## Fractions, tables

If I write 15 over 45 down on a whiteboard and ask about common factors or cancelling down, most people think of 5 as a common factor and then will spot 3. A few will go for the highest common factor of 15 directly.

I have had some success in two lessons now by stressing the common factors approach to cancelling fractions to their lowest terms, and in solving puzzles like 25 / 35 = 5 / ? and 2 / 3 = 12 / ?.

• One student said she found the questions with the unknown on the bottom the hardest to do, especially when the question involved a division rather than a multiplication
• I found (again) that the commonest error is to write down the common factor itself as the answer, not the result of dividing by the factor
• Students who ‘know their tables’ can grasp these exercises very quickly, those who are still ‘counting on’ are suffering

By ‘knowing your tables’, I mean being able to spot that 63 and 49 both have something to do with 7. More on errors and the stories behind what students write when they are trying to solve fractions questions later.