This rule states that a number is divisible by 9 if the sum of its digits of the number is divisible by 9
For Example: Check whether 729 is divisible by 9 or not?
Sum of the digits = 7 + 2 + 9 = 18
Now 18 is divisible by 9 hence, 729 is also divisible by 9
Here are few examples illustrated on the divisibility rule of 9
1. Check whether the following number is divisible by 9 or not?
(i) 9729
(ii) 5256
(iii) 8852
(iv) 2136
(v) 4086
(vi) 5103
(vii) 8811
(viii) 813
(ix) 891
(x) 45363
Solution:
(i) 9729
Sum of the digits = 9 + 7 + 2 + 9 = 27
As, 27 is divisible by 9 hence, 9729 is also divisible by 9
(ii) 5256
Sum of the digits = 5 + 2 + 5 + 6 = 18
5256 is divisible by 9 as 18 is divisible by 9
(iii) 8852
Sum of the digits = 8 + 8 + 5 + 2 = 23
As, 23 is not divisible by 9 hence, 8852 is not divisible by 9
(iv) 2136
Sum of the digits = 2 + 1 + 3 + 6 = 12
As, 12 is not divisible by 9 hence, 2136 is not divisible by 9
(v) 4086
Sum of the digits = 4 + 0 + 8 + 6= 18
18 is divisible by 9 hence, 4086 is also divisible by 9
(vi) 5103
Sum of the digits = 5 + 1 + 0 + 3 = 9
As, 9 is divisible by 9 hence the number I divisible by 9
(vii) 8811
Sum of digits = 8 + 8 + 1 + 1 = 18
8811 is divisible by 9 as 18 is a multiple of 9
(viii) 813
Sum of the digits = 8 + 1 + 3= 12
813 is not divisible by as 12 is a multiple of 9
(ix) 891
Sum of the digits = 8 + 9 + 1 = 18
18 is a multiple of 9 hence, 891 is divisible by 9
(x) 45363
Sum of the digits = 4 + 5 + 3 + 6 + 3 = 21
As, 21 is not divisible by 9 hence, 45363 is not divisible by 9
2. Rewrite the series in a different color with numbers that are divisible by 9.
8581 7272 2345 9090 3027 981 3203 6580 6057
Solution:
8581 7272 2345 9090 3027 981 3203 6580 6057
3. Fill in the blanks with digits to make the following numbers divisible by 9:
(i) 7 … 96
(ii) 45 … 1
(iii) 10 … 3
(iv) 9 … 56
(v) 7 … 11
(vi) 4 … 23
(vii) 125 …
(viii) … 525
(ix) 332 …
(x) 556 …
Solution:
(i) 7596
(ii) 4581
(iii) 1053
(iv) 9756
(v) 7011
(vi) 4023
(vii) 1251
(viii) 6525
(ix) 3321
(x) 5562
Note: In the above example fill in with such digit so as to make the sum of the digits divisible by 9
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