Pre-Algebra Foundations Cheat Sheet

Key Facts

• The absolute value $|a|$ is the distance from $a$ to $0$ on a number line, so $|-7| = 7$ and $|7| = 7$.
• To add integers with the same sign, add their absolute values and keep the common sign, such as $-4 + (-6) = -10$.
• To add integers with different signs, subtract the smaller absolute value from the larger absolute value and keep the sign of the number with greater absolute value.
• The order of operations is parentheses, exponents, multiplication and division from left to right, then addition and subtraction from left to right.
• The distributive property is $a(b + c) = ab + ac$, such as $3(x + 4) = 3x + 12$.
• Like terms have the same variable parts, so $5x + 2x = 7x$ but $5x + 2y$ cannot be combined.
• To solve a one-step equation, use inverse operations to isolate the variable, such as $x + 9 = 14$ becoming $x = 5$.
• A proportion states that two ratios are equal, and $\frac{a}{b} = \frac{c}{d}$ can be checked with $ad = bc$ when $b \ne 0$ and $d \ne 0$.

Vocabulary

Integer

An integer is a whole number or its opposite, such as $-3$, $0$, or $8$.

Absolute Value

Absolute value is the distance a number is from $0$ on the number line.

Variable

A variable is a letter or symbol that represents an unknown or changing number.

Expression

An expression is a mathematical phrase with numbers, variables, and operations but no equals sign.

Equation

An equation is a statement that two expressions are equal, such as $2x + 3 = 11$.

Ratio

A ratio compares two quantities by division, such as $\frac{3}{5}$ or $3:5$.