Anonymous asked:

Question: When the positive integer k is divided by 7, the remainder is 6. What is the remainder when k+2 is divided by 7? Please state and explain a method to solve this question.

It’s best to solve this one by plugging in. In fact, I introduce the concept of plugging in with a similar question on my site and in my book because this is such a perfect plug in question. 

You need a find a number that, when divided by 7, gives a remainder of 6. Another way to think of this is that you need to find a number that is 6 greater than a multiple of 7. 13 works nicely. So do 20, 27, 34, etc. Let’s just stick with 13.

So k = 13. Which means k + 2 = 15. What’s the remainder when 15 is divided by 7?

7 goes into 15 twice, giving you 14. There’s 1 left over to get from 14 to 15, so you’ve got a remainder of 1.

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