Teaching fractions

There is more to knowing and teaching fractions than meets the eye. Paper by H. Wu.

1 Definition of a Fraction . . . . . . . . . . . . . . . . . . . . . . 4
2 Equal Division of a Segment by Ruler and Compass . . . . . . 20
3 Equivalent Fractions (Cancellation Law) . . . . . . . . . . . . 22
4 Fraction as Division . . . . . . . . . . . . . . . . . . . . . . . . 30
5 Ordering Fractions (the Cross-Multiplication Algorithm) . . . 38
6 Addition and Subtraction of Fractions . . . . . . . . . . . . . 46
7 Multiplication of Fractions . . . . . . . . . . . . . . . . . . . . 62
7.1 Formula for the product, and first consequences . . . . . . . . 64
7.2 The first alternative approach . . . . . . . . . . . . . . . . . . 74
7.3 The second alternative approach . . . . . . . . . . . . . . . . . 78
8 Division of Fractions . . . . . . . . . . . . . . . . . . . . . . . 80
9 Complex Fractions . . . . . . . . . . . . . . . . . . . . . . . . 88
10 “Of” and Percent . . . . . . . . . . . . . . . . . . . . . . . . . 93
11 Ratio, Rates, and the Fundamental Assumption of School
Mathematics (FASM) . . . . . . . . . . . . . . . . . . . . . . . 99
12 Word Problems . . . . . . . . . . . . . . . . . . . . . . . . . . 108
13 APPENDIX: Some Remarks on the Teaching of Fractions in
Elementary School . . . . . . . . . . . . . . . . . . . . . . . . 117