**70 increased by 40% is the same ****as 40 increased by 70%.**** **

Although the additional statement is false if "same as" is taken to refer to the outcomes, the increases (28 in the case of the prompt) are the same. It follows that the gaps between the two starting numbers (40 and 70) and the outcomes (68 and 98) are also the same. A proof (right) that if the outcomes are the same, then the two starting numbers (*a* and *b*) must be the same is accessible to students as early as year 7 (grade 6).