Download 8.5   Multiplying and Dividing Real Numbers 

8.5 Multiplying and Dividing Real Numbers Learning Objectives: 1. Multiplying real numbers. 2. Find the reciprocal of a real number. 3. Dividing real numbers. 4. Simplifying expressions. 1. Multiplying Real Numbers Sign Rules and Rules for Multiplication: 1. 2. Example 1. Multiply each of the following. 1. 6 ⋅ 7 2. − 4 ⋅ 2 Rules for Exponents 1. 2. Example 2. Find each of the following. 1. (− 4)
3. 3. (− 2.1) ⋅ (− 3.01) 3. 4. 4. ⎛ 7⎞
3. ⎜ − ⎟ ⎝ 9⎠
2
2
2. − 5 3
2. The Reciprocal Real Numbers Reciprocal or Multiplicative Inverse: Two numbers whose product is 1 are called reciprocals or multiplicative inverse. Example 3. Find the reciprocal of the real number. 3
1. − 2. 5 3. − 0.3 7
3. Dividing Real Numbers Sign Rules and Rules for Division: 1. 2. 3. 4. 5. Example 4. Divide each of the following 1 ⎛ 8⎞
− 18
1. 2. 49 ÷ (− 7 ) 3. − ÷ ⎜ − ⎟ 2 ⎝ 15 ⎠
9
4. Simplifying Expressions Example 5. Simplify each expression. 0(− 5)
1. 4
2
5 + (− 4) + 4 ⋅ 8
2. 4(6 − 4)
3
5(− 2 ) + 52
3. − 4 +1
7(− 5) − (− 2 )
4. 3 2 + (− 9)
− 6x − 4 y
when x = 5, y = −1 and z = 0 Example 6. Evaluate: − 2 z + 3 − (− 10)
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Read: Sections 8.7