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Purdue MA 11100 - A Absolute Value
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1 Lesson 2-3, Section 1.2 A Absolute Value a Definition: The absolute value of a is the distance (number of units) between 0 and a. Find each absolute value: 1 523 57.4 5 5 32 3 100 π− = = − == − = + − == − = B Inequalities Number Line: A number to the left of a given number is less than the given number. A number to the right of a given number is greater than the given number. 00or 00 00 toequalor an greater th 52or 52 52 toequalor than less 104 an greater th 52 than less =<→≥≥=<→≤≤−>−><−< Write or state the meaning. Determine whether True or False. 1. 06.4<− 2. 812>− 3. 44≥ 4. 33−<− 5. 613122 ≥ 6. 3245.4 < 7. 24−< 8. 212−≥ 0 2 4 6 10 8 -2 -4 -6 -8 -10 A little word can mean a big difference. Compare the two translations below. 4 less than 10 4 104 less than 10 10 ( 4)− − <− − −is In the first translation, ‘less than’ indicates an inequality symbol (because of the word ‘is’). In the second translation, ‘less than’ indicates subtraction.2 Write each as an inequality. A) Five is less than or equal to seven B) Twelve is greater than negative one C Addition and Subtraction of Rational Numbers Laws of Inverses: Additive inverse or Opposites: 0)(=−+aa Multiplicative inverses or Reciprocals: 11=×aa Double Negative Rules: aaaa =−−=−−1 )( Never use ‘double signs’. Always rewrite the arithmetic problem without double signs. 5 ( 6) 5 61 ( 2) 1 25 2 5 24 3 4 3+ − → −− + − → − − − − → +   To Add or Subtract two rational numbers: 1. Eliminate any ‘double signs’. 2. If both number are plus (positive) or both minus (negative) a) Add the absolute values of the numbers. b) Use the same sign. 3. If the numbers have opposite signs: a) Find the difference of the absolute values. b) Use the sign of the larger absolute value. 1) =−+−)6(12 2) =+−2.634.4 3) =+−6134 4) 6 6− + = ()( )( )( )+ − → −− + → −− − → ++ + → + Many of you may have used ‘double signs’ previously. You will be wise to stop using such notation. Basically, a negative sign and subtract are equivalent and a positive sign and addition are equivalent. Yes, you do have to remember how to perform arithmetic (addition, subtraction, multiplication, and division) with integers, decimals, and fractions.3 5) =−106 6) =−−21134 7) =−−5.414.8 8) =−+−28.105.46.4 9) =−+−213254 10) =+−−+−18220128 Given x, find x− (opposite of x). Note: x− does not always denote a negative value. 12 3 41.25 x xx xx x= − == − − == − − = D Multiplication and Division of Rational Numbers Write the reciprocals of each. Note: Reciprocals have the same sign. 4.64 34 2 32− 46Hint: 4.6 ?10= = To Multiply or Divide two rational numbers: 1. Multiply or Divide the absolute values. 2. If the two numbers have the ‘same’ sign, the answer is positive. 3. If the two numbers have ‘different’ signs, the answer is negative. 4. If there are more than two numbers, count the number of negatives. If odd, the answer is negative; if even, the answer is positive. 5. With fractions, bababa−=−=− 6. 12 is undefined; for example is undefined0 00 00 ; for example 0n 6n−= =4 Multiply or Divide: 1) =−−−)8)(4)(6( 2) =−÷2187 3) =−×−61.3 4) 2 123 7 − − =   5) =−−624 6) =÷23.0288.1 E Order of Operations with Rational Numbers 1. Work within groupings (parentheses) first. 2. Evaluate all exponents next. 3. Perform multiplication and/or division, left to right. 4. Perform addition and/or subtraction, left to right. Note: 442 (2)(2)(2)(2) 16( 2) ( 2)( 2)( 2)( 2) 16− = − = −− = − − − − = Evaluate each. 1) 2 24 (2 3 )− − 2) )5(247)2(542+−−5 3) 28 4 6 4 5÷ ⋅ ⋅ − 4) 2)5(41004)6(48−−− 5) 2 24 (1 9) 6 2 8+ − − ÷ ⋅ 6) +−−61312425543226 F Distributive Property )( 0R )(cbaacabacabcba+=++=+ Note: The second part of the property above is commonly called factoring out the greatest common factor. Write an equivalent expression using the distributive property. 1) =+)2(4x 2) 2( 8)x y− + = 3) 5 ( )x y z w− + = 4) [ 3( 4)]m x a− + = Find an equivalent expression by factoring. 1) 7 14a+ = 2) 39ab b+


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Purdue MA 11100 - A Absolute Value

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