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

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

Subtracting Two Rational Numbers 1. a =___b. 6 + (- 2) =___ 2. a =___b. 3 + (- 9) =___ 3. a (- 2) =___b =___ 4. a (- 9) =___b =___ 5. a. 6 - (- 2) =___b =___ 6. a = ___b (- 9) =___ Evaluate each expression, and compare the results obtained in the left column with the corresponding results in the right column. 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. Chapter 1 Discovery 3

Multiplying Two Rational Numbers. 1. a. 3 2 =___b. |3| |2| =___ 2. a. - 3 (- 2) =___b. |-3| |-2| =___ 3. a. 3 (- 2) =___b. |3| |-2| =___ 4. a =___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. Evaluate each expression, and compare the results obtained in the left column with the corresponding results in the right column. Chapter 1 Discovery 4

Dividing Two Rational Numbers 1. a. 8 2 =___b. |8| |2| =___ 2. a. - 8 (- 2) =___b. |-8| |-2| =___ 3. a. 8 (- 2) =___b. |8| |-2| =___ 4. a =___ 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. Evaluate each expression, and compare the results obtained in the left column with the corresponding results in the right column. Chapter 1 Discovery 5

Division Involving Zero =___ =___ =___4. 0 (- 5) =___ =___ 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. Evaluate each expression. Chapter 1 Discovery 6

Multiplying Three or More Nonzero Rational Numbers 1. One negative factor2. Two negative factors = ___- 6 (- 3) 4 1 = ___ 3. Three negative factors4. 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. Evaluate each expression, and compare the results obtained in the left column with the results in the right column. Chapter 1 Discovery 7

Order of Operations Consider the expression 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. Chapter 1 Discovery 8

Expressions with an Exponent of 1 or 0 Evaluate each expression =___ =___ 2. (-10) 1 =___5. (-10) 0 =___ =___ =___ 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. Chapter 1 Discovery 9

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

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