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Understanding Divisibility: Rules and Mental Math Strategies

This guide explores the concept of divisibility and the rules that govern it, providing essential vocabulary and mental math techniques. Learn how to determine if a number is divisible by another without performing long division. The document details divisibility rules for numbers 2 through 10, including strategies such as summing digits and checking evenness. With examples and explanations, this resource is ideal for students and anyone looking to enhance their math skills. Master the basics of divisibility and improve your mental math confidence!

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Understanding Divisibility: Rules and Mental Math Strategies

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  1. Divisibility and Mental Math

  2. 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.

  3. 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. 4 divides into numbers where the last two digits are divisible by 4. 5 divides into numbers that end with a 5 or 0.

  4. Divisibility Rules (continued) 6 divides into a number if it is divisible by both 2 and 3. 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.

  5. Example: Test each number for divisibility by 3. 216 2 + 1 + 6 = 9 9 is divisible by 3, so 216 is divisible by 3. yes 437 4 + 3 + 7 = 14 14 is not divisible by 3, so 437 is not divisible by 3. no

  6. 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. 4 + 5 + 4 + 3 + 2 + 0 = 18. Is the number divisible by 9? 18 is divisible by 9, so 454,320 is also divisible by 9.

  7. Example: Test the number for divisibility by 4 216 16 ÷ 4 = 4 16 is divisible by 4, so 216 is divisible by 4. yes

  8. Example: Test the number for divisibility by 6 2 works because the number is even. 210 2 + 1 + 0 = 3 3 is divisible by 3, so 210 is divisible by 3. yes Because 2 & 3 both work…… then 6 automatically works. 436 2 works because the number is even. 4 + 3 + 6 = 13 no 13 is not divisible by 3, so 436 is not divisible by 3. Since 3 doesn’t work, then 6 can’t work.

  9. Homework Time

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