## How to Use the Rules of Divisibility and Estimation

Mathematics, Numbers and Numerations, Operations (+, -, x, /, etc.)

### Objective

Students learn that there are rules that make division easier because of a pattern which indicates that a certain dividend is divisible by a certain divisor.

### Directions

Tell students that when they are working on division problems, there are rules that they can utilize to make their problem solving easier. These rules are based on patterns within the numbers. Explain to students the following rules, writing the examples on the board as you go along.
If the divisor is 2, the rule is that a number is divisible by 2 if the last digit of the dividend (or ones digit) is 0, 2, 4, 6, or 8. For example, 42 รท 2 = 21.
If the divisor is 3, the rule is that a number is divisible by 3 if the sum of the digits in the dividend is divisible by 3. For example, 126: 1 + 2 + 6 = 9; 9 is divisible by 3, so 126 is divisible by 3.
If the divisor is 4, the rule is that a number is divisible by 4 if the number formed by the last two digits of the dividend is divisible by four. For example, 428: the last two digits are 28; 28 is divisible by 4, so 428 is divisible by 4.
If the divisor is 5, the rule is that a number is divisible by 5 if the last digit of the dividend is 0 or 5. For example, 115 is divisible by 5 but 412 is not divisible by 5.
If the divisor is 6, the rule is that a number is divisible by 6 if the dividend is divisible by 2 and 3. For example, 642: ones digit is even so it is divisible by 2, and the sum of the digits 6 + 4 + 2 = 12, which is divisible by 3, so 642 is divisible by 6.
If the divisor is 9, the rule is that a number is divisible by 9 if the sum of the digits in the dividend is divisible by 9. For example, 693: the sum of the digits 6 + 9 + 3 = 18; 18 is divisible by 9, so 693 is divisible by 9.
If the divisor is 10, the rule is that a number is divisible by 10 if the last digit (or ones digit) is 0. For example, 250: the last digit of the number is 0, so 250 is divisible by 10.

### Resources

• Using the Divisibility Rules activity sheets (one each per student)
• pencils