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# Divisibility Rules

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by

## Shelley Lim

on 23 November 2012

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#### Transcript of Divisibility Rules

Objectives Divisibility rules can help with:
Division, factors, prime factorization, simplifying fractions, and finding the lowest common denominator
Students should be able to:
Memorize divisibility rules to simplify algebraic equations
Recall concepts from previous lessons:Quotient, factors, lowest common factor, solving for x, basic math operations

Students will show that they have acquired this skill through an online worksheet
Direct instruction
and
guided practice This is the part of the lesson plan where the teaching takes place.
We will introduce the topic of discussion, which is Divisibility Rules (Grade 8 Math).The first part of the lesson will be to introduce to the students what the rules are and provide Divisibility Rules The rules are more like tips and tricks. They help determine whether a number can be evenly divided by another smaller number to produce an integer. What are divisibility rules? Any EVEN number can be divided by 2
Even numbers end with 2, 4, 6, 8, or 0.

For example:
1876442866
All these numbers are divisible by 2 Numbers Divisible by 2 In order to determine whether a number is divisible by 3, you must:

1. Add up all the digits in the number.
2. Take the sum of all the digits and divide that number by 3.
3. If the sum is divisible by 3, then so is the number.For

Example:
12123 -> 1 + 2 + 1 + 2 + 3 = 9 -> 9 ÷ 3 = 3

The sum of all the digits is 9, which is divisible by 3, therefore the number itself is divisible by 3. Dividing by 4 Dividing by 3 A number can only be divisible by 5 if its last digit is either a 5 or a 0.

55, 250, 455 are all divisible by 5.
48, 99, 169 are not divisible by 5. Divisible by 5 A number is divisible by 6 if it is also divisible by 2 AND 3.

In other words, if the number follows the rules for both 2 and 3, then the number will be divisible by 6.

For example:
114
It is an even number, so it is divisible by 2.
1 + 1 + 4 = 6, which is divisible by 3.

Therefore 114 is divisible by 6. Dividing by 6 To determine if a number is divisible by 7, take its last digit and double it, then subtract that number from the remaining digits. If the result is 0 or a number divisible by 7, then the original number is divisible by 7.

For example:
Consider the number 357.
7 x 2 = 14
35 – 14 = 21
21 can be divided by 7, therefore 357 is divisible by 7. Divisible by 7 A number is divisible by 8 if it’s last 3 digits are divisible by 8.For example:Consider the number 7120The last three digits (120) are divisible by 8. 120 ÷ 8 = 15Therefore the number 7120 is also divisible by 8. Divisible by 8 The rule for dividing by 9 is the same as the rule for number 3, except you divide the sum with 9 and not 3.

Add all the digits of the number. If the sum is divisible by 9, then so is your original number.

For example:
Consider the number 43785
4 + 3 + 7 + 8 + 5 = 27
27 ÷ 9 = 3
27 is divisible by 9, therefore 43785 is also divisible by 9. Divisible by 9 The easiest rule to remember out of all of them
A number can only be divisible by 10 if its last digit is a 0.

100, 8270, 4030 are all divisible by 10.

9873, 23, 293 are not divisible by 10. Here, you determine what supplies are required to help your students achieve the stated lesson objectives.

Students will need access to a computer with internet in order to do the online practice, assignments, and quizzes. In addition to that, students will also need pencil and paper in order to do some extra practice, assignments, and quizzes in class.
Teachers will need a computer with internet access and any kind of projector or smart board to create a visual for students to see on the board and post assignments online. The students can then follow along with us, the teachers, as we instruct them and go over problems on the computer. Divisible by 10 The lesson doesn't end after your students complete a worksheet. The assessment section is one of the most important parts of all.

Students will be given open book quizzes and assignments online, but will also be given quizzes and assignments in class, on paper, in order for us, the teachers, to assess how everyone is progressing with the divisibility rules without the help of a book or internet resources.
If students are not coming along as we would like, extra practice could be given through online help.

To conclude, the lesson will be finished off with a closed book exam on divisibility rules, that will include problem solving and equations, to assess how well the students can do it on their own without any help other than their own knowledge.

If the last two digits of your number are divisible by 4, then your whole number is also divisible by 4!

Example:
for the number 358912: the last two digits are 12.

Since 12 is divisible by 4, so is your original number.
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