The divisibility rule for 7 says 10a + b is a multiple of 7 if only and only if a - 2b is a multiple of 7 Explain.

Step-by-step explanation:

Well I can show you by example. Try 28

a = 2

b = 8

2 - 2*8 = 2 - 16 = -14

- 14 is divisible by 7. You get - 2.

That means that 28 is also divisible by 8

We'll try one more. Try 56

a = 5

b = 6

5 - 2*6 = 5 - 12 = - 7

- 7 is divisible by 7 so 56 must be as well. What I'm wondering is if the rule in some form works for 735 and if it does how?

a = 73

b = 5

73 - 10 = 63

63 is divisible by 7 (giving 9)

so 10*73 + b is divisible by 7.

Try something a bit harder.

115444

a = 11544

b = 4

a - 2*4

11544 - 8

11536 / 7

1648 which works perfectly.

115444 is divisible by 28 which is a multiple of 7

Really amazing! Thanks for posting.