Observe the following formulas: 21-12 = 9; 75-57 = 18; 96-69 = 27; 84-48 = 36; 45-54 = - 9; 27-72 = - 45; 19-91 = - 72 (1) Please complete the above rule with words: exchange the ten and one digits of a two digit number. What is the difference between the new two digits and the original two digits______ (2) can you explain this rule with what you have learned? Give it a try

Observe the following formulas: 21-12 = 9; 75-57 = 18; 96-69 = 27; 84-48 = 36; 45-54 = - 9; 27-72 = - 45; 19-91 = - 72 (1) Please complete the above rule with words: exchange the ten and one digits of a two digit number. What is the difference between the new two digits and the original two digits______ (2) can you explain this rule with what you have learned? Give it a try

(1) (2) if the original two digit ten digit is a and the single digit is B, then the new two digit is (10b + a) and the original two digit is (10a + b). From the meaning of the question, (10b + a) - (10a + b) = 10B + a-10a-b = 9b-9a = 9 (B-A) because a and B are integers, B-A is an integer, so the difference between the new two digit and the original two digit is a multiple of 9