Sure, let's break down these statements:
1) "18:3 (∆ 9, 12, 15)" means:
* First, perform the division of 18 by 3. The result is 6.
* Then, take the differences between consecutive numbers in the set {9, 12, 15} i.e., subtract 9 from 12 and 12 from 15. The results are 3 and 3, respectively.
2) "20:3 (∆ 8, 11, 14)" means:
* First, perform the division of 20 by 3. The result is approximately 6.67 (to two decimal places).
* Then, calculate the differences between consecutive numbers in the set {8, 11, 14} i.e., subtract 8 from 11 and 11 from 14. The results are 3 and 3, respectively.
3) "18:2 (∆ 9, 12)" means:
* First, perform the division of 18 by 2. The result is 9.
* Then, calculate the difference between 9 and 12. The result is 3.
Therefore, we can say:
* The division operations yield answers of 6, approximately 6.67, and 9.
* The difference operations all yield results of 3. The first two cases have two instances of the difference (between each pair of numbers) while the last case only has a single instance since there is only one pair of numbers.