Gord was looking at these multiples of 9: 18, 45, 63, 72, 81, 108, 216. He claimed that the sum of the digits in any multiple of 9 will add to 9. Do you agree or disagree? Justify your decision.

Question

Gord was looking at these multiples of 9: 18, 45, 63, 72, 81, 108, 216. He claimed that the sum of the digits in any multiple of 9 will add to 9. Do you agree or disagree? Justify your decision.

Answer 1

What is your decision?

Answer 2

I know it might sound stupid, but I said that I disagreed with him. The sum of the digits in any multiple of 9 will not add to 9, because the number will get bigger and bigger as the number that it multiplied by 9 gets bigger. F.E., 9x4=36. The sum of the digits is 9, and the times they've been multiplied by 9 is 4 times. Was I completely wrong?

Answer 3

sorry, I meant the sum of the digits is 36 and not 9.

Answer 4

1+8=9

2+7=9
3+6=9
4+5=9
etc.

Keep going. What do you find?

Answer 5

"sum of the digits is 36" -- 3 + 6 = 9

2 + 1 + 6 = 9

28 * 9 = 252
2 + 5 + 2 = 9

Can you think of any sum of the digits in any multiple of 9 that will NOT add to 9?

Answer 6

Oh, multiple. I read it as multiply. I see why I'm wrong now, I kept thinking that the numbers have to be multiplied by 9, and not they have to be multiples of 9.

Thank you,

When I said "sum of the digits is 36", I had meant that 4x9=36 when I tried to offer an example. Though it makes sense that you reworded it, Thank you Ms. Sue and Writeacher once more.

Answer 7

You're welcome.

Answer 8

Gord was looking at these multiples of 9: 18, 45, 63, 72, 81, 108, 216. he claimed that the sum of the digits in any multiple of 9. do you agree or disagree? justify your decision.

Answer 9

I agree with Gord's claim that the sum of the digits in any multiple of 9 will add to 9. This is because 9 has a special property where it is the only non-zero digit where the sum of its factors (1 and itself) add up to 9. So any multiple of 9 will have factors that add up to 9, which means that the sum of the digits will add up to 9 as well. The provided examples of multiples of 9, such as 18 (1+8=9), 45 (4+5=9), and 81 (8+1=9), all follow this pattern.

Answer 10

Zoe made the following conjecture. (Zoe’s conjecture: when any number is multiplied by itself, the product will be greater than this starting number. For example, 3x3=9, the product is greater than the starting number 3.) Sage disagreed with Zoe’s conjecture. Sage pointed out that 1/3x1/3=1/9 and 1/9 is less than 1/3. How could Zoe’s conjecture be improved? Explain any change or changes you would make.