The mathematics dealt with in the previous chapters has been concerned with using numbers to describe things. This chapter is about describing parts of things with numbers. There are three ways mathematics goes about this task, fractions, decimals and percentages, with important differences and similarities between the three forms. Each form is dealt with in a chapter of its own, but this chapter describes the essential characteristics of each and how they interrelate.
‘Fractions’ is a topic which causes difficulty for learners across the world and considerable anxiety for adults. In developing the Test of Cognitive Style (1986), we had to take out an item on fractions because it caused so much anxiety in the trials. Subjects would just stop at that item and not attempt any more items, even though they were not about fractions.
However, we do use some fractions, mainly half and quarter, in everyday life; decimals, mainly for money, for example £4.63 or $13.99; and percentages for example, as interest rates for money and for discounts, for example ‘up to 70% off’ at sale time in shops.
This chapter will explore the relationship between these formats in an attempt to strengthen an understanding of each format. As ever, we will work from the familiar to the new, so our key relationship will be:
All three are ...