Evaluate, Simplify, and Translate Expressions
In this chapter, you will look at identifying expressions and terms and building and solving equations with these expressions. Many of the calculations we do in nursing are a combination of many different items that we need to combine appropriately to get the answers we seek. This lesson will create the building block for solving these problems in the various formal types we use in nursing.
Learning Objectives
By the end of this section, you will be able to:
Evaluate Expressions
In this section, we’ll evaluate expressions following the order of operations.
To evaluate an algebraic expression means to find the value of the expression when a given number replaces the variable. To evaluate an expression, we substitute the given number for the variable in the expression, and then simplify the expression using the order of operations.
Example 2.13
Evaluate when:
- ⓐ
- ⓑ
Solution:
ⓐ To evaluate, substitute the given number for in the expression, and then simplify.
| Write the expression to be evaluated. | |
| Substitute. | |
| Add. |
When , the expression has a value of .
ⓑ To evaluate, substitute the given number for in the expression, and then simplify.
| Write the expression to be evaluated. | |
| Substitute. | |
| Add. |
When , the expression has a value of .
Notice that we got different results for parts ⓐ and ⓑ even though we started with the same expression. This is because the values used for were different. When we evaluate an expression, the result varies depending on the value used for the variable.
Try It
Example 2.14
Evaluate , when:
- ⓐ
- ⓑ
Solution:
Remember, means times , so means times .
ⓐ To evaluate, substitute the given number for in the expression, and then simplify.
| Write the expression to be evaluated. | |
| Substitute for . | |
| Multiply. | |
| Subtract. |
ⓑ To evaluate, substitute the given number for in the expression, and then simplify.
| Write the expression to be evaluated. | |
| Substitute for . | |
| Multiply. | |
| Subtract. |
Notice that in part ⓐ we wrote , and in part ⓑ we wrote . Both the dot and the parenthesis tell us to multiply.
Try It
Example 2.17
Evaluate when and .
Solution:
This expression contains two variables, so we must make two substitutions.
| Write the expression to be evaluated. | |
| Substitute for and for . | |
| Multiply. | |
| Add and subtract left to right. |
When and , the expression has a value of .
Try It
Identify Terms, Coefficients, and Like Terms
Algebraic expressions are made up of terms. A term is a constant or the product of a constant and one or more variables. Some examples of terms are , , , and .
The constant that multiplies the variable(s) in a term is called the coefficient. We can think of the coefficient as the number in front of the variable. The coefficient of the term is . When we write , the coefficient is , since . Table 2.5 gives some example terms in the left column and the coefficients for each term in the right column.
| T