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# Rules of Divisibility

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Learn how to divide without having to do long division!

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### Rules of Divisibility

1. 1. Rules of Divisibility Mrs. Young EMC 1
2. 2. I need somebody to raise their hand and give me any two – digit number… I will then tell you what numbers this is divisible by without having do write anything down!
3. 3. Objective To use rules of divisibility for larger numbers <ul><li>Definition </li></ul><ul><ul><li>Divisibility: the ability to determine what numbers a larger number is divisible by evenly. </li></ul></ul><ul><ul><li>There are some tricks that we can use to help us determine what numbers larger numbers are divisible by without doing long division. </li></ul></ul>
4. 4. Rules of Divisibility for 2 <ul><li>A number is divisible by 2 if the one’s digit is even. </li></ul><ul><li>Therefore, any number that ends with 0, 2, 4, 6, or 8 is divisible by 2 evenly. </li></ul><ul><ul><li>Examples: 78; 102; 1,046; 6,550 </li></ul></ul>
5. 5. Rules of Divisibility for 3 <ul><li>A number is divisible by 3 if the sum of the digits is a multiple of three. </li></ul><ul><ul><li>Is 96 divisible by 3? </li></ul></ul><ul><ul><ul><li>In order to find out, we must add the digits 9 + 6 </li></ul></ul></ul><ul><li>9 + 6 = 15 </li></ul><ul><ul><li>Is 15 a multiple of 3??? YES, which means that 96 is divisible by 3. </li></ul></ul>
6. 6. Rules of Divisibility for 3 continued… <ul><li>How about 108… is this number divisible by 3??? </li></ul><ul><ul><li>Add the digits together </li></ul></ul><ul><li>1 + 0 + 8 = 9 </li></ul><ul><ul><li>Is 9 a multiple of 3??? YES, which means that 108 is divisible by 3! </li></ul></ul>
7. 7. Rules of Divisibility for 4 <ul><li>A number is divisible by 4 if the last two digits are divisible by four. </li></ul><ul><ul><li>Let’s take 124 for example: </li></ul></ul><ul><ul><ul><li>The last two digits in 124 are 24 </li></ul></ul></ul><ul><ul><li>Is 24 divisible by 4? YES, this means that 124 is divisible by 4! </li></ul></ul>
8. 8. Rules of Divisibility for 4 continued… <ul><li>How about 1,312… is this number divisible by 4??? </li></ul><ul><ul><li>The last two digits in 1,312 are 12 </li></ul></ul><ul><ul><li>Is 12 divisible by 4??? YES, again, this means that 1,312 is divisible by 4! </li></ul></ul>
9. 9. Rules of Divisibility for 5 <ul><li>A number is divisible by 5 if the one’s digit is 0 or 5. </li></ul><ul><ul><li>So, any number that ends with a 0 or a 5 is definitely divisible by 5! </li></ul></ul><ul><ul><ul><li>Examples: 10; 95; 115; 690; 4,615 </li></ul></ul></ul>
10. 10. Rules of Divisibility for 6 <ul><li>A number is divisible by 6 if the sum of the digits is a multiple of three and even. </li></ul><ul><ul><li>Let’s look at the number 132… </li></ul></ul><ul><ul><ul><li>132 is an even number </li></ul></ul></ul><ul><ul><ul><li>And, if we add up all of the digits 1 + 3 + 2 = 6 </li></ul></ul></ul><ul><ul><ul><li>6 is a multiple of 3, which means that 132 is divisible by 6. </li></ul></ul></ul>
11. 11. Rules of Divisibility for 6 continued… <ul><li>Let’s try 804 </li></ul><ul><ul><li>804 is an even number </li></ul></ul><ul><ul><ul><li>8 + 0 + 4 = 12 </li></ul></ul></ul><ul><ul><ul><li>12 is a multiple of 3, which means that 804 is divisible by 6. </li></ul></ul></ul>
12. 12. Rules of Divisibility for 7 <ul><li>A number is divisible by 7 : </li></ul><ul><li>1) Take the last digit </li></ul><ul><li>2) Double it </li></ul><ul><li>3) Then subtract it from the rest of the number. Is this number a multiple of 7? </li></ul>
13. 13. Rules of Divisibility for 7 continued… <ul><li>Example: 203 </li></ul><ul><ul><li>The last digit of 203 is 3 </li></ul></ul><ul><ul><li>Double 3, means 3 x 2 = 6 </li></ul></ul><ul><ul><li>Subtract 6 from 20 </li></ul></ul><ul><ul><ul><li>20 – 6 = 14 </li></ul></ul></ul><ul><ul><li>Is 14 a multiple of 7?? YES, which means that 203 is divisible by 7. </li></ul></ul>
14. 14. Rules of Divisibility for 7 continued… <ul><li>Example: 714 </li></ul><ul><ul><li>Take the last digit 4, and double it. </li></ul></ul><ul><ul><li>4 x 2 = 8 </li></ul></ul><ul><ul><li>Subtract 8 from 71 </li></ul></ul><ul><ul><li>71 – 8 = 63 </li></ul></ul><ul><ul><li>Is 63 a multiple of 7?? YES, which means that 714 is divisible by 7. </li></ul></ul>
15. 15. Rules of Divisibility for 8 <ul><li>A number is divisible by 8 if the last three digits are divisible by eight. </li></ul><ul><li>Examples: </li></ul><ul><li>9,640 </li></ul><ul><li>640 ÷ 8 = 80 so the whole number, 9,640, is divisible by 8 </li></ul><ul><li>77, 184 </li></ul><ul><li>184 ÷ 8 = 23 so  77,184 passes this divisibility test. </li></ul>
16. 16. Rules of Divisibility for 8 continued… <ul><li>How about a huge number like: 20,233,322,496 </li></ul><ul><li>Well, maybe you were wondering if this divisibility rule was really helpful or not. </li></ul><ul><li>Once you get a giant number like 20,233,322,496, you start to realize what a nice trick this is to have up your sleeve! </li></ul><ul><li>All you have to do is divide 496 by 8 to learn that the entire number is divisible by 8. </li></ul>
17. 17. Rules of Divisibility for 9 <ul><li>A number is divisible by 9 if the sum of the digits is divisible by 9. </li></ul><ul><ul><li>Example: 702 </li></ul></ul><ul><ul><ul><li>Add the digits: 7 + 0 + 2 = 9 </li></ul></ul></ul><ul><ul><ul><li>Is 9 divisible by 9? YES, which means that 702 is also divisible by 9. </li></ul></ul></ul>
18. 18. Rules of Divisibility for 9 continued… <ul><li>Example: 3,276 </li></ul><ul><ul><li>Add the digits: 3 + 2 + 7 + 6 = 18 </li></ul></ul><ul><ul><li>Is 18 a multiple of 9??? YES, which means that 3,276 is also divisible by 9. </li></ul></ul>
19. 19. <ul><li>Turn to your neighbor when I give you the signal, and discuss why you think this skill is useful. </li></ul>