CHAPTER 1 Whole Numbers, Integers, and Introduction to Algebra
CHAPTER 1 Whole Numbers, Integers, and Introduction to Algebra
1.2 Use the Language of Algebra
Learning Objectives
By the end of this section, you will be able to:
- Use variables and algebraic symbols
- Identify expressions and equations
- Simplify expressions with exponents
- Simplify expressions using the order of operations
Use Variables and Algebraic Symbols
Greg and Alex have the same birthday, but they were born in different years. This year Greg is years old and Alex is , so Alex is years older than Greg. When Greg was , Alex was . When Greg is , Alex will be . No matter what Greg’s age is, Alex’s age will always be years more, right?
In the language of algebra, we say that Greg’s age and Alex’s age are variable and the three is a constant. The ages change, or vary, so age is a variable. The years between them always stays the same, so the age difference is the constant.
In algebra, letters of the alphabet are used to represent variables. Suppose we call Greg’s age . Then we could use to represent Alex’s age. See the table below.
| Greg’s age | Alex’s age |
|---|---|
Letters are used to represent variables. Letters often used for variables are .
Variables and Constants
A variable is a letter that represents a number or quantity whose value may change.
A constant is a number whose value always stays the same.
To write algebraically, we need some symbols as well as numbers and variables. There are several types of symbols we will be using. In 1.1 Whole Numbers, we introduced the symbols for the four basic arithmetic operations: addition, subtraction, multiplication, and division. We will summarize them here, along with words we use for the operations and the result.
| Operation | Notation | Say: | The result is… |
|---|---|---|---|
| Addition | the sum of and | ||
| Subtraction | the difference of and | ||
| Multiplication | The product of and | ||
| Division | divided by | The quotient of and |
In algebra, the cross symbol, ×, is not used to show multiplication because that symbol may cause confusion. Does mean (three times ) or (three times )? To make it clear, use • or parentheses for multiplication.
We perform these operations on two numbers. When translating from symbolic form to words, or from words to symbolic form, pay attention to the words of or and to help you find the numbers.
- The sum of and means add plus , which we write as .
- The difference of and means subtract minus , which we write as .
- The product of and means multiply times , which we can write as .
- The quotient of and means divide by , which we can write as .
EXAMPLE 1
Translate from algebra to words:
| a. |
| 12 plus 14 |
| the sum of twelve and fourteen |
| b. |
| 30 times 5 |
| the product of thirty and five |
| c. |
| 64 divided by 8 |
| the quotient of sixty-four and eight |
| d. |
| minus |
| the difference of and |
TRY IT 1.1
Translate from algebra to words.
Show Answer
- 18 plus 11; the sum of eighteen and eleven
- 27 times 9; the product of twenty-seven