Check exact fraction addition, subtraction, multiplication, and division responses while exposing denominator, reciprocal, sign, and simplification evidence.
Runs in this browser tabEditable downloadUp to 500 structured rows and 30,000 characters per field. Use anonymous or fictional labels.
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Review output
Your learning artifact appears here
Load the worked example to inspect realistic inputs, or enter anonymous classroom or laboratory evidence. Results remain in this browser tab until you copy or download them.
Transparent method
How the fraction operation models misconception diagnostic works
For addition and subtraction, a/b plus or minus c/d equals (ad plus or minus cb)/bd. Multiplication gives ac/bd. Division by nonzero c/d gives ad/bc. The result is normalized so the denominator is positive, then numerator and denominator are divided by their greatest common divisor. Equality is exact within the accepted integer range; no decimal approximation is used. A supported response has the same reduced numerator and denominator as the calculated value. An equivalent but unreduced response is mathematically correct and receives a simplification reminder. Other labels compare the response with limited alternative calculations, including an opposite sign, separately combined denominators, or division without a reciprocal. These labels are hypotheses for discussion, and a learner explanation or visual model is needed to understand the reasoning.
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Before generation
Confirm the prompt, source values, units, signs, notation, precision, and model required by the current course. Keep an untouched copy of observations or responses before changing a row.
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During review
Run the worked example first, inspect every intermediate row, and compare the table with a hand calculation, diagram, number line, periodic table, or approved laboratory method.
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Before use
Record the method, assumptions, units, rounding, limits, and any row that needs review. Use the exported report as editable evidence and verify it independently before assessment or laboratory use.
Use this diagnostic after learners have represented fraction operations with area, length, set, or number-line models and need a transparent arithmetic check. It is useful for distinguishing an incorrect result from a correct but unreduced result, and for spotting bounded patterns such as combining denominators separately or failing to use a reciprocal in division. The table supports a follow-up question; it does not prove that a learner understands the operation or that one error pattern will recur.
Worked example
The worked set adds two thirds and one fourth to obtain eleven twelfths; subtracts one third from five sixths, where the entered four sixths conflicts with the expected one half; multiplies negative two fifths by three fourths, accepting negative six twentieths as equivalent to negative three tenths; and divides three sevenths by two fifths to obtain fifteen fourteenths. Each row preserves the original expression, reduced expected value, reduced response, and diagnostic label.
Formula or methodology
For addition and subtraction, a/b plus or minus c/d equals (ad plus or minus cb)/bd. Multiplication gives ac/bd. Division by nonzero c/d gives ad/bc. The result is normalized so the denominator is positive, then numerator and denominator are divided by their greatest common divisor. Equality is exact within the accepted integer range; no decimal approximation is used.
How to interpret the result
A supported response has the same reduced numerator and denominator as the calculated value. An equivalent but unreduced response is mathematically correct and receives a simplification reminder. Other labels compare the response with limited alternative calculations, including an opposite sign, separately combined denominators, or division without a reciprocal. These labels are hypotheses for discussion, and a learner explanation or visual model is needed to understand the reasoning.
Common mistakes
Do not add denominators when finding a sum, change a mixed number without preserving its value, multiply before converting a division to multiplication by the reciprocal, cancel terms across addition, ignore negative signs, or reject every unreduced answer as numerically wrong. Ask what quantity each denominator partitions, estimate the answer before calculating, keep equality signs between equivalent forms, and connect the symbolic steps with a model appropriate to the prompt.
This browser-local workbench applies only the disclosed rules to entered values. It cannot diagnose learning, establish a chemical structure, certify a measurement system, validate an experiment, or replace the method and judgment required by a teacher, curriculum, laboratory, or institution.
Review checklist
Human review before educational use
Every value, symbol, sign, unit, and response comes from the intended prompt or evidence source.
The implemented arithmetic or scientific rule matches the current course method.
Intermediate rows and flagged alternatives have been inspected rather than using only the headline.
A teacher or learner verifies the report with an independent method and the original context.
Does Nirmion upload these responses or observations?
No. Processing occurs in the current browser tab. Avoid names and other personal information, and retain authoritative records only in the system approved by the school.
Can the result identify a learner misconception by itself?
No. A matched pattern describes one entered response. Ask the learner to explain, use another representation, and review several evidence sources before deciding the next teaching step.
Can I submit the downloaded report as finished work?
Treat it as an editable calculation aid. Show your own reasoning, use the method requested by the course, cite required sources, and follow the applicable academic-integrity rules.
