Questions and Answers
What is a variable?
Symbols that represent unknown numbers or changeable quantities.
What is an example of a variable?
In the equation 4x - 5y = 9, the variables are x and y.
What is a mathematical expression?
A collection of numbers and operations arranged in a meaningful order.
What is an algebraic expression?
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What is an expression?
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What is an equation?
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What is an example of an equation?
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What is an inequality?
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What is an example of an inequality?
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What is the difference between an algebraic expression and an algebraic equation?
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What is a factor?
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What is a term?
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What is a coefficient?
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What is a constant?
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What is the order of operations?
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What is the distributive property?
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What is combining like terms?
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Study Notes
Variables and Expressions
- Variables represent unknown numbers or changeable quantities in mathematics.
- Example of variables: In the equation 4x - 5y = 9, the variables are x and y.
- A mathematical expression is a structured arrangement of numbers and operations.
- An algebraic expression contains one or more variables, like x² + 2x + 1.
Equations and Inequalities
- An equation declares that two expressions are equal, such as 2x = 6.
- An inequality features two or more expressions linked by inequality signs (e.g., ≤, ≥, ≠).
- Example of an inequality: To solve 4x - 5 ≥ 11, add 5 to each side then divide by 4.
Key Terminology
- An expression is a combination of numbers, variables, and operations that lacks an equals or inequality sign.
- "A variable" implies an unknown or indeterminate number.
- "Difference of," "minus," and "less than" indicate subtraction operations.
- "Sum of," "plus," and "more than" signify addition operations.
- "Product of" and "times" denote multiplication.
- "Quotient of" and "divided by" represent division.
- "Power of" refers to exponents (e.g., squared).
- "Root of" is symbolized by √.
Additional Concepts
- The reciprocal of a number is obtained by flipping its fraction (e.g., 2/3 becomes 3/2).
- The absolute value represents the magnitude of a real number, ignoring its sign.
- A factor is a number or expression that can be multiplied to produce a specific product (e.g., in x²y², 4, x, 6, and y are factors).
- A term can be a number, variable, or product of a number and variables; terms are separated by addition or subtraction.
- A coefficient is the numerical factor in a term that multiplies a variable (e.g., in 4x, the coefficient is 4).
- A constant is an unchanging value in an expression (e.g., in 10, the constant is 10).
Differences and Operations
- Factors are parts of multiplication problems, while terms can consist of numbers, variables, and their products.
- The order of operations sets the sequence for calculations, starting with the innermost groupings (parentheses, brackets).
- The distributive property allows multiplication across sums or differences, facilitating expansion of expressions.
- Combining like terms is crucial for simplifying expressions; like terms share identical variable factors raised to the same powers, and simplifying results in the absence of like terms.
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Description
Test your understanding of variables and expressions in algebra. This quiz covers essential concepts including equations, inequalities, and key terminology. See how well you can apply your knowledge to solve problems involving algebraic expressions!