Introduction to Algebra

Introduction to Algebra

• Algebra is a branch of mathematics
• It uses letters and symbols to represent numbers and mathematical operations.

Preliminary Concepts

• Algebra involves representing unknown numbers in numerical expressions to perform operations such as addition, subtraction, multiplication, or division.

Variables

• A variable is a letter or symbol that represents an unknown or changing value.
• Variable values can change depending on the equation.
• Examples include: 4ab, 6b, 7x.

Constants

• A constant is a number that does not change.
• Examples include: 4ab, 6b, 7x.

Algebraic Expressions

• An algebraic expression is a mathematical phrase that includes constants, variables, and algebraic operators
• Expressions are written in terms of factors and coefficients.
• Example: 2abc, factors include 2, a, b, c. Constant =2 Variables=a, b, c

Parts of expression

• An algebraic expression is made up of terms, constants, coefficients, and variables.
• Example: 2x + 4y - 9.
• Coefficients are 2 and 4
• Constant is 9
• Variables are x and y
• Terms are 2x, 4y and 9

Terms

• A term is a single number, variable, or combination of both, separated by operations (+, -, x , /).
• Examples: 2x, 4y, 9.

Coefficients

• Coefficients are numbers in front of variables indicating how many times a variable is multiplied
• Numerical coefficient is the numerical factor of a term.
• Literal coefficient is the product of variables in a term.

What is meant by terms in expression

• An algebraic expression contains terms
• A term can be a single constant or a variable, or a variable with a coefficient

What are the factors in an algebraic expression

• A factor in an expression is something that is multiplied by another thing.
• Factors can be a number, variable, or an expression
• Example: the factors of 2xy are 2, x, and y

What is a coefficient

• A coefficient is a numerical value that is multiplied by a variable
• Example: in 7x, the coefficient is 7

What is a coefficient, term of an expression

• In an expression, the numbers in front of the variables are called coefficients
• The terms are parts of the expressions separated by operations ( +,- )
• Example: in 5x+8y. the coefficients are 5 and 8 and the terms are 5x and 8y.

What is a constant

• A constant is a numerical value that does not change.
• In an expression like 2x + 6, the number 6 is a constant.

Identify the variables, terms, constant, and coefficients

• Variables are x and y
• Terms include 9x, 2y, and -3
• Constant is -3
• coefficients are 9, 2

Similar and dissimilar terms

• Similar terms have the same variables with the same exponents
• Dissimilar terms have different variables or different exponents

Exponents

• An exponent is a number or variable written above and to the right of another number or variable that shows how many times that number or variable is multiplied by itself.
• 4 x 4 x 4 = 4³

Simplifying algebraic expressions

• An algebraic expression is considered simplified when grouping symbols are removed
• Similar terms are combined

Steps in simplifying algebraic expressions

• Remove grouping symbols first
• Start with a term in the parentheses, or brackets or braces
• Combine like terms

Combining like terms

• To combine like terms, combine coefficients and keep the variables the same.
• Terms with the same variable and exponent are combined

Properties of equality

• Commutative, associative, and distributive properties
• These properties can help simplify expressions by rearranging terms or distributing factors.

Examples of combining like terms, simplifying the expressions and using equality properties in algebraic expressions.

Explore the fundamentals of algebra in this introductory quiz. Understand key concepts such as variables, constants, and algebraic expressions. Test your knowledge on how to represent unknown values and perform basic operations.