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**Divisibility and Mental Math**

Lesson 3-1

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Vocabulary A number is divisible by another number if it can be divided into and result in a remainder of 0. 24 is divisible by 4, because 24 ÷ 4 = 6. 24 is not divisible by 5, because 24 ÷ 5 = 4.8 (or 4R4). An even number ends with a 0, 2, 4, 6, or 8. An odd number ends with a 1, 3, 5, 7, or 9.

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**Divisibility Rules 2 divides into all even numbers.**

3 divides into a number if the sum of the digits of that number is divisible by 3. 5 divides into numbers that end with a 5 or 0. 9 divides into a number if the sum of the digits of that number is divisible by 9. 10 divides into numbers that end with 0.

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**Example: Test each number for divisibility by 3.**

216 = 9 9 is divisible by 3, so 216 is divisible by 3. yes 437 = 14 14 is not divisible by 3, so 437 is not divisible by 3. no

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**Example: Test the number for divisibility by 2, 5, or 10.**

454,320 2 works because the number is even. 5 works because the number ends with 0. 10 works because the number ends with 0. = 18. Is the number divisible by 9? 18 is divisible by 9, so 454,320 is also divisible by 9.

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Homework Time

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Divisibility Rules. What Are Divisibility Rules? They are a quick way to tell if one number can be completely divided into another without a remainder.

Divisibility Rules. What Are Divisibility Rules? They are a quick way to tell if one number can be completely divided into another without a remainder.

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