1. 2-1 Variables and Expressions Learn to identify and evaluate expressions.

2. 2-1 Variables and Expressions Vocabulary variable constant algebraic expression evaluate

3. 2-1 Variables and Expressions A variable is a letter or symbol that represents a quantity that can change. A constant is a quantity that does not change.

4. 2-1 Variables and Expressions An algebraic expression contains one or more variables and may contain operation symbols. So p  7 is an algebraic expression. Algebraic Expressions NOT Algebraic Expressions 150 + y85 ÷ 5 35  w + z 10 + 3  5 To evaluate an algebraic expression, substitute a number for the variable and then find the value.

5. 2-1 Variables and Expressions Evaluate the expression to find the missing values in the table. Additional Example 1A: Evaluating Algebraic Expressions Substitute for y in 5  y. y 5  y 16 27 35 80 y = 16; 5  16 = 80 135 175 27135 35175 y = 27; 5  = y = 35; 5  = The missing values are 135 and 175.

6. 2-1 Variables and Expressions Evaluate the expression to find the missing values in the table. Additional Example 1B: Evaluating Algebraic Expressions z z  5 + 4 2 20 45 60 20 z = 20; 20  5 + 16 = 20 z = 45; __  5 + 16 = __ z = 60; __  5 + 16 = __ 25 28 45 25 60 28 The missing values are 25 and 28. Substitute for z in z  5 + 4 2.

7. 2-1 Variables and Expressions Check It Out: Example 1A Evaluate the expression to find the missing values in the table. Substitute for x in x  9. x x  9 18 36 54 2 x = 18; 18  9 = 2 4 6 4 54 6 x = 36;  9 = x = 54;  9 = 36 The missing values are 4 and 6.

8. 2-1 Variables and Expressions Evaluate the expression to find the missing values in the table. Check It Out: Example 1B z 8  z + 2 3 7 9 11 64 z = 7; 8  7 + 8 = 64 z = 9; 8  __+ 8 = __ z = 11; 8  __ + 8 = __ 80 96 980 1196 The missing values are 80 and 96. Substitute for z in 8  z + 2 3.

9. 2-1 Variables and Expressions You can write multiplication and division expressions without using the symbols  and . Instead of... You can write... x  3 x  3 35 ÷ y x(3) 3x3x 35 y When you are multiplying a number times a variable, the number is written first. Write “3x” not “x3.” Read 3x as “three x.” Writing Math

10. 2-1 Variables and Expressions A rectangle is 4 units wide. How many square units does the rectangle cover if it is 3, 4, 5, or 6 units long? Additional Example 2: Evaluating Expressions with Two Variables Make a table to help you find the number of square units for each length. 3 x 4 = square units 20 16 lwl x w 3412 44 54 64 The rectangle will cover 12, 16, 20, or 24 square units. 4 x 4 = square units 5 x 4 = square units 6 x 4 = square units 12 16 20 24

11. 2-1 Variables and Expressions A rectangle is 3 units wide. How many square units does the rectangle cover if it is 2, 3, 4, or 5 units long? Check It Out: Example 2 Make a table to help you find the number of square units for each length. 2 x 3 = square units 12 9 lwl x w 236 33 43 53 The rectangle will cover 6, 9, 12, or 15 square units. 3 x 3 = square units 4 x 3 = square units 5 x 3 = square units 6 9 12 15