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Integers: Comparing and Ordering

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EQ How do we compare and order rational numbers?

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Rational Numbers Integers Whole Numbers (Positive Integers) Negative Integers Fractions/Decimals

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Rational numbers Numbers that can be written as a fraction. Example: 2 = 2 = 2 ÷ 1 = 2 1

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Whole Numbers Positive numbers that are not fractions or decimals. 1 2 3 4 5 6

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Integers The set of whole numbers and their opposites. -7 -6 -5 -4 -3 -2 -1 0 1 2 3 4 5

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Positive Integers Integers greater than zero. 0 1 2 3 4 5 6

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Negative Integers Integers less than zero. -6 -5 -4 -3 -2 -1 0

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Comparing Integers The further a number is to the right on the number line, the greater it’s value. Ex: -3 ___ -1 -5 -4 -3 -2 -1 0 1 2 3 4 5 -1 is on the right of -3, so it is the greatest... <

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Comparing Integers The farther a number is to the right on the number line, the greater it’s value. Ex: 2 ___ -5 -5 -4 -3 -2 -1 0 1 2 3 4 5 2 is on the right of -5, so it is the greatest... >

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Comparing Integers The farther a number is to the right on the number line, the greater it’s value. Ex: 0 ___ -2 -5 -4 -3 -2 -1 0 1 2 3 4 5 0 is on the right of -2, so it is the greatest... >

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Ordering Integers When ordering integers from least to greatest follow the order on the number line from left to right. Ex: 4, -5, 0, 2 -5 -4 -3 -2 -1 0 1 2 3 4 5 Least to greatest: -5, 0, 2, 4....

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Ordering Integers When ordering integers from greatest to least follow the order on the number line from right to left. Ex: -4, 3, 0, -1 -5 -4 -3 -2 -1 0 1 2 3 4 5 Greatest to least: 3, 0, -1, -4....

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Try This: a. -13 ___ 4 b. -4 ___ -7 c. -156 ___ 32 < < < d. Order from least to greatest: 15, -9, -3, 5 _______________ e. Order from greatest to least: -16, -7, -8, 2 _______________ -9, -3, 5, 15 2, -7, -8, -16

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EQ How do we find the absolute value of a number?

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Absolute Value The distance a number is from zero on the number line. Symbols: |2| = the absolute value of 2 -5 -4 -3 -2 -1 0 1 2 3 4 5 It takes two jumps from 0 to 2. Start at 0, count the jumps to 2. |2| = 2

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Absolute Value The distance a number is from zero on the number line. Ex: |-4| = -5 -4 -3 -2 -1 0 1 2 3 4 5 It takes four jumps from 0 to -4. Start at 0, count the jumps to -4. |-4| = 4

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Solving Problems with Absolute Value When there is an operation inside the absolute value symbols; solve the problem first, then take the absolute value of the answer. Ex: |3+4| =|7| = 7 Ex: |3|- 2 =3-2 = 1 Hint: They are kind of like parentheses – do them first!

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Try This: a.|15| = _____ b. |-12| = _____ c. |-9| + 4 = _____ d. |13 - 5| = _____ 15 12 13 8

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