Adding and subtracting fractions 22 Adding and subtracting fractions [N2.2 Extension Starter] How many different fractions less than one can be made by choosing two of these cards at a time? For example: Put your fractions in order of their size and find the difference between each of them and their neighbour. What do you notice? What is the middle fraction in the list? Repeat the above using the whole numbers from 1 to 6 (and 1 to 7 if time). Jot down anything interesting you notice. Preamble An investigation, suitable for pairs or individuals, involving ordering and subtracting fractions. It is based on the Farey sequence. There are several opportunities for pupils to spot patterns and make conjectures. Extending to beyond 7 cards to check conjectures would constitute a useful homework task. Possible content Ordering and subtracting fractions, investigating fractions. Resources None. Solution/Notes For 5 cards: For 6 cards: 1/6 1/5 ¼ 1/3 2/5 ½ 3/5 2/3 ¾ 4/5 5/6 For 7 cards: 1/7 1/6 1/5 ¼ 2/7 1/3 2/5 3/7 ½ 4/7 3/5 2/3 5/7 ¾ 4/5 5/6 6/7 The middle number is always a half, and the difference between terms follows the pattern as illustrated above. The list of fraction’s differences is symmetrical. Original Material © Cambridge University Press 2010 Original Material © Cambridge University Press 2010