Numerical Expression A numerical expression is a string of numbers and operational signs that names a number.

9 + 2 • 6 3 + 9 9 − 5 6 − (4 + 3)

Numerical Expression A numerical expression must be evaluated using the order of operations.

Order of Operations Symbols of grouping–evaluate quantities within symbols of grouping first. Exponents–evaluate a term with an exponent before performing other operations.

Order of Operations Multiplication and division– perform these operations in order from left to right. Addition and subtraction– perform these operations last, in order from left to right.

2 + 3 • 4 − 5

4 ÷ 2 − 3 • 6

2 • 42 ÷ (6 + 2)

Algebraic Expression An algebraic expression is a mathematical expression containing numbers, variables, and operational signs.

Example 1 Evaluate when n = 8. n + 6 = 14

Example 2 Evaluate when a = −12. a + 7 = −5

Example 3 Evaluate when n = −3. −7 − n = −4

Example Evaluate when m = −5. 6m = −30

Example Evaluate when n = 4. = 12 n 3

Example Evaluate when x = 2. 18 − 4x = 10

Example Evaluate when y = 36. = y 9 21 − 17

Example 4 Evaluate when x = 9 and y = 3. x − (y + 7) = −1

Example 5 Evaluate when x = -3 and y = 12. 2x − = y 3 −10

Example 6 Evaluate when a = −2 and b = −3. 2ab − 3b = 21

Example Evaluate when a = 6 and b = 4. 8a − 5b + 4 = 32

Example Evaluate when x = 2 and y = −4. 5xy = −40

Example Evaluate when m = 5 and n = 1. 4m 9 + n = 2

Example Evaluate when x = 2 and y = 3. = 6x + 2y xy 3

Example Evaluate when a = 2, b = 3, c = 4, and d = 5. bc + ad a + c + d = 2

Example Evaluate when a = 2, b = 3, c = 4, and d = 5. (db − ab)(ad) = 90