RIC-0563 Developing algebraic thinking
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DIVISIBILITY RULES<br />
Teachers notes<br />
Introduction<br />
Looking at<br />
the algebra<br />
We often need to know quickly whether one number will divide evenly<br />
into another number. Knowing simple divisibility rules can make later<br />
factoring tasks in algebra much easier. The activities in this section<br />
provide opportunities to use the most common divisibility tests to create<br />
numbers satisfying the rules. Starting with tasks involving a limited<br />
number of tiles and divisibility rules, the pages become increasingly<br />
more difficult until all 10 number tiles are used.<br />
A number is said to be divisible by another number if and only if the<br />
first number divides evenly into the second number, leaving a remainder<br />
of 0. Divisibility tests are helpful in algebra when students began<br />
factoring various polynomials. Below is a list of the most common<br />
divisibility rules.<br />
A number is divisible by:<br />
• 2, if it ends with an even number in the ones place. That is, the ones<br />
digit is 0, 2, 4, 6, or 8.<br />
Examples: 54, 806, 3798.<br />
• 3, if the sum of the digits in the number is divisible by 3.<br />
Examples: 57, 321, 5412.<br />
• 4, if the last two-digit number is divisible by 4.<br />
Examples: 124, 6380, 999912.<br />
• 5, if the ones digit is 0 or 5.<br />
Examples: 75, 200, 4070, 99995<br />
• 6, if the number is divisible by 2 and by 3.<br />
Examples: 48, 234, 7236.<br />
• 8, if the last three-digit number is divisible by 8.<br />
Examples: 1240, 3568, 765032.<br />
• 9, if the sum of the digits in the number is divisible by 9.<br />
Example: 468, 5247, 71559.<br />
• 10, if the number ends in 0.<br />
Example: 50, 700, 4080.<br />
Tests for 7, 11, and other numbers do exist, but they are sometimes very<br />
awkward to use. Long division or using a calculator are often quicker.<br />
46 DEVELOPING ALGEBRAIC THINKING www.ricgroup.com.au R.I.C. Publications ®<br />
ISBN 978-1-74126-088-5