**Unlocking fractions**

November 29, 2016

On exams like the SAT where calculators are not always allowed, fractions can be intimidating. Students that have moved on to more advanced maths such as algebra often relegate fractions to the calculator zone. But when the no-calculator exam day comes along, students come head to head with a fractions problems and freeze.

The concept of fractions is familiar: students often make use of fractions (i.e. division) without even knowing it. Nevertheless, students tend to overlook the link between fractions and division in the context of an exam and needlessly lose points and time.

There are many techniques available that can be tailored to a student’s learning style to help unlock the concept of fractions for good: linguistic patterns, visualisation tools and kinaesthetic exercises, to name a few. And once students have mastered the concept, they can also learn strategies that can make fractions questions an opportunity to gain (rather than lose) time and points on exams.

Of course, students have much more to gain from understanding fractions than just exam points. Like most of mathematics, the study of fractions reveals a rich underlying structure that can stimulate even the most advanced learners. Consider a typical fractions question: is the value of the fraction a/b greater than fraction c/d? (e.g.: is 19/11 greater than 30/17?). Around 400BC, the mathematician Eudoxes showed that the answer to this problem could be expressed in terms of the properties of rectangles. It was one of the first clues that there exists an intrinsic connection between numbers (arithmetic) and shapes (geometry). But why? Why should it be so, and does it have deeper applications? These questions have revealed themselves to be fundamental to modern mathematics and can be explored endlessly by a curious mind.

Back to fractions on exams: the conclusion is that if you have any doubts on fractions, there are ways you can overcome this hurdle. In fact, one day you may even see that fractions are not something problematic, but are actually a powerful problem-solving tool.