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**Opening Objective By the end of this PowerPoint you should be able to:**

Use divisibility rules to factor numbers. Divide two and three digit numbers by one and two digits numbers Perform division and see how its inverse is closely correlated to it.

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**There is an inverse relationship between multiplication and division.**

Content Slide #1 There is an inverse relationship between multiplication and division. The equation 45 ÷ 5 = 9 has the inverse relationships following are also true: 5 x 9 = x 5 = 45 Similar relationships exist for multiplication. The equation 3 x 7 = 21 has the relationships: 21 ÷ 3 = ÷ 7 = 3

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Brainstorming There are 960 3rd grade students in a school. The students are to be equally divided into 64 classes. How many students do we have in each class? If 15 x 64=960 then 64√960=?

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**Content Slide #2 Last digit is even**

The sum of the digits is divisible by three The last two digits form a sum that is divisible by four The last digit is zero or five Number is divisible by both two and three

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Content Slide #3 Take the last digit, double it, and subtract it from the rest of the number. If you get an answer divisible by 7 (including zero), then the original number is divisible by seven. If you don't know the new number's divisibility, you can apply the rule again. Ex. Check to see if 203 is divisible by seven. double the last digit: 3 x 2 = 6 subtract that from the rest of the number: = 14. check to see if the difference is divisible by 7: 14 is divisible by 7, therefore 203 is also divisible by seven Last three digits form a number divisible by eight The sum of the digits is divisible by nine The numeral ends in zero

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Content Slide #4 The (sum of the odd numbered digits) - (sum of the even numbered digits) is divisible by 11. Ex = = = is divisible by 11 The number is divisible by both tree and four Delete the last digit from the number, then subtract 9 times the deleted digit from the remaining number. If what is left is divisible by 13, then so is the original number. The last four digits form a number that is divisible by 16

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QUESTIONS

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Content Slide #5 1. Divide 84 ÷ 6 is the problem. Look at the first number only in the dividend so the problem is 8 ÷ 6. The answer is 1. Write it above the 8. 2. Multiply. 1 x 6 = 6. Write the number 6 under the 8. 3. Subtract The answer is 2. Write it down under the 6 4. Compare what is left over after subtracting with the divisor. It must be less than the divisor, if not, then go back to step 1 and choose a larger number to multiple. 5. Bring down the 4. Then go through steps 1 through 4 again. 24 ÷ 6 = 4. Multiple. Subtract. Compare. There is not another number to bring down. The final answer is ÷ 6 = 14.

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**Focused Listing Is 150 divisible by 2, 3, 4, 5, 6, 9 and 10?**

150 is divisible by 2 since the last digit is 0. 150 is divisible by 3 since the sum of the digits is 6 (1+5+0 = 6), and 6 is divisible by 3. 150 is not divisible by 4 since 50 is not divisible by 4. 150 is divisible by 5 since the last digit is 0. 150 is divisible by 6 since it is divisible by 2 AND by 3. 150 is not divisible by 9 since the sum of the digits is 6, and 6 is not divisible by 9. 150 is divisible by 10 since the last digit is 0.

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**We’re at the end and you should be able to:**

Closing Objective We’re at the end and you should be able to: Use divisibility rules to factor numbers. Divide two and three digit numbers by one and two digits numbers Perform division and see how its inverse is closely correlated to it.

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