Missing digit

What digit must replace the star to make the number a multiple of 11?

Student Solutions



Answer: 9 (so the number is 12349678)

Using division

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Missing Digit


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Missing Digit
 

The number is divisible by 11 so there must have been a remainder of 8 to give 88

 
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Missing Digit


___7 gives a remainder of 8

107 = 99 + 8

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Missing Digit


___6 gives a remainder of 10
76 = 66 + 10

 2__ gives a remainder of 7

22 + 7 = 29

9 is missing

Using a divisibility test

A test for divisibility by 11 is to add alternate digits:


1 + 3 + * + 7 = 11 + *; 2 + 4 + 6 + 8 = 20.


If the original number is a multiple of 11 then these two totals will be the same or will differ by a multiple of 11. In this case, 11 + * = 20 gives * = 9.




Using place value and algebra
1234*678 = 12340678 + 1000* = (11 x 1121879 +9) + 11 x 90* + 10*


and hence is divisible by 11 if and only if 10* + 9 is divisible by 11. So * = 9.