Algebra Expressions Flashcards

What is an algebraic expression?

Which of the following is an example of an algebraic expression?

Which of the following is NOT an example of an algebraic expression?

What are the parts of an algebraic expression called?

What are letters that represent one or more unknown numbers called?

What is the numerical factor of a term that contains a variable called?

What are the terms called that do not contain a variable?

What does the expression n⁵ mean?

Identify the base and exponent in the expression: 5x⁴

Identify the terms, coefficients, and constants in the expression: 12 + 10c.

Identify the terms, coefficients, and constants in the expression: 15 + 3w + ½.

Identify the terms, coefficients, and constants in the expression: z² + 9w - 2.

Identify the terms, coefficients, and constants in the expression: 6r(8r - 13).

Identify the terms, coefficients, and constants in the expression: 4x² - 7y + ¾.

Identify the terms, coefficients, and constants in the expression: 2x(x - 3y + 4).

Algebraic Expression Fundamentals

An algebraic expression consists of numbers, operations, and one or more symbols.
Examples of algebraic expressions include:
- 2n + 5
- 6(4d)
- 2 - 8d²
- 5n³ ÷ 6y²

Non-Examples

Non-examples exclude expressions that are not algebraic, such as:
- Standalone numbers (e.g., 145)
- Equations (e.g., 8x + 15 = 55)
- Fractions (e.g., ¾)
- Equalities with algebraic terms (e.g., 3x³ ÷ 4y² = 124)

Components of Algebraic Expressions

Parts of an algebraic expression are called terms.
Terms are separated by addition or subtraction signs, illustrated by the expression 3 + 2x + 7y, which consists of three terms: 3, 2x, and 7y.

Variables and Coefficients

Variable: Letters representing one or more unknown numbers (e.g., in 3 + 2x + 7y, x and y are variables).
Coefficient: The numerical factor of a term with a variable (in 3 + 2x + 7y, coefficients are 2 and 7).

Constants

A constant is a term without a variable. Example: In 3 + 2x + 7y, the constant is 3.

Exponents

The expression n⁵ represents n multiplied by itself five times: n × n × n × n × n.
In the expression 5x⁴, the base is x and the exponent is 4 (with 5 as the coefficient).

Analyzing Expressions

Terms, coefficients, and constants breakdown:
- For 12 + 10c:
  - Terms: 12, 10c
  - Coefficient: 10
  - Constant: 12
- For 15 + 3w + ½:
  - Terms: 15, 3w, ½
  - Coefficient: 3
  - Constants: 15, ½
- For z² + 9w - 2:
  - Terms: z², 9w, -2
  - Coefficients: 9, 1 (in front of z)
  - Constant: -2
- For 6r(8r - 13):
  - Terms: 8r, 13
  - Coefficients: 6, 8
  - Constant: 13
- For 4x² - 7y + ¾:
  - Terms: 4x², -7y, ¾
  - Coefficients: 4, -7
  - Constant: ¾
- For 2x(x - 3y + 4):
  - Terms: x, -3y, 4
  - Coefficient: 2, 1 (in front of x)
  - Constant: 4

This quiz consists of flashcards designed to help you identify and understand the components of algebraic expressions. You will learn the definitions, examples, and non-examples of algebraic expressions. Great for students looking to solidify their understanding of algebra concepts.