Unit 1: Number Properties
Just as in life, there are certain things in math that make you shrug and say, "Well, duh. I knew that; it's common sense." This unit will discuss some of the basic algebraic properties which you already know, but may not necessarily know the names of, because they are what some math teachers refer to as the "common sense" properties.
The really neat thing about these properties is that you can see their uses in everyday, non-mathematical ways. For example, if you drive to work, you "commute." Whether you are driving to work from home, or to home from work, you are making the same trip. (Ignoring those times you take a back road because you do not want to spend two hours sitting on the interstate, of course!) In math, the commutative property tells us when we can move numbers around and still get the same answer. Another example is the associative property. The people you hang out with are also known as your "associates." If you are hanging out with two friends, but one of them is in a different room, you still have the same group of friends. The same applies to certain mathematical situations. If you are grouping numbers, depending upon the situation, the grouping is not going to change anything.
Completing this unit should take you approximately 6 hours.
Upon successful completion of this unit, the student will be able to:
- apply the associative law of addition and multiplication;
- apply the commutative law of addition and multiplication;
- apply the identity property of addition and multiplication;
- apply the inverse property of addition and multiplication;
- apply the zero property of addition and multiplication; and
- apply the distributive property.
1.1: Laws and Properties of Addition
1.1.1: Commutative Law of Addition
Take notes as you watch this video to learn about the Commutative Law of Addition (also known as the Commutative Property of Addition). Watch the presentation carefully two or three times until you are able to explain how changing the order of the addition of two numbers obtains the same result.
Study the "Commutative Property of Addition" on pages 15 and 16 of the textbook, stopping at "Grouping Symbols." The material may also be located through the bookmark on the left side (1 The Whole Numbers, 1.2 Adding and Subtracting Whole Numbers, "The Commutative Property of Addition"), which will take you directly to the reading. This reading provides an example of the property and the formal definition of the Commutative Property of Addition.
1.1.2: Associative Law of Addition
Take notes as you watch this video to learn about the Associative Law of Addition (also known as the Associative Property of Addition). Watch the presentation carefully two or three times until you are able to explain how to associate the addition of three numbers to obtain the same result.
Study the "Associative Property of Addition" on page 17 of the textbook, stopping at "The Additive Identity." The material may also be located through the bookmark on the left side (1 The Whole Numbers, 1.2 Adding and Subtracting Whole Numbers, "The Associative Property of Addition"), which will take you directly to the reading. This reading provides an example of the property and the formal definition of the Associative Property of Addition.
1.1.3: Identity Property of Addition
Take notes as you watch this video. Watch the presentation carefully two or three times until you are able to explain how adding zero to any number is the original number.
Study "The Additive Identity" located on pages 17 and 18 of the textbook, stopping at "Adding Larger Whole Numbers." The material can also be located through the bookmark on the left side (1 The Whole Numbers, 1.2 Adding and Subtracting Whole Numbers, "The Additive Identity"), which will take you directly to the reading. This reading provides an example of the property and the formal definition of the Additive Identity Property.
1.1.4: Property Recognition Activity
- College of the Redwoods: "Pre-Algebra Textbook: Adding and Subtracting Whole Numbers Exercises" File
Complete the odd-numbered exercises for 51-65 on pages 26 and 27 of the textbook. These exercises can also be located through the bookmark on the left side (1 The Whole Numbers, 1.2 Adding and Subtracting Whole Numbers, "Exercises"), which will take you directly to the assignment. These exercises will provide you with the opportunity to apply addition laws and properties. The solutions to these problems are located in the "Answers" section on page 30 of the textbook. The solutions page can also be located through the bookmark on the left side (1 The Whole Numbers, 1.2 Adding and Subtracting Whole Numbers, "Answers").
Study the section titled "Applications - Geometry" on pages 21 and 22 of the textbook. The material can also be located through the bookmark on the left side (1 The Whole Numbers, 1.2 Adding and Subtracting Whole Numbers, "Applications - Geometry"), which will take you directly to the reading. After reading and studying this section, complete the "You Try It" problems beside Example 5 on page 21 and Examples 6 and 7 on page 22. This reading provides applications to the properties and laws of addition.
- College of the Redwoods: "Pre-Algebra Textbook: Adding and Subtracting Whole Numbers Exercises" File
Complete the odd-numbered exercises for 11-27 on page 25 and the odd-numbered exercises for 67-79 on page 27 of the textbook. These exercises can also be located through the bookmark on the left side (1 The Whole Numbers, 1.2 Adding and Subtracting Whole Numbers, "Exercises"), which will take you directly to the assignment. These exercises will provide you with the opportunity to recognize addition laws and properties and apply the concepts. The solutions to these problems are located in the "Answers" section on page 30 of the textbook. The solutions page can also be located through the bookmark on the left side (1 The Whole Numbers, 1.2 Adding and Subtracting Whole Numbers, "Answers").
1.1.5: Inverse Property of Addition
Study the "Additive Inverse" located on page 120 of the textbook, including Example 8. The material can also be located through the bookmark on the left side (2 The Integers, 2.2 Adding Integers, "Properties of Addition of Integers"), which will take you directly to the reading. After you study and read this section, complete the "You Try It" problem next to Exercise 8. This reading provides an example of the property and the formal definition of the Additive Inverse Property.
Take notes as you watch this video. Watch the presentation carefully two or three times until you are able to explain how the Inverse Property of Addition results in zero.
1.2: Laws and Properties of Multiplication
1.2.1: Commutative Law of Multiplication
Take notes as you watch this video. Watch the presentation carefully two or three times until you are able to explain how changing the order of the multiplication of two numbers obtains the same result.
Study the introduction to "Multiplication and Division of Whole Numbers" on page 33 and continue through "The Commutative Property of Multiplication" on page 34. The material can also be located through the bookmark on the left side (1 The Whole Numbers, 1.3 Multiplication and Division of Whole Numbers), which will take you directly to the reading. This reading provides an example of the property and the formal definition of the Commutative Property of Multiplication.
1.2.2: Associative Law of Multiplication
Study "The Associative Property of Multiplication" on page 35 of the textbook. The material can also be located through the bookmark on the left side (1 The Whole Numbers, 1.3 Multiplication and Division of Whole Numbers, "The Associative Property of Multiplication), which will take you directly to the reading. This reading provides an example of the property and the formal definition of the Associative Property of Multiplication.
Take notes as you watch this video. Watch the presentation carefully two or three times until you are able to explain how to associate the multiplication of three numbers to obtain the same result.
1.2.3: Identity Property of Multiplication
Take notes as you watch this video. Watch the presentation carefully two or three times until you are able to explain how multiplying any number by one results in the original number.
Study "The Multiplicative Identity" on page 34 of the textbook. The material can also be located through the bookmark on the left side (1 The Whole Numbers, 1.3 Multiplication and Division of Whole Numbers, "The Multiplicative Identity"), which will take you directly to the reading. This reading provides an example of the property and the formal definition of the Multiplicative Property.
1.2.4: Property Recognition Activity
Complete the odd-numbered exercises for 5-27 on page 44 of the textbook. These exercises can also be located through the bookmark on the left side (1 The Whole Numbers, 1.3 Multiplication and Division of Whole Numbers, "Exercises"), which will take you directly to the assignment. These exercises will provide you with the opportunity to recognize addition laws and properties and apply these concepts. The solutions to these problems are located in the "Answers" section on page 49 of the textbook. The solutions page can also be located through the bookmark on the left side (1 The Whole Numbers, 1.3 Multiplication and Division of Whole Numbers, "Answers").
Study the section titled "Application -Area" through Example 4 on pages 42 and 43 of the textbook. The material can also be located through the bookmark on the left side (1 The Whole Numbers, 1.3 Multiplication and Division of Whole Numbers, "Applications - Area"), which will take you directly to the reading. After reading and studying this section, complete the "You Try It" problems beside Example 4 on page 43. This reading provides applications to the properties and laws of multiplication.
Complete the odd-numbered exercises for 49-59 on pages 45 and 46 of the textbook. These exercises can also be located through the bookmark on the left side (1 The Whole Numbers, 1.3 Multiplication and Division of Whole Numbers, "Exercises"), which will take you directly to the assignment. These exercises will provide you with the opportunity to find the area of rectangles as well apply multiplication such as if a math tutor was paid $20 per hour and worked 20 hours, how much would the tutor get paid? The solutions to these problems are located in the "Answers" section on page 50 of the textbook. The solutions page can also be located through the bookmark on the left side (1 The Whole Numbers, 1.3 Multiplication and Division of Whole Numbers, "Answers").
1.2.5: Inverse Property of Multiplication
Take notes as you watch this video. Watch the presentation carefully two or three times until you are able to explain how the inverse property of multiplication results in one.
Study "The Multiplicative Inverse Property" through Example 1 on pages 266 and 267 of the textbook. The material can also be located through the bookmark on the left side (4 Fractions, 4.3 Reciprocals, "The Multiplicative Inverse Property"), which will take you directly to the material. After you read and study this section, attempt the "You Try It" problem beside Example 1. Check your answer on page 267. This reading provides an example of the property and the formal definition of the Multiplicative Inverse Property.
1.2.6: Multiplication by Zero
Study the section titled "Multiplication by Zero" on pages 34 and 35 of the textbook. You may stop when you reach the section titled "The Associative Property of Multiplication." The material can also be located through the bookmark on the left side (1 Whole Numbers, 1.3 Multiplication and Division of Whole Numbers, "Multiplication by Zero"), which will take you directly to the reading. This reading provides an example of the property and the formal definition of the Multiplication by Zero.
1.3: Dividing by Zero Is Undefined
Study the section titled "Division by Zero Is Undefined" on page 40 of the textbook, stopping at "Dividing Larger Whole Numbers." The material can also be located through the bookmark on the left side (1 The Whole Numbers, 1.3 Multiplication and Division of Whole Numbers, "Division by Zero is Undefined"), which will take you directly to the reading. This reading provides an example of the property and the formal definition of why division by zero is undefined.
Complete the odd-numbered exercises for 69-75 on page 46 of the textbook. The exercises can also be located through the bookmark on the left side (1 The Whole Numbers, 1.3 Multiplication and Division of Whole Numbers, "Exercises"), which will take you directly to the assignment. These exercises will provide you with the opportunity to apply multiplication laws and properties. The solutions to these problems are located in the "Answers" section on page 50 of the textbook. The solutions page can also be located through the bookmark on the left side (1 The Whole Numbers, 1.3 Multiplication and Division of Whole Numbers, "Answers").
Take notes as you watch this video. Watch the presentation carefully two or three times until you are able to explain why dividing by zero is undefined.
1.4: Distributive Property
Take notes as you watch these videos. Watch the first presentation carefully two or three times until you are able to explain how the distributive property applies with an addition expression. Watch the second presentation carefully two or three times until you are able to explain how the distributive property applies with a subtraction expression.
Read "The Distributive Property" section through "Sample Set A." Then, complete "Practice Set A," exercises 1-7. The solutions to the problems are revealed below each problem. These problems will allow you to practice using the distributive property to simplify algebraic expressions.
Unit 1 Assessment
Take this assessment to see how well you understood this unit.
- This assessment does not count towards your grade. It is just for practice!
- You will see the correct answers when you submit your answers. Use this to help you study for the final exam!
- You can take this assessment as many times as you want, whenever you want.