Learn to evaluate algebraic expressions.

Vocabulary variable constant algebraic expression evaluate

Ron Howard was born in You can find out what year Ron turned 16 by adding the year he was born to his age In algebra, letters are often used to represent numbers. You can use a letter such as a to represent Ron Howard’s age. When he turns a years old, the year will be a.

The letter a has a value that can change, or vary. When a letter represents a number that can vary, it is called a variable. The year 1954 is a constant because the number cannot change. An algebraic expression consists of one or more variables. It usually contains constants and operations. For example, a is an algebraic expression for the year Ron Howard turns a certain age.

To evaluate an algebraic expression, substitute a number for the variable. AgeYear born + age = year at age a a

Evaluate k + 9 for each value of k. Ex 1: Evaluating Algebraic Expressions A. k = -5 k Substitute 5 for k. Add. B. k = -2 k Substitute 2 for k. 7 Add.

Example 2 Evaluate a + 6 for each value of a. A. a = -3 a Substitute -3 for a. Add. B. a = -5 a Substitute -5 for a. 1 Add.

Multiplication and division of variables can be written in several ways, as shown in the table. When evaluating expressions, use the order of operations.

Evaluate the expression for the given value of the variable. Evaluating Algebraic Expressions Involving Order of Operations 3. 4x – 3 for when x = -2 4(-2) – 3 -8 – Substitute 2 for x. Multiply. Subtract.

Additional Example 2: Evaluating Algebraic Expressions Involving Order of Operations 4. s ÷ 5 + s, for s = ÷ (-15) x 2 + 3x, for x = -2 5(-2) 2 + 3(-2) 5(4) + 3(-2) 20 + (-6) 14 Substitute -15 for s. Divide. Add. Substitute -2 for x. Evaluate the power. Multiply. Add.

Example 6 Evaluate the expression for the given value of the variable. A. -3x – 2 for x = 3 -3(3) – 2 -9 – Substitute 3 for x. Multiply. Subtract.

7. r ÷ (-3) + r, for r = ÷ (-4) y 2 + 2y, for y = (3) 2 + 2(3) 4 - (9) + 2(3) (-5) Substitute 12 for r. Divide. Add. Substitute 3 for y. Evaluate the power. Multiply. Add.

Evaluate Example 9: Evaluating Algebraic Expressions with Two Variables 6a6a + 4b, for a = 3 and b = 2. 6a6a + 4b (2) Substitute 3 for a and 2 for b. Divide and multiply from left to right. Add.

Example 10 Evaluate 8w8w + 2x, for w = 4 and x = 2. 8w8w + 2x (2) Substitute 4 for w and 2 for x. Divide and multiply from left to right. Add.

Evaluate n + 7 for each value of n. 1. n = n = -31 Evaluate each algebraic expression for the given value of the variables 3. -6y – 5 for y = x x for x = y for x = 4 and y = 3 6. The expression 7d gives the number of days in d weeks. Evaluate 7d for d = 12. How many days are in 12 weeks? x -5 84