BackFoundations of Algebra: Numerical Coefficients, Simplifying Expressions, and Translating Word Problems
Study Guide - Smart Notes
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Numerical Coefficients
Definition and Identification
The numerical coefficient of a term is the number that multiplies the variable(s) in an algebraic expression. It tells us how many times the variable is being counted.
Key Point: In the term 7x, the numerical coefficient is 7.
Key Point: If the variable stands alone (e.g., x), the coefficient is 1.
Example: In -3y, the numerical coefficient is -3.
Simplifying Expressions by Combining Like Terms
Like Terms and Simplification
Like terms are terms that have the same variable(s) raised to the same power. To simplify an expression, add or subtract the coefficients of like terms.
Key Point: Only like terms can be combined.
Key Point: The variables and their exponents must match exactly.
Example: Simplify :
Example: Simplify :
Translating Word Problems into Algebraic Expressions
Writing and Simplifying Algebraic Expressions
Word problems often describe mathematical relationships. To solve them, translate the words into algebraic expressions using a variable (often x or n) for the unknown number.
Key Point: "A number increased by 5" becomes .
Key Point: "Three fifths of a number, increased by ten" becomes .
Example: "The sum of a number and 8" is .
Using the Distributive Property
Definition and Application
The distributive property allows you to multiply a single term by each term inside a set of parentheses.
Key Point:
Key Point: Use the distributive property to remove parentheses and simplify expressions.
Example: Simplify :
Example: Simplify :
Summary Table: Key Concepts
Concept | Definition | Example |
|---|---|---|
Numerical Coefficient | The number multiplying the variable | In , coefficient is 5 |
Like Terms | Terms with identical variable parts | and |
Distributive Property | ||
Translating Words to Algebra | Expressing phrases as algebraic expressions | "A number plus 4" is |
Practice Problems
Identify the numerical coefficient: In , the coefficient is -8.
Simplify:
Translate: "Twice a number decreased by 7" is
Distribute:
