Chapter 1 Discovery 1

1. Chapter 1 Discovery 1 Adding Rational Numbers with Like Signs Evaluate each expression, and compare the results obtained in the left column with the corresponding results in the right column. 1. a. 6 + 2 = ___ b. |6| + |2| = ___ 2. a. 3 + 9 = ___ b. |3| + |9| = ___ 3. a. - 6 + (- 2) = ___ b. |-6| + |-2| = ___ 4. a - 3 + (-9) = ___ b. |-3| + |-9| = ___ State a rule for writing the sum of two rational numbers with like signs.

2. Chapter 1 Discovery 2 Adding Rational Numbers with Unlike Signs Evaluate each expression, and compare the results obtained in the left column with the corresponding results in the right column. 1. a. 6 + (- 2) = ___ b. Since |6| > |-2|, then |6| - |-2| = ___ 2. a. 3 + (-9) = ___ b. Since |-9| > |3|, then |-9| - |3| = ___ 3. a. - 6 + 2 = ___ b. Since |-6| > |2|, then |-6| - |2| = ___ 4. a. - 3 + 9 = ___ b. Since |9| > |-3|, then |9| - |-3| = ___ State a rule for writing the sum of a positive and a negative rational number.

3. Chapter 1 Discovery 3 Subtracting Two Rational Numbers Evaluate each expression, and compare the results obtained in the left column with the corresponding results in the right column. 1. a. 6 - 2 =___ b. 6 + (- 2) = ___ 2. a. 3 - 9 =___ b. 3 + (- 9) =___ 3. a. - 6 - (- 2) =___ b. - 6 + 2 =___ 4. a. - 3 - (- 9) =___ b. - 3 + 9 =___ 5. a. 6 - (- 2) =___ b. 6 + 2 =___ 6. a. - 3 - 9 = ___ b. - 3 + (- 9) =___ For exercises 1 and 2, state a rule for writing the difference of two positive rational numbers. For exercises 3 and 4, state a rule for writing the difference of two negative rational numbers. For exercises 5 and 6, state a rule for writing the difference of a positive and a negative rational number.

4. Chapter 1 Discovery 4 Multiplying Two Rational Numbers . Evaluate each expression, and compare the results obtained in the left column with the corresponding results in the right column. 1. a. 3 • 2 =___ b. |3| • |2| =___ 2. a. - 3 • (- 2) =___ b. |-3| • |-2| =___ 3. a. 3 • (- 2) =___ b. |3| • |-2| =___ 4. a. - 3 • 2 =___ b. |-3| • |2| =___ For exercises 1 and 2, state a rule for writing the product of two rational numbers with like signs. For exercises 3 and 4, state a rule for writing the product of two rational numbers with unlike signs.

5. Chapter 1 Discovery 5 Dividing Two Rational Numbers Evaluate each expression, and compare the results obtained in the left column with the corresponding results in the right column. 1. a. 8  2 =___ b. |8| |2| =___ 2. a. - 8  (- 2) =___ b. |-8|  |-2| =___ 3. a. 8  (- 2) =___ b. |8|  |-2| =___ 4. a. - 8  2 =___ b. |-8|  |2| =___ In exercises 1 and 2, state a rule for writing the quotient of two rational numbers with like signs. In exercises 3 and 4, state a rule for writing the quotient of two rational numbers with unlike signs.

6. Chapter 1 Discovery 6 Division Involving Zero Evaluate each expression. 1. 8  0 =___ 2. - 8  0 =___ 3. 0  2 =___ 4. 0  (- 5) =___ 5. 0  0 =___ In exercises 1 and 2, state a rule for dividing a rational number by 0. In exercises 3 and 4, state a rule for dividing 0 by a rational number other than 0. In exercise 5, state a rule for dividing 0 by 0.

7. Chapter 1 Discovery 7 Multiplying Three or More Nonzero Rational Numbers Evaluate each expression, and compare the results obtained in the left column with the results in the right column. 1. One negative factor 2. Two negative factors - 6 • 3 • 4 • 1 = ___ - 6 • (- 3) • 4 • 1 = ___ 3. Three negative factors 4. Four negative factors - 6 • (- 3) • (- 4) • 1 = ___ - 6 • (- 3) • (- 4) • (- 1) = ___ State a rule for determining the sign of the product of three or more rational numbers.

8. Chapter 1 Discovery 8 Order of Operations Consider the expression 6  2 + 1 • 3 - 5. Complete the possible methods of evaluation: 1. Evaluate in order from left to right. 2. First, evaluate all additions and subtractions in order from left to right. Then, evaluate all multiplications and divisions in order form left to right. 3. First, evaluate all multiplications and divisions in order form left to right. Then, evaluate all additions and subtractions in order from left to right. 4. Enter the expression into your calculator. Write a rule for performing the order of operations by comparing the calculator value with the values obtained in Exercises 1, 2, and 3.

9. Chapter 1 Discovery 9 Expressions with an Exponent of 1 or 0 Evaluate each expression. 1. 101 =___ 4. -100 =___ 2. (-10)1 =___ 5. (-10)0 =___ 3. 01 =___ 6. 00 =___ State a rule for evaluating an exponential expression with an exponent of 1. State a rule for evaluating an exponential expression with an exponent of 0.

10. Chapter 1 Discovery 10 Nonzero Integer Bases with Negative Integer Exponents Evaluate each expression, and compare the results obtained in the left column with the corresponding results in the right column. 1. a. 10-1 = ___ b. 2. a. 10-2 = ___b. 3. a. 10-3 = ___b. 4. a b. 101 = ___ 5. a. b. 102 = ___ 6. a. b. 103 = ___ State a rule for evaluating an exponential expression with a nonzero integer base and a negative integer exponent.

11. Chapter 1 Discovery 11 Combining Multiplication and Addition Evaluate each expression, and compare the results obtained in the left column with the corresponding results in the right column. 1. a. 2 (6 + 4) =___ b. 2 (6) + 2 (4) =___ 2. b. - 2 (- 6 + 4) =___ b. - 2 (- 6) + (- 2) (4) =___ In your own words, state a rule for combining multiplication and addition.