**ERIC Number:**EJ859714

**Record Type:**Journal

**Publication Date:**2009-Jan

**Pages:**2

**Abstractor:**ERIC

**Reference Count:**0

**ISBN:**N/A

**ISSN:**ISSN-0025-5785

Explaining the Cross-Multiplication Algorithm

Handa, Yuichi

Mathematics Teaching, n212 p8-9 Jan 2009

Many high-school mathematics teachers have likely been asked by a student, "Why does the cross-multiplication algorithm work?" It is a commonly used algorithm when dealing with proportion problems, conversion of units, or fractional linear equations. For most teachers, the explanation usually involves the idea of finding a common denominator--one in particular. One might even draw arrows in the first equation, showing how the "a" and the "d" come together, and so on. In this article, the author offers a surprising visual "proof" for the algorithm in a manner that is appropriate for a high-school mathematics classroom. The author also explores some important mathematical ideas appropriate for high-school students, especially if they have been exploring the topic of similarity among geometric figures. (Contains 5 figures.)

Descriptors: Geometric Concepts, Equations (Mathematics), Algebra, Mathematics Instruction, Mathematical Concepts, Secondary School Mathematics, High Schools, Mathematical Logic, Validity, Multiplication

Association of Teachers of Mathematics. Unit 7 Prime Industrial Park, Shaftesbury Street, Derby, DE23 8YB, UK. Tel: +44-1332-346599; e-mail: admin@atm.org.uk; Web site: http://www.atm.org.uk/mt/index.html

**Publication Type:**Journal Articles; Reports - Descriptive

**Education Level:**High Schools

**Audience:**N/A

**Language:**English

**Sponsor:**N/A

**Authoring Institution:**N/A