Translating and Simplifying Algebraic Expressions

Comprehensive vocabulary flashcards covering translation of algebraic expressions, operational keywords, switch and grouping rules, and combining like terms in standard form.

Term

An addend of an algebraic expression; separated by plus signs.

Constant

A number in an algebraic expression that is not being multiplied by a variable; a number that stands alone and whose value always remains the same.

Coefficient

A number in an algebraic expression that is being multiplied by a variable; it is written directly in front of the variable.

Like Terms

Terms in an algebraic expression that are either constants or contain the exact same variables raised to the same exponents.

Combining Like Terms

The process of adding together like terms in an algebraic expression to simplify it by adding their coefficients while keeping the variables and exponents the same.

Standard Form

The arrangement of an algebraic expression where terms are written in alphabetical order and in descending order of exponents (highest to lowest), always placing constant terms last.

Quantity

The amount, taken all together; a phrase signaling that grouping symbols (such as parentheses) must be placed around what follows.

Switch Phrases

Phrases in verbal expressions—specifically "more than," "less than," "fewer than," and "subtracted from"—that reverse the written order of the terms when translating into an algebraic expression.

Grouping Words

Key words—specifically "quantity," "sum," and "difference"—that indicate grouping symbols should be placed around the expression that immediately follows.

Sum

The mathematical result of addition, associated with phrases like "plus," "increased by," "exceeded by," and "more than."

Difference

The mathematical result of subtraction, associated with phrases like "minus," "decreased by," "diminished by," "subtracted by," "subtracted from," "less than," and "fewer than."

Product

The mathematical result of multiplication, associated with phrases like "multiplied by," "of," "double," "twice," "squared," "tripled," and "cubed."

Quotient

The mathematical result of division, associated with words like "divided by."

Twice / Double

Multiplying a variable or value by $2$ (represented algebraically as $2 \times x$ or $2x$).

Tripled

Multiplying a variable or value by $3$ (represented algebraically as $3 \times x$ or $3x$).

Squared

Multiplying a value or variable by itself (represented algebraically as $x \times x$ or $x^2$).

Cubed

Multiplying a value or variable by itself three times (represented algebraically as $x \times x \times x$ or $x^3$).