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Basic Math and Pre-Algebra - Integers and Rationals

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    Study Guide Basic Math and Pre - Algebra – Integers and Ra Ɵ onals 1. Quiz: Ra Ɵ onals (Signed Numbers Including Frac Ɵ ons) 1. Question Which of the following is NOT equivalent to – (5/6)? Answer Choices • 5/ − 6 • − 5/ − 6 • − 5/6 Correct Answer ࿨ ࿩ ࿪ − 5/ − 6 Why 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 is not equivalent. 2. Question − (3/4) + − (1/2) Answer Choices • +1(1/4) • − (2/3) • − 1(1/4)

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    Study Guide Correct Answer ࿨ ࿩ ࿪ − 1(1/4) Why This Is Correct Convert to common denominators: 3/4 = 6/8 1/2 = 4/8 − 6/8 − 4/8 = − 10/8 = − 5/4 = − 1 1/4 3. Question − ( 5/6 ) − ( − 1/3) Answer Choices • 1/2 • − 1/2 • − 1(1/6) Correct Answer ࿨ ࿩ ࿪ − 1/2 Why This Is Correct Subtracting a negative means add : − 5/6 + 1/3 1/3 = 2/6 − 5/6 + 2/6 = − 3/6 = − 1/2 4. Question ( 3/4 ) – ( 1/6 )

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

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    Study Guide 6. Question ( − 5/6)(12/25) Answer Choices • − 5/2 • − 2/5 • 2/5 Correct Answer ࿨ ࿩ ࿪ − 2/5 Why This Is Correct Cancel first: 12 ÷ 6 = 2 Now multiply: ( − 5 × 2) / 25 = − 10/25 = − 2/5 7. Question (12/3) ÷ ( − 3/4) Answer Choices • − 3/16 • − 5(1/3) • 16/3 Correct Answer ࿨ ࿩ ࿪ − 5(1/3)

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    Study Guide Why This Is Correct 12/3 = 4 Dividing by − 3/4 means multiply by − 4/3: 4 × − 4/3 = − 16/3 = − 5 1/3 8. 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 Correct 4½ = 27/6 − 12 ⅔ = − 76/6 27/6 − 76/6 = − 49/6 = − 8 1/6 9. Question ( − 2 ( 3/4 )) − ( − 1 ( 1/2) ) Answer Choices • 4(1/4) • − 1(1/4) • − 3(2/3)

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    Study Guide Correct Answer ࿨ ࿩ ࿪ − 1(1/4) Why This Is Correct Subtracting a negative means add: − 2¾ + 1½ − 11/4 + 6/4 = − 5/4 = − 1 1/4 10. Question Which of the following will 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 Correct Two negatives multiply to a positive. The third expression has two negative factors , so the answer is positive. 11. Question Which of the following will have a negative answer?

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    Study Guide Answer 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 Correct 5 − 7 = − 2 1/2 − 1 = − 1/2 Positive ÷ negative × negative = negative × negative = negative 12. Question ( 3(1/3) ) × ( − 4(1/2) ) Answer Choices • − 12 ( 1/6 ) • 12 ( 1/6 ) • − 15 Correct Answer ࿨ ࿩ ࿪ − 15 Why This Is Correct 3 ⅓ = 10/3 − 4½ = − 9/2 (10/3)( − 9/2) = − 90/6 = − 15

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    Study Guide 13. Question ( − 5 ( 2/3) ) ÷ ( − 1/3) Answer Choices • 17 • 0 • − 17 Correct Answer ࿨ ࿩ ࿪ 17 Why This Is Correct − 5 ⅔ = − 17/3 Dividing by − 1/3 means multiply by − 3: ( − 17/3)( − 3) = 17 14. Question ( − 3 ( 1/2) ) ÷ ( (1/2) × 2 ) − (1 ( 1/2) ) (4) Answer Choices • 8 • − 2 ( 1/2 ) • − 20 Correct Answer ࿨ ࿩ ࿪ − 20

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    Study Guide Why This Is Correct − 3½ = − 7/2 ( − 7/2) ÷ (1/2) = − 7 − 7 × 2 = − 14 1½ = 3/2 (3/2)(4) = 6 − 14 − 6 = − 20 15. Question Which 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, positive or 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, positive or negative, as adding three negative values together. Why This Is Correct Three negatives multiplied = negative. Adding three negatives = negative. So both results are negative.

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    Study Guide 16. Question Which of the following shortcut 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 × 11/2 Correct Answer ࿨ ࿩ ࿪ − 6/7 × 11/2 = − 1/7 × 11/2 Why This Is Correct You can reduce before multiplying (cancel common factors). You cannot reduce across addition or subtraction. 17. Question Which of the following example has no errors in 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 = 2 Correct Answer ࿨ ࿩ ࿪ − 1 1/2 ÷ ( − 3/4) = − 3/2 × − 4/3 = 2 Why This Is Correct − 1½ = − 3/2 Divide by − 3/4 → multiply by − 4/3 ( − 3/2)( − 4/3) = 12/6 = 2

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