Algebraic Expressions and Terms, Lecture notes of Algebra

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Algebraic Expressions and Terms

Variables and Expressions,

Order of Operations

Notes 1.1 and 1.

I. Expressions

You are familiar with the following type of numerical expressions : 12 + 6 3 (12) 6 (3 + 2) 15 - 4 (6)

III. Algebraic Expressions

When variables are used with other numbers, parentheses, or operations, they create an algebraic expression.

a + 2

(a) (b)

3m + 6n - 6

Expressions vs. Equations

Expressions Equations

No = sign = sign

Simplify Solve

IV. Terms

A term is the name given to a number, a variable, or a number and a variable combined by multiplication or division. Algebraic Expressions a + 2 3m + 6n - 6 Terms a, 2 3m, 6n, - 6

V. Constants

• A constant is a number that cannot change its value. In the expression: 5x + 7y + 2 the constant is 2 In the expression: x - 3 the constant is -^3

VII. Powers, Bases and Exponents

This is a Power 7

This is a base This is an exponent

Let’s Practice!

Identify the terms, coefficients, and constants. TERMS COEFFICIENTS CONSTANTS 12a – 6b + 4 4x – 2y C - 32 3x + 2 12a, - 6b, 4 12,- 6 4 4x, - 2y 4, - 2 0 C, - 32 1 - 32 3x, 2 3 2

B. Key words to look for:

• Addition:
  • Add
  • Plus
  • Sum
  • Total
  • Increased by
  • More than
    • Subtraction:
      • Minus
      • Difference
      • Subtract
      • Less than
      • Decreased by
      • less

Cont…

• Multiplication
  • Product
  • Times
  • Multiply
  • per
    • Division
      • Quotient
      • Divide
      • Split Between

D. Write an algebraic phrase for these

situations

1. A car was traveling 35 miles per hour

for a number of hours.

2. Bob ran 7 times a week for a number of

weeks.

3. The plumber added an extra $35 to her

bill.

4. Thirty-five fewer people came than the

number expected.

When an expression contains more than one operation, the order of operations tells you which operation to perform first.

IX. ORDER OF OPERATIONS

Helpful Hint Fraction bars, radical symbols, and absolute-value symbols can also be used as grouping symbols. Remember that a fraction bar indicates division. Grouping symbols include parentheses ( ), brackets [ ], and braces { }. If an expression contains more than one set of grouping symbols, begin with the innermost set. Follow the order of operations within that set of grouping symbols and then work outward.

A. 15 – 2  3 + 1 15 – 2  3 + 1 There are no grouping symbols. 15 – 6 + 1 Multiply. 9 + 1 Subtract. 10 Add. **B. 12 + 3 2

• 10 ÷ 2** 12 + 3 2
• 10 ÷ 2 12 + 9 + 10 ÷ 2 26 Ex 1: Simplifying Numerical Expressions Simplify each expression. There are no grouping symbols. Evaluate powers. The exponent applies only to the 3. Add. 12 + 9 + (^5) Divide.