Mathematics Terminology Study Guide for McGraw-Hill's Firefighter Exams

Many firefighter exams include mathematical problems pertaining to the job of firefighting. Knowledge of basic arithmetic, algebra, and geometry is necessary in the fire service. Measuring gas/oil mixtures that fuel portable power saws, mixing cleaning fluids with water during maintenance chores, determining the placement of a ladder for proper climbing angle, and monitoring gallons per minute (GPM) flowing through hose lines are just a few examples of how firefighters use numbers. The mathematics selected for this review includes the most common areas included in previous firefighter examinations.

Basic Terminology, Symbols, and Order of Operations

Terminology (The Language of Mathematics)

There are many terms used in mathematics that you should understand. A list of some of the more common terms and their definitions follows:

Real Numbers: both rational and irrational numbers.

Whole Numbers: the counting numbers that include zero.

Example: 0, 1, 2, 3, ...

Natural (Positive) Numbers: all whole (counting) numbers greater than zero.

Example: 1, 2, 3, 4, …

Negative Numbers: all numbers less than zero.

Example: -1,-2,-3, …

Integers: all positive and negative whole numbers, including zero, but not including fractions and decimals.

Example: -2,-1, 0, 1, 2, …

Fraction: part of a whole number.

Example:

Mixed Number: a whole number and a fraction.

Example:

Rational Numbers: all numbers that can be expressed as the ratio of two integers (fractions and integers).

Example:x/y where xand y are integers

Irrational Numbers: all numbers that cannot be expressed as the ratio of two integers.

Example: π (3.14) and many square roots, etc.

Term: a single number or the product of one or more numerical (number) coefficient and/or literal (letter) coefficient factors. Like terms have the same literal factor. Unlike terms do not have a common literal factor.

Example: (like terms): 2a and 3a.

Example: (unlike terms): 6, 3x, and yz

Factor: an individual number (numerical) or letter (literal) in a term.

Example: 2, A, and b are factors of the term 2ab

Algebraic Expression: two or more terms connected by plus or minus signs.

Example: 4k + 7

Algebraic Equation: a statement representing two things that are equal to one another.

Example: 12x – 8x = 4x