There is a new divisibility rule by 9 that I just derived which I like to share in this post. The new rule is tested with numbers that are multiples of 9 to show that it works for all numbers that are divisible by 9.

## The New Rule:

A number is divisible by 9 if the **SUM** of the **unit digit** and the **number formed by the rest digits** is a multiple of 9

This is what it means: if you have **162**, the unit digit is **2** and the number formed by the rest digit is **16**.

Below are three examples to test this rule

**Example 1**: Test 153 for divisibility by 9

To use the rule, split the **153** into 15 and 3

Adding the numbers: 15 + 3

Result: **18** which is 9 x 2

Since 18 is divisible by 9, therefore, 153 is divisible by 9

**Example 2**: Test 414

Split 414 into 41 and 4

Adding: 41 + 4 = 45

45 = 9 x 5

Since 45 is divisible by 9, therefore, 414 is divisible by 9

**Example 3**: Test 7101

Split 7101 into 710 and 1

Adding: 710 + 1 = 711

If the sum is too high to determine if it’s a multiple of 9, like 711 above, repeat the steps for the rule on this new number –

Split 711 into 71 and 1

Adding: 71 + 1= 72

72 = 9 x 8 which is a multiple of 9

Since 72 is divisible by 9, therefore, 7101 is divisible by 9

Have fun with this **new rule** as you test for multiples of 9

Contact me if you have any question

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