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# Pre algebra chapter 2 notes

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### Pre algebra chapter 2 notes

1. 1. 2.1 Integers and Absolute Value <ul><li>Integers – positive whole numbers, negative whole numbers and zero. </li></ul><ul><li>Absolute Value – the distance of a number away from zero. Symbol | | </li></ul><ul><li>Example: | 2| = 2 ; | -4| = 4 </li></ul><ul><li>Opposites – a number that is the same distance away from zero on the other side </li></ul><ul><li>Example: 5 opposite is -5; -7 opposite is 7 </li></ul>-11 -10 -9 -8 -7 -6 -5 -4 -3 -2 -1 0 1 2 3 4 5 6 7 8 9 10 11 12 M7A1.2.3 M7A1.2.1
2. 2. 2.2 Addition of Integers M7A3.2.2 M8A3.3.1 <ul><li>Adding numbers with the same sign: </li></ul><ul><ul><li>Add the numbers together </li></ul></ul><ul><ul><li>The answer is the same sign as the numbers </li></ul></ul><ul><ul><ul><li>Examples: 3 + 12 = 15; -6 + -3 = -9 </li></ul></ul></ul><ul><li>Adding numbers of different signs: </li></ul><ul><ul><li>Subtract the numbers </li></ul></ul><ul><ul><li>The answer is the same sign as the larger number </li></ul></ul><ul><ul><ul><li>Examples: 10 + (-2) = 8; -15 + 4 = -11 </li></ul></ul></ul>
3. 3. 2.3 Subtraction of Integers <ul><li>Subtracting Integers: </li></ul><ul><ul><li>Change the subtraction to addition </li></ul></ul><ul><ul><li>Change the second number to it’s opposite </li></ul></ul><ul><ul><li>Follow the addition rules </li></ul></ul><ul><ul><li>Examples: </li></ul></ul><ul><ul><li>9 – 12 = 9 + (-12) = -3 </li></ul></ul><ul><ul><li>-5 –10 = -5 + (-10) = -15 </li></ul></ul>M7A3.2.2 M8A3.3.1
4. 4. 2.4 Multiplication of Integers <ul><li>Multiplying numbers with the same sign: </li></ul><ul><ul><li>Multiply the numbers </li></ul></ul><ul><ul><li>The answer is positive </li></ul></ul><ul><ul><ul><li>Examples: 3 x 12 = 36 </li></ul></ul></ul><ul><li>Multiplying numbers with the different signs : </li></ul><ul><ul><li>Multiply the numbers </li></ul></ul><ul><ul><li>The answer is negative </li></ul></ul><ul><ul><ul><li>Examples: 10 x (-2) = -20 </li></ul></ul></ul>M8A3.3.1
5. 5. 2.5 Division of Integers <ul><li>Dividing numbers with the same sign : </li></ul><ul><ul><li>Divide the numbers </li></ul></ul><ul><ul><li>The answer is positive </li></ul></ul><ul><ul><ul><li>Examples: -6 ÷ -3 = 2 15/(3) = 5 </li></ul></ul></ul><ul><li>Dividing numbers with the different signs : </li></ul><ul><ul><li>Divide the numbers </li></ul></ul><ul><ul><li>The answer is negative </li></ul></ul><ul><ul><ul><li>Examples: 10 ÷ (-2) = -5 -12/3 = 4 </li></ul></ul></ul>
6. 6. 2.8 Integers in the Coordinate system <ul><li>Coordinate system – is a grid created when you cross the x and y axis at zero </li></ul><ul><li>X-axis – the horizontal axis </li></ul><ul><li>Y-axis – the vertical axis </li></ul><ul><li>Origin – the point (0,0) </li></ul><ul><li>Ordered pair – (x coordinate, y coordinate) </li></ul><ul><li>Example: A (2, -3); B (-3, 2) </li></ul>origin -1 -3 -2 -4 -1 -2 -3 3 3 2 2 1 1 Quadrant I Quadrant II Quadrant III Quadrant IV ● A ● B M8C3.1.1 M7C3.1.1 M7C3.1.2
7. 7. 2.7 Distributive property <ul><li>6(2+3) = 6(2) + 6(3) = 12 +18 = 30 </li></ul><ul><li>3(a+2) = 3(a) + 3(2) = 3a + 2 </li></ul><ul><li>2(x+7) + x + 6 = </li></ul><ul><li>distribute first: 2x+ 2(7) + x + 6 = </li></ul><ul><li>simplify: 2x + 14 + x + 6 </li></ul><ul><li>combine like terms: 3x + 20 </li></ul><ul><li>Final answer: 3x + 20 </li></ul>Distributive property is your best friend in Algebra
8. 8. 2. 9 Open Ended <ul><li>Work Explain </li></ul><ul><li>Show all your work </li></ul><ul><li>Even your things you </li></ul><ul><li>did on the calculator </li></ul>Use Magic Words: To find To show Therefore Since