EDUCATION DECISION WORKBENCH
Check equivalence claims with exact cross-products and visible evidence for numerator and denominator scaling.
Review output
Load the worked example to inspect realistic inputs, or enter anonymous, policy-approved information. Results remain in this browser tab until you copy or download them.
Transparent method
For nonzero denominators, a/b equals c/d exactly when a times d equals c times b. This follows from multiplying both fractions by the common nonzero denominator bd. The engine uses integer products within the accepted range and therefore does not introduce repeating-decimal or floating-point comparison error. Claim supported means the learner yes-or-no judgment matches the exact products. A conflict shows both products and the actual relationship so the next discussion can focus on multiplicative structure. Cross-products verify equivalence but do not by themselves show whether a learner understands why; ask for a scale factor, common-denominator argument, or visual representation.
Confirm the question, variables, units, source data, measurement precision, and the model expected by the current course or laboratory. Keep an untouched copy of observations before excluding or transforming any value.
Run the worked example first, inspect every intermediate row, compare units and signs, and look for a result that conflicts with the graph, physical system, chemical equation, or learning objective.
Record the method, assumptions, units, rounding, data limitations, and any excluded observations. Compare the exported report with an independent calculation or approved reference before assessment or laboratory use.
How to interpret the result
Use this diagnostic after a fraction equivalence check when the reasoning behind a yes-or-no response matters. Exact cross-products reveal whether both numerator and denominator were scaled consistently and avoid decimal rounding. Reviewing several rows can expose numerator-only, denominator-only, or additive thinking. Follow the table with area, length, set, or number-line models when conceptual understanding needs more evidence.
Two thirds and eight twelfths are equivalent because 2 times 12 and 8 times 3 both equal 24. Three fifths and nine tenths are not equivalent because the products are 30 and 45, so a yes claim conflicts. Seven eighths and twenty-one twenty-fourths match, while four sixths and ten fifteenths are equivalent despite the worked no claim.
For nonzero denominators, a/b equals c/d exactly when a times d equals c times b. This follows from multiplying both fractions by the common nonzero denominator bd. The engine uses integer products within the accepted range and therefore does not introduce repeating-decimal or floating-point comparison error.
Claim supported means the learner yes-or-no judgment matches the exact products. A conflict shows both products and the actual relationship so the next discussion can focus on multiplicative structure. Cross-products verify equivalence but do not by themselves show whether a learner understands why; ask for a scale factor, common-denominator argument, or visual representation.
Do not add the same number to numerator and denominator, scale only one part, compare denominator size alone, divide and round repeating decimals, cross-multiply with a zero denominator, or treat cross-products as an unexplained trick. Identify the common factor, simplify when useful, preserve signs, and connect the arithmetic with equal quantities on a visual model or number line.
Learning boundary
This browser-local workbench calculates only from the entered model and observations. It cannot validate an experiment, balance an equation, establish causation, certify laboratory safety, diagnose learning, or replace the method required by a teacher, curriculum, laboratory, or institution.
Review checklist
Practical questions
No. The calculation runs in the current browser tab. Avoid personal information and retain laboratory data in the system authorized by the school.
Treat it as an editable analysis aid. Show your own reasoning, cite the required sources, follow academic-integrity rules, and use the method requested by your course.
No. Check dimensions, graph shape, assumptions, measurement uncertainty, significant figures, and whether another model explains the observations better.
YOUR NIRMION
