Certainly the problem can be solved using guess and check and some other approaches. However, we think that the nicest way to do it is to just observe that in the left subtraction, we get a 5 in the units column. In the right subtraction we get a b in the units column. Hence b has to be 5 because the two answers are the same.
Now tackle the tens column. Since b = 5, the number that is to be found in the units column of the answer of the left subtraction is 4. So going to the right subtraction we see that a = 4. Just check that there is nothing wrong with a = 4 and b = 5.
Changing 5 to 2 will give a = 1 and b = 8; changing 5 to 8 will give a = 7 and b = 2. Are you getting to see a pattern yet? (5 x 9 = 45; 2 x 9 = 18; …)
Incidentally this is a problem where a lot of knowledge is a dangerous thing. Many secondary students will attempt this using algebra. While algebra works it isn’t the slickest method in the initial stages.
No comments:
Post a Comment