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9. Replace by the smallest digit to make the following divisible by 11.
(a) 4*3271
(b) 22*0978
(c) 2*45678
(d) 2472*9
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Sagot :

Sqdancefanidn

Answer:

  (a)  0

  (b)  1

  (c)  8

  (d)  6

Step-by-step explanation:

You want the digit in the * position that makes each number divisible by 11.

Divisibility rule

If the difference of the sum of digits in odd positions and the sum of digits in even positions is divisible by 11, the number is divisible by 11.

(a) 4*3271

The difference of interest is ...

  (4 +3 +7) -(x +2 +1) = 11 -x

This will be a multiple of 11 for x = 0.

  403271 = 11 · 36661

(b) 22*0978

The difference of interest is ...

  (2 +x +9 +8) -(2 +0 +7) = 10 +x

This will be a multiple of 11 for x = 1.

  2210978 = 11 · 200998

(c) 2*45678

The difference of interest is ...

  (2 +4 +6 +8) -(x +5 +7) = 8 -x

This will be a multiple of 11 for x = 8.

  2845678 = 11 · 258698

(d) 2472*9

​The difference of interest is ...

  (2 +7 +x) -(4 +2 +9) = x -6

This will be a multiple of 11 for x = 6.

  247269 = 11 · 22479

The needed digits are 0, 1, 8, 6.

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