# Part 4i: Fraction Arithmetic Introduction

One of the most difficult challenges for any elementary school teacher is teaching fraction arithmetic. More often than not, the rules for adding, subtracting, multiplying and dividing fractions are taught as procedures, with little to no discussion of **why** the rules are what they are. In this section we start from the beginning, with a discussion of fraction basics such as the definition of a fraction and what specific roles are played by the numerator and denominator. We then discuss the rules for adding, subtracting, and multiplying fractions by showing why the familiar procedures make sense. With division, we give two seemingly different (albeit equivalent, as the last clip illustrates) procedures; the familiar ‘multiply by the reciprocal of the divisor’ technique, and a ‘common denominator’ approach. As with every mathematical topic, the more ways a teacher has to explain a topic, the better.

**Notes:**

- Somehow I completely forgot to discuss equivalent fractions and the process for adding and subtracting fractions with like denominators in clip 4 ii, so I included a document containing those explanations immediately following the clip.
- Clip 4 v contains a review of the interpretations of division discussed in clip 1 xii for whole numbers (partitive and measurement), followed by a discussion of how these interpretations can be extended to fraction division. Clip 4 vi is a much shorter clip that skips the whole number review and focuses solely on how the interpretations extend to fraction division.