miscon:math.fractions.cross-multiply-to-multiply · draft · trust low · v0.1.1 · kind procedural-bug

Cross-multiplying to multiply fractions

To multiply two fractions you multiply diagonally: the first numerator by the second denominator over the first denominator by the second numerator.

Stable URI
https://open-misconceptions.github.io/miscon-data/m/math.fractions.cross-multiply-to-multiply
UUID
fef262fa-6980-416d-bd92-851b64e59458
Domain
math.fractions
Level band
middle, secondary
Locale
en
About
CCSS 5.NF.B.4 http://corestandards.org/Math/Content/5/NF/B/4/

Evidence patterns

Pattern 0: multiply two proper fractions

product numerator = a x d and product denominator = b x c for a/b x c/d

Item2/3 x 4/5 = ?
Expected8/15
Response10/12

Discriminators

vs a slip. Consistent across items and usually accompanied by the word 'cross-multiply'. A slip is one diagonal product.

vs math.fractions.multiply-with-common-denominator. Common-denominator multipliers show a conversion step in their working; cross-multipliers do not.

Relations

conflicts_with
CCSS 5.NF.B.4: multiply a fraction or whole number by a fraction http://corestandards.org/Math/Content/5/NF/B/4/
resolved_by
CCSS 5.NF.B.4: multiply a fraction or whole number by a fraction http://corestandards.org/Math/Content/5/NF/B/4/
confusable_with
math.fractions.multiply-with-common-denominator

Alignments

Provenance

Origin: llm-drafted

  1. Ashlock, R. B. (2010). Error Patterns in Computation: Using Error Patterns to Help Each Student Learn (10th ed.). Allyn & Bacon.
  2. Newton, K. J. (2008). An extensive analysis of preservice elementary teachers' knowledge of fractions. American Educational Research Journal, 45(4), 1080-1110. doi:10.3102/0002831208320851
    Cross-multiplication misapplied to multiplication and addition.

Drafted from the cited literature for the Open Misconceptions seed pack; statement, examples and discriminators are original text. Awaiting maintainer review.

Review status

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Formats

Cite

miscon:math.fractions.cross-multiply-to-multiply
https://open-misconceptions.github.io/miscon-data/m/math.fractions.cross-multiply-to-multiply