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Questions and Answers
Which of the following best defines a constant in algebra?
Which of the following best defines a constant in algebra?
In the expression 5xy + 3x, what are the coefficients?
In the expression 5xy + 3x, what are the coefficients?
Which of the following pairs are considered similar terms?
Which of the following pairs are considered similar terms?
What is the result of simplifying the expression 3a + 2a - 5?
What is the result of simplifying the expression 3a + 2a - 5?
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In the expression 7x + 4y - 2x, which part is considered a term?
In the expression 7x + 4y - 2x, which part is considered a term?
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What is the coefficient in the term 8xyz?
What is the coefficient in the term 8xyz?
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Which of the following represents a dissimilar term to 3x?
Which of the following represents a dissimilar term to 3x?
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When dealing with algebraic expressions, the terms in the expression 9xy - 4y + 2x are?
When dealing with algebraic expressions, the terms in the expression 9xy - 4y + 2x are?
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What is a constant in an algebraic expression?
What is a constant in an algebraic expression?
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In the expression $9x + 2y - 3$, which of the following is the coefficient of the variable $y$?
In the expression $9x + 2y - 3$, which of the following is the coefficient of the variable $y$?
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Which of the following terms is considered dissimilar to $4x^2$?
Which of the following terms is considered dissimilar to $4x^2$?
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Which step is NOT part of simplifying an algebraic expression?
Which step is NOT part of simplifying an algebraic expression?
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Given the expression $-2a + 5a - 7$, what is its simplest form?
Given the expression $-2a + 5a - 7$, what is its simplest form?
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The Commutative Property of Equality allows one to do which of the following?
The Commutative Property of Equality allows one to do which of the following?
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Which expression contains similar terms?
Which expression contains similar terms?
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In the expression $7xyz$, what is the numerical coefficient?
In the expression $7xyz$, what is the numerical coefficient?
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Study Notes
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.
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Description
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.
