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Dividing fractions is performed by multiplying the first fraction by the reciprocal of the second fraction.

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SUPPORTED
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Recorded sources
6 sources for · 0 against

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Is it true that dividing fractions is performed by multiplying the first fraction by the reciprocal of the second fraction?

Yes. Standard mathematical definitions and reference texts uniformly confirm that dividing fractions is performed by multiplying the first fraction by the reciprocal of the second.

Verdict: SUPPORTED · 6 sources for, 0 against · Last checked

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Evidence for · 6
LibreTexts: LibreTexts: 1.04: Fractions
States explicitly that to divide fractions, we multiply the first fraction by the reciprocal of the second.
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LibreTexts: LibreTexts: 1.04%3A Fractions. (n.d.). LibreTexts. https://math.libretexts.org/Workbench/Intermediate_Algebra_2e_(OpenStax)/01%3A_Foundations/1.04%3A_Fractions

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More for · 5
OpenStax: OpenStax Prealgebra: 4.2 Multiply and Divide Fractions
Confirms the procedure for fraction division is multiplying the first fraction by the reciprocal.
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OpenStax: OpenStax Prealgebra: 4.2 Multiply and Divide Fractions. (n.d.). OpenStax. https://openstax.org/books/prealgebra/pages/b3b92ee9-65f9-481a-9c54-81a50fd5c901@

Wikibooks: Wikibooks: Arithmetic/Multiplying Fractions
Explains dividing fractions by flipping the second fraction (reciprocal) and multiplying.
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Wikibooks: Wikibooks: Arithmetic/Multiplying Fractions. (n.d.). Wikibooks. https://en.wikibooks.org/wiki/Arithmetic/Multiplying_Fractions

LibreTexts: LibreTexts: 7.02: Multiply and Divide Rational Expressions
States that division of rational expressions is performed by multiplying by the reciprocal.
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LibreTexts: LibreTexts: 7.02%3A Multiply and Divide Rational Expressions. (n.d.). LibreTexts. https://math.libretexts.org/Workbench/Intermediate_Algebra_2e_(OpenStax)/07%3A_Rational_Expressions_and_Functions/7.02%3A_Multiply_and_Divide_Rational_Expressions

OpenStax: OpenStax Intermediate Algebra: 1.3 Fractions
States directly that to divide fractions, we multiply the first fraction by the reciprocal of the second.
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OpenStax: OpenStax Intermediate Algebra: 1.3 Fractions. (n.d.). OpenStax. https://openstax.org/books/intermediate-algebra/pages/425620d9-51dd-45e5-8a21-953998a4a77f@

Wikibooks: Wikibooks: Arithmetic/Printable version
States that dividing fractions involves flipping the second fraction to get the reciprocal and multiplying.
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Wikibooks: Wikibooks: Arithmetic/Printable version. (n.d.). Wikibooks. https://en.wikibooks.org/wiki/Arithmetic/Printable_version

also asked as
  • Is it true that you divide fractions by multiplying the first by the reciprocal of the second?
  • Does dividing fractions work by multiplying by the reciprocal of the second fraction?
  • Is the rule for dividing fractions to multiply by the second fraction's reciprocal?
  • Can you divide fractions by multiplying the first fraction by the reciprocal?
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