miscon:math.fractions.multiply-with-common-denominator · draft · trust low · v0.1.1 · kind overgeneralization

Multiplying needs a common denominator

Before multiplying fractions you must write them with a common denominator, then multiply the numerators and keep the denominator.

Stable URI
https://open-misconceptions.github.io/miscon-data/m/math.fractions.multiply-with-common-denominator
UUID
116cbd32-81bd-4fbb-b5b2-31a47ff576b4
Domain
math.fractions
Level band
primary, middle
Locale
en
About
CCSS 5.NF.B.4 http://corestandards.org/Math/Content/5/NF/B/4/

Evidence patterns

Pattern 0: multiply two fractions with unlike denominators

converts to a common denominator, multiplies numerators and keeps the common denominator

Item1/2 x 1/3 = ?
Expected1/6
Response3/6 x 2/6 = 6/6 = 1

Pattern 1: multiply two fractions with like denominators

multiplies numerators and keeps the shared denominator

Item2/5 x 3/5 = ?
Expected6/25
Response6/5

Discriminators

vs a slip. The extra common-denominator step is visible in the working and repeated across items. A slip does not add that step.

vs math.fractions.cross-multiply-to-multiply. Cross-multipliers do not convert denominators; they give 1/2 x 1/3 = (1x3)/(2x1) = 3/2.

vs math.fractions.add-across. Add-across is the mirror error (addition treated like multiplication). A learner with both answers 1/2 + 1/3 = 2/5 and 1/2 x 1/3 = 6/6.

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.cross-multiply-to-multiply
math.fractions.multiply-mixed-parts-separately

Alignments

Provenance

Origin: llm-drafted

  1. 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
    Overgeneralisation of the addition procedure to multiplication.
  2. Siegler, R. S., & Lortie-Forgues, H. (2015). Conceptual knowledge of fraction arithmetic. Journal of Educational Psychology, 107(3), 909-918. doi:10.1037/edu0000025
  3. Braithwaite, D. W., Pyke, A. A., & Siegler, R. S. (2017). A computational model of fraction arithmetic. Psychological Review, 124(5), 603-625. doi:10.1037/rev0000072

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

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Formats

Cite

miscon:math.fractions.multiply-with-common-denominator
https://open-misconceptions.github.io/miscon-data/m/math.fractions.multiply-with-common-denominator