The quickest route to learning a subject is through a solid grounding in the basics. So what you won’t find in *Easy Mathematics Step-by-Step* is a lot of endless drills.

Instead, you get a clear explanation that breaks down complex concepts into easy-to-understand steps, followed by highly focused exercises that are linked to core skills—enabling learners to grasp when and how to apply those techniques.

• Large step-by-step charts breaking down each step within a process and showing clear connections between topics and annotations to clarify difficulties;

• Stay-in-step panels show how to cope with variations to the core steps;

• Step-it-up exercises link practice to the core steps already presented;

• Missteps and stumbles highlight common errors to avoid.

1. Check whether meets the criteria for a monomial. is a constant, so it is a monomial. Step 1. Check whether meets the criteria for a monomial. contains a negative exponent, so it is not a monomial. Step 1. Check whether meets the criteria for a monomial. is a term, but it contains a variable as the radicand of a simplified radical, so it is not a monomial. The constants in monomials can be divisors, have negative exponents, or be radicands in a radical. For instance, is a monomial.

Polynomials A polynomial is a single monomial or a sum of monomials. A polynomial that has exactly one term is a monomial. A polynomial that has exactly two terms is a binomial. A polynomial that has exactly three terms is a trinomial. A polynomial that has more than three terms is just a general polynomial. Problem State the most specific name for the given polynomial. Solution Step 1. Count the terms of the polynomial. has exactly two terms. Step 2. State the specific name. is a

A right triangle has exactly one right angle. An obtuse triangle has exactly one obtuse angle. Because the sum of the angles of a triangle is 180°, the other two angles of an obtuse triangle are acute angles. Problem Name the triangle according to its angles. Solution Step 1. Describe the angles of the triangle. All three angles of the triangle are acute. Step 2. Name the triangle according to its angles. The triangle has three acute angles, so the triangle is an acute triangle.

Count the “leaves” at the base of the diagram to determine the number of possible ways to select one cap and one pair of tennis shoes. Step 4. State the answer. There are 12 leaves, so there are 12 possible ways to select one cap and one pair of tennis shoes. Notice in the tree diagram that each leaf represents a choice. For instance, the first leaf represents the choice of selecting a blue cap and black tennis shoes. This choice is different from the choice represented by the fourth leaf,

12–13, 47–52 associative property of, 11 closure property of, 10 commutative property of, 11, 14, 100, 159 of decimals, 67–68 in denominator, 55–61, 64, 68, 123 distributive property, 12–13 in dividend, 68 division and, 13, 47–49, 60–61 exponential notation for, 35–43 of fractions, 14, 60, 64 of mixed numbers, 64 of negative numbers, 28–31, 111 in numerator about, 60 in algebraic expressions, 123–124 cancellation law for, 55–56, 59 for decimals, 68 for division, 60–61 for mixed