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Integers Unit I, Lesson 2 Online Algebra VHS@PWCS

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Integers and the number line. Integers are defined as whole numbers and their opposites. They include the positive numbers, zero and negative numbers. -5 -4 -3 -2 -1 0 1 2 3 4 5 Zero on the number line is called the origin. Positive numbers are to the right of zero and get larger the farther away they are from zero. Negative numbers are to the left of zero and get smaller the farther they are from 0

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Comparing Integers. 1. -5 ? -3 2. -2 ? 3 3. -2 ? -5 1. -5 < -3 -5 is to the left of -3 so it is less than -3 2. -2 < 3 Negative numbers are always less than positive numbers. 3. -2 > -5 -2 is to the right of -5 so it is larger than -5. -5 -4 -3 -2 -1 0 1 2 3 4 5 Using the number line below compare the following integers, using. Click for the answer and an explanation. Larger numbersSmaller Numbers

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Integers and Absolute Value Absolute Value is the distance a number is from zero. Because it is distance it is never a negative number! |-3| means the absolute value of -3. Since -3 is 3 spaces from zero: |-3| = 3 -5 -4 -3 -2 -1 0 1 2 3 4 5

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Simplify each expression. 1. |-8| 2. |6| 3. |-4| 4. |0| 1. 8 2. 6 3. 4 4. 0 -5 -4 -3 -2 -1 0 1 2 3 4 5

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Opposites The opposite of a number is a number that is on the opposite side of the origin, but with the same absolute value. Examples: the opposite of 5 is -5 The opposite of -8 is 8

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Adding Integerswith the same sign. To add integers with the same sign: 1. Add 2. Keep the sign Examples: -5 + -9 = -(5 + 9) = -14 -11 + -25 = -(11 = 25) = - 36

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Try these on your own! Click for the answer. 1. -18+ -12 2. -21 + -16 3. -125 + -631 4. -18 + -14 + -63 5. -22 + -21+ -5 1. - 30 2. - 37 3. - 756 4. - 95 5. - 48

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Adding Integers With Different Signs. To add numbers with different signs (-9 + 15) 1. Subtract the absolute values of each number. 2. Keep the sign of the number with the largest absolute value. Example: - 9 + 15: 1. Subtract 15 – 9 = 6 2. Keep the sign of the “larger” Since 15 has the larger absolute value and is positive, the answer is positive. SO – 9 + 15 = 6

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Try these on your own! Click for the answer. 1. -11 + 8 2. 24 + - 16 3. 13 + (-12) Sometimes you will see expressions written this way. The parentheses just separate the operation and the integer. 4. 12 + - 45 1. -11 + 8 = -3 11 – 8 = 3 and 11 is the “larger” 2. 24 + -16 = 8 24 – 16 = 9, and 24 is the “larger” 3. 13 + (-12) = 1 13 – 12 = 1 and 13 is the “larger” 4. 12 + - 45 = - 33 45 – 12 = 33 and 45 is the “larger”

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Subtracting Integers The algebraic definition of subtraction is: a – b = a + - b Essentially this means that subtraction is the same as adding the opposite. So by definition: 9 – 11 = -9 + -11 We changed the subtraction to addition and the 11 to it’s opposite – 11.

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Subtracting Integers We will use the definition of subtraction to subtract integers. It’s just easier that way. And it makes a lot of things in algebra easier. To Subtract Integers: 1. Leave the first number alone 2. Change the subtraction to addition 3. Change the number after the subtraction to it’s opposite. 4. Follow the rules for adding integers.

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Subtracting Integers -18 – 28 1. Leave the first number alone -18 - 28 2. Change the subtraction to addition -18 - 28 -18 + 28 3. Change the number after the subtraction to it’s opposite. -18 + 28 -18 + - 28 4. Follow the rules for adding integers. -18 + -28 = -46

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Try these on your own! Click for the answer. 1. -15 – (-18) Again, the parentheses just separate the operation and the integer. 2. 25 - 18 3. -11 – 16 4. 17 – (- 24) 1. -15 – (-18) = -15 + 18 = 3 2. 25 – 18 = 25 + -18 = 7 3. -11 – 16 = -11 + -16 = -27 4. 17 – (-24) = 17 + 24 = 41

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Multiplying Integers The rules for multiplying integers are the following: (positive) x (positive) = positive (negative) x (negative) = positive (positive) x (negative) = negative (negative) x (positive) = negative So: -7(-4) = 28 7(4) = 28 - 7(4) = -28 7(-4) = -28

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Dividing integers The rules for dividing integers are the same as the rules for multiplying integers: Positive/positive = positive Negative/negative = positive Positive/negative = negative Negative/positive = negative

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Try these on your own! Click for the answer. 1. -8(-9) 2. -16/-4 3. 6(-8) 4. 45/-5 5. -12/3 1. -8(-9) = 72 2. -16/-4 = 4 3. 6(-8) = -48 4. 45/-5 = -9 5. -12/3 = -4

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Review Wow we went over a lot in this lesson. Absolute value Opposites Adding, subtracting, multiplying and dividing integers. Check out the video from United Streaming for another view point

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Homework Text book Page 23: 13 – 28 Page 27: 7 - 16

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