error. Evidence makes the conversation more productive than simply asserting that the book is wrong.
Keep the explanation, then try a fresh comparison
When you find a real error, mark its first appearance and repair that transition. Keep the valid earlier work. A note such as “I treated 18% as 18 instead of 0.18” tells you what to inspect next time; “I got it wrong” does not. The mistake review guide shows how a short correction can become a focused new practice question.
Try this original comparison before reading the explanation: a rectangle measures 7.5 cm by 4 cm. Your area answer is 30 cm²; a displayed result says 23 cm. Are the two values necessarily competing answers to the same request? The area is 7.5 × 4 = 30 cm², while the perimeter is 2(7.5 + 4) = 23 cm. The first useful move is to check which quantity the task and key request.
Now compare 2/5 with 0.40. They are equal as values, but the written decimal may communicate a different presentation choice. If the instruction asks for a simplified fraction, finish with 2/5. If it asks for two decimal places, finish with 0.40. Neither representation decides the required format independently of the prompt.
Leave one specific clue beside the finished exercise. It might be “compare the quantity before the digits” or “substitute into the original brackets”. Close the worked answer and use the clue on a different task. The purpose of resolving a mismatch is to recover a method you can explain and reuse, rather than to make your page look identical to an answer key.
Questions about this method
Can a different-looking answer still be right?
Yes. Fractions, decimals and factored expressions can represent the same value or relationship. Check equivalence, the original conditions and the requested format. A different appearance alone proves neither an error nor correctness.
Does passing substitution prove that I found every solution?
No. It verifies the candidate you tested. A task asking for all real solutions also requires a completeness argument. Both −7 and 7 satisfy x² = 49; a physical context may add a condition that changes which values are allowed.
Should I replace my answer with the printed one?
First locate the disagreement. Preserve your attempt, compare the exact question, check format and conditions, and test the result. If the mismatch remains, ask your teacher with that evidence rather than copying a result you cannot explain.