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Math Course - Divisibility Rules

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Refresher Course in Mathematics - Number Theory</div>
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<b>Divisibility Rules</b><br />
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<b>Divisibility by</b></div>
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<b>Rule</b></div>
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<b><i>2</i></b></div>
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If the number is an even number</div>
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<b><i>3</i></b></div>
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If the sum of all individual digits in the number is divisible by 3</div>
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<b><i>4</i></b></div>
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If the last two digits of the number is divisible by 4</div>
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<b><i>5</i></b></div>
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If the last digit of the number is 0 or 5</div>
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<b><i>6</i></b></div>
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If the number is even and is divisible by 3</div>
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<b><i>7</i></b></div>
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Double the last digit. Subtract the doubled last digit from the number without the last digit. If the difference is a multiple of 7, then it is divisible by 7.</div>
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<b><i>8</i></b></div>
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If the last three digits of the number is divisible by 8</div>
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<b><i>9</i></b></div>
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If the sum of the individual digits in the number is divisible by 9</div>
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<b><i>10</i></b></div>
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If the last digit of the number is 0</div>
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<b><i>11</i></b></div>
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If after subtracting and adding the digits successively the result is divisible by 11</div>
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<b>Examples</b><br />
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1) 124 is divisible by 2 since the last digit 4 is divisible by 2.<br />
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2) 258 is divisible by 3 since the sum of the digits is 15 (2+5+8=15), and 15 is divisible by 3.<br />
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3) 516 is divisible by 4 since 16 is divisible by 4.<br />
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4) 395 is divisible by 5 since the last digit is 5.<br />
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5) 258 is divisible by 6 since it is divisible by 2 AND it is divisible by 3.<br />
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6) 1,603 is divisible by 7, since 160-3(2)=154, 15-4(2)=7, and 7 is divisible by 7.<br />
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7) 8,120 is divisible by 8 since 120 is divisible by 8.<br />
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8) 549 is divisible by 9 since the sum of the digits is 18 (5+4+9=18), and 18 is divisible by 9.<br />
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9) 3,770 is divisible by 10 since the last digit is 0.<br />
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10) 9,284 is divisible by 11 since the alternating sum of the digits is 11 (9-2+8-4)<br />
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<b>Practice Test - Give it  a try!</b><br />
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1. The number 477 is divisible by each of the following numbers EXCEPT: 3, 6, 9<br />
A. 3<br />
B. 9<br />
<b>C. 6</b><br />
D. None of the above.<br />
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2. The number 348 is divisible by each of the following numbers EXCEPT: 2, 3, 4, 5, 6<br />
A. 6<br />
<b>B. 5</b><br />
C. 4<br />
D. None of the above.<br />
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3. If a number is divisible by 9, then it is also divisible by which number?<br />
A. 2<br />
B. 6<br />
<b>C. 3</b><br />
D. None of the above.<br />
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4. Which number is divisible by 8?<br />
<b>A. 23,624</b><br />
B. 39,126<br />
C. 120,458<br />
D. None of the above.<br />
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5. Which number is divisible by 6?<br />
A. 213<br />
<b>B. 468</b><br />
C. 621<br />
D. None of the above.<br />
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Math Course - Divisibility Rules

Refresher Course in Mathematics - Number Theory Divisibility Rules Divisibility by Rule 2 If the number is an e...

Math Course - Properties of Number

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Refresher Course in Mathematics - Properties of Number</div>
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<b>Number Properties</b><br />
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<b>Property</b></div>
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<b>Definition</b></div>
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<b>Examples</b></div>
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<b><i>Closure
  Property</i></b></div>
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§ When we add or multiply any element in a set of numbers, the sum or product is a unique real number which belongs to that same set.</div>
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<i>14  + 25 + 44 + 52 = 135</i></div>
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<i>23 x 14 x 10 = 3 220</i></div>
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<b><i>Commutative Property</i></b></div>
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§ states that changing the position of the addends or the factors does not affect the sum or the product</div>
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<i>33 + 10 = 10 + 33</i></div>
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<i>18 x 9 = 9 x 18</i></div>
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<b><i>Associative Property</i></b></div>
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§ states that changing the grouping of addends in a sum or the grouping of factors in a product does not change the resulting sum or product</div>
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<i>(5 + 6) + 7 = 5 + (6 + 7)</i></div>
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<i>2 x (4 x 6) = (2 x 4) x 6</i></div>
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<b><i>Identity Property</i></b></div>
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<i>Addition</i></div>
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§ The sum of any number and zero is the same number.</div>
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§ 0 is the identity.</div>
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<i>512 + 0 = 512</i></div>
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<i>Multiplication</i></div>
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§ The product of any number and one is the same number.</div>
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§ 1 is the identity</div>
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<i>512 x 1 = 512</i></div>
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<b><i>Distributive Property of Multiplication over Addition / Subtraction</i></b></div>
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§ states that multiplication distributes over addition and subtraction</div>
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<i>7(9 + 12) = 7(9) + 7(12)</i></div>
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</tbody></table>
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Math Course - Properties of Number

Refresher Course in Mathematics - Properties of Number Number Properties Property Definition Examples Closu...

Math Course - Analytic Geometry

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Refresher Course in Mathematics - Analytic Geometry</div>
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I. The Cartesian Plane<br />
<br />
II. The Straight Line<br />
A. Distance Between Two Points<br />
B. Slope of a Line<br />
C. Equation of the Line<br />
D. Different forms of the Equation of the Line<br />
E. Parallel and Perpendicular Lines<br />
F. Segment Division<br />
G. Distance of a Point from a Line<br />
<br />
III. Conic Section<br />
A. The Circle<br />
B. The Parabola<br />
C. The Ellipse<br />
D. The Hyperbola<br />
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Math Course - Analytic Geometry

Refresher Course in Mathematics - Analytic Geometry I. The Cartesian Plane II. The Straight Line A. Distance Between Two Points B. ...

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