Basic Math and Pre-Algebra - Integers and Rationals - Quick Guides | Mathematics

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Study GuideBasic Math and Pre-Algebra–Integers and RaƟonals1. Quiz: RaƟonals (Signed Numbers Including FracƟons)1. QuestionWhich of the following isNOTequivalent to–(5/6)?Answer Choices•5/−6•−5/−6•−5/6Correct Answer࿨࿩࿪−5/−6Why This Is Correct–(5/6) =−5/6.5/−6 is also−5/6 (negative in the denominator).But−5/−6 = +5/6 (a negative divided by a negative is positive).So this one isnotequivalent.2. Question−(3/4) +−(1/2)Answer Choices•+1(1/4)•−(2/3)•−1(1/4)

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Study GuideCorrect Answer࿨࿩࿪−1(1/4)Why This Is CorrectConvert to common denominators:3/4 = 6/81/2 = 4/8−6/8−4/8 =−10/8 =−5/4 =−1 1/43. Question−(5/6)−(−1/3)Answer Choices•1/2•−1/2•−1(1/6)Correct Answer࿨࿩࿪−1/2Why This Is CorrectSubtracting a negative meansadd:−5/6 + 1/31/3 = 2/6−5/6 + 2/6 =−3/6 =−1/24. Question(3/4)–(1/6)

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Study GuideAnswer Choices•−1•−7/12•7/12Correct Answer࿨࿩࿪7/12Why This Is CorrectCommon denominator is 12:3/4 = 9/121/6 = 2/129/12−2/12 = 7/125. Question−(2/3)–(3/4)Answer Choices•−1(5/12)•1/12•5Correct Answer࿨࿩࿪−1(5/12)Why This Is CorrectCommon denominator is 12:−8/12−9/12 =−17/12 =−1 5/12

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Study Guide6. Question(−5/6)(12/25)Answer Choices•−5/2•−2/5•2/5Correct Answer࿨࿩࿪−2/5Why This Is CorrectCancel first:12 ÷ 6 = 2Now multiply:(−5 × 2) / 25 =−10/25 =−2/57. Question(12/3) ÷ (−3/4)Answer Choices•−3/16•−5(1/3)•16/3Correct Answer࿨࿩࿪−5(1/3)

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Study GuideWhy This Is Correct12/3 = 4Dividing by−3/4 means multiply by−4/3:4 ×−4/3 =−16/3 =−5 1/38. Question(4(1/2))+(−12(2/3))Answer Choices•−8(1/6)•−7(5/6)•17(1/6)Correct Answer࿨࿩࿪−8(1/6)Why This Is Correct4½ = 27/6−12⅔=−76/627/6−76/6 =−49/6 =−8 1/69. Question(−2(3/4))−(−1(1/2))Answer Choices•4(1/4)•−1(1/4)•−3(2/3)

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Study GuideCorrect Answer࿨࿩࿪−1(1/4)Why This Is CorrectSubtracting a negative means add:−2¾ + 1½−11/4 + 6/4 =−5/4 =−1 1/410. QuestionWhichof the followingwill have a positive answer?Answer Choices•(−2/3)(3/4)(4/5)•(2/3)(3/4)(−4/5)•(2/3)(−3/4)(−4/5)Correct Answer࿨࿩࿪(2/3)(−3/4)(−4/5)Why This Is CorrectTwo negatives multiply to a positive.The third expression hastwo negative factors, so the answer is positive.11. QuestionWhichof the followingwill have a negative answer?

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Study GuideAnswer Choices•(−3/4) ÷ (5−7) × (1/2−1)•(−3/4) ÷ (5−7) × (1/2−(−1))•(3/4) ÷ (5−7) × (1/2−1)Correct Answer࿨࿩࿪(3/4) ÷ (5−7) × (1/2−1)Why This Is Correct5−7 =−21/2−1 =−1/2Positive ÷ negative × negative= negative × negative= negative12. Question(3(1/3))×(−4(1/2))Answer Choices•−12(1/6)•12(1/6)•−15Correct Answer࿨࿩࿪−15Why This Is Correct3⅓= 10/3−4½ =−9/2(10/3)(−9/2) =−90/6 =−15

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Study Guide13. Question(−5(2/3))÷ (−1/3)Answer Choices•17•0•−17Correct Answer࿨࿩࿪17Why This Is Correct−5⅔=−17/3Dividing by−1/3 means multiply by−3:(−17/3)(−3) = 1714. Question(−3(1/2))÷((1/2) × 2)−(1(1/2))(4)Answer Choices•8•−2(1/2)•−20Correct Answer࿨࿩࿪−20

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Study GuideWhy This Is Correct−3½ =−7/2(−7/2) ÷ (1/2) =−7−7 × 2 =−141½ = 3/2(3/2)(4) = 6−14−6 =−2015. QuestionWhich statement is ALWAYS true?Answer Choices•Multiplying three negative fraction values together will produce the same type of answer,positive or negative, as adding three negative values together.•Dividing three negative fraction values together will produce the same type of answer, positiveor negative, as subtracting three negative values together.•Multiplying a positive value with a negative value will produce the same type of answer,positive or negative, as adding a negative value with a positive value.Correct Answer࿨࿩࿪Multiplying three negative fraction values together will produce the same type of answer, positiveor negative, as adding three negative values together.Why This Is CorrectThree negatives multiplied = negative.Adding three negatives = negative.So both results are negative.

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Study Guide16. QuestionWhichof the followingshortcut is allowed?Answer Choices•−6/7 + 11/2 =−1/7 + 11/2•−6/7 ÷ 11/2 =−1/7 ÷ 11/2•−6/7 × 11/2 =−1/7 × 11/2Correct Answer࿨࿩࿪−6/7 × 11/2 =−1/7 × 11/2Why This Is CorrectYou can reduce before multiplying (cancel common factors).You cannot reduce across addition or subtraction.17. QuestionWhichof the followingexample has no errorsin it?Answer Choices•−1(1/2)÷ (−3/4) =−3/4 × 2/3 =−1/2•−1(1/2)÷ (−3/4) =−3/1 × 4/3 = 2•−1(1/2)÷ (−3/4) =−3/2 ×−4/3 = 2Correct Answer࿨࿩࿪−1 1/2 ÷ (−3/4) =−3/2 ×−4/3 = 2Why This Is Correct−1½ =−3/2Divide by−3/4→multiply by−4/3(−3/2)(−4/3) = 12/6 = 2

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