## Interpreting notation

Alternatively, when determining which fraction is larger, 9/10 or 12/13, a student could argue that the two fractions are the same size because you could go from 9/10 to 12/13 by adding 3 to the top and the bottom. This error is due to an additive interpretation of the fraction notation rather than a multiplicative interpretation, which underpins forming a common denominator.

Which is larger, 7/8 or 11/12?

### Aspect 6 which number is larger

An additive interpretation of the fraction notation is quite common. When 52 808 students in Year 7 were asked to approximate 4/5 + 11/12, 58.4% selected answers of 15 or 17. Of the 50,882 Year 8 students who were asked the same question, 51.2% also selected answers of 15 or 17.

Approximately half of all students in the middle years of schooling appear to have an additive interpretation of fractions. When the fraction notation is introduced as a way of recording the result of two counts (the number of parts for the numerator and the total number of parts for the denominator) it is readily interpreted as an additive notation.