How to Simplify and Evaluate Expressions and Functions
Two types of mathematical problems are expressions and functions. Expressions are any mathematical terms or a sum or difference of math terms. Numbers, variables or both are used in expressions. Expressions can be simplified and evaluated for different values, but there is no solution. Functions are equations where only one answer is produced for various values of the variable. You first simplify an expression or function and then evaluate the problem.
Other People Are Reading
Instructions
-
-
1
Combine "like terms" to simplify the expression or function. Like terms are any terms that have the same variables (letters) raised to the same exponents or any constant numbers (no variables or exponents) you can combine. For example, "4x^2 + 3 -- 2x^2 +7 -- 3x^3" is simplified to "2x^2+10-3x^3." In this case, "4x^2" and "-2x^2" had similar variables and exponents and could therefore be combined. "3" and "7" are both constants and can be combined.
-
2
Plug in the values. Put the value you are given for the variable into each place the variable appears in the equation. To keep everything in order, put parentheses around each number you insert into the problem. For the example above, use "x=3." In a function, the value for the variable is given as "f(x)=3" rather than just "x=3." The example would now look like this: "2(3)^2+10-3(3)^3." Some expressions may have more than one variable. You will be given values for each variable. Plug them in the same way you did with only one variable.
-
-
3
Follow the order of operations to evaluate the expression or function. The order of operations is: parentheses, exponents, multiplication, division, addition and subtraction.
-
4
Look for any terms in parentheses to combine. Because there are no expressions in parentheses to combine, look for exponents. In the example above, evaluate "3^2" and "3^3." Three to the second power is "3 x 3" or 9. Three to the third power is "3 x 3 x 3" or 27. Keep the numbers in parentheses. The example now looks like this: "2(9)+10-3(27)."
-
5
Complete any multiplication or division, working from left to right. In the example, solve "2 x 9" which equals 18 and "3 x 27" which equals 81. The example now appears: "18+10-81."
-
6
Complete any addition or subtraction. Start at the left and work to the right. For the above example, "18+10" is 28 and "28-81" is -53. Therefore, -53 is the answer to the function or the expression simplified as far as possible.
-
1
References
- Photo Credit Jupiterimages/Photos.com/Getty Images
