Monomial is a polynomial expression with one term. It is the most basic unit of polynomials which is quite frequently used in everyday life like in business, finance, accounts, and management. For instance, to determine the average sales of a whole year a supervisor may use a monomial 12X where X represents average sales in a month. Similarly, other polynomials can be applied to figure out overhead costs, wages, payroll taxes, etc. The other types of polynomials are binomials, trinomials, and so on.
Mono means one, and a monomial is a polynomial with exactly one term. It is an algebraic expression that contains only variables and a coefficient. It does not include the addition or subtraction of terms. It contains only numbers and letters related through multiplication and the exponents of the letters as natural numbers. For example, 4x; this expression has only one term. The degree of a monomial is the sum of the degrees of its variables.
Learning to solve monomials is extremely important as it forms the basic understanding of solving polynomial expressions. The application of these vital skills is found in various math topics and real-life situations. KIds mostly learn the concept of polynomials in 5th or 6th grade where they have to solve polynomials with higher degrees. Lacking the basic understanding of solving monomials sometimes results in failure. Pre-algebra worksheets and games are quite helpful for kids to form a base for later algebra studies These resources for primary grades like 1st and 2nd grade math worksheets help young kids to attain critical thinking and problem-solving skills for advanced math learning.
Parts of a Monomial
Basic knowledge about parts of a monomial will enable you to simplify them by determining their degree or coefficient. A monomial has three parts, a coefficient, a literal part, and a degree. All these parts are explained below in detail:
Coefficient: It is the number part of the monomials to which the letters are multiplied. In other words, when any constant is multiplied by the variable, it becomes a coefficient.
Examples of coefficients: 2x means 2 times x. In this expression, x is a variable, and 7 is a coefficient. 9 y ^2 means 9 times y square. In this expression, y is a variable, and 9 is a coefficient.
Degree: The degree of a monomial is the sum of the exponents of the letters or variables. For example, the degree of 4 x ^2 y ^3 is 5. The constant has a degree equal to one.
Literal Part: The literal part is constituted by the letters displayed in the monomial with exponents. Exponents are also known as powers of the variables. For example, the exponent of x ^ 2 is two and the exponent of y ^ 3 is three.
To understand this in detail let’s consider an expression: 9x^2 y.
- In this monomial, ‘x’ and ‘y’ are the variables with exponents 2 and 1. So the degree of this monomial is ‘3’.
- A variable with no visible exponent like y is assumed to have an exponent of 1.
- The coefficient is ‘9’ and the literal part is x ^2 y.
What are two similar monomials?
Two monomials are said to be similar if they both have exactly the same literal part. For example, 2xy^2 and xy^2 have the same literal part and can be added or subtracted from each other. Two similar monomials can be simplified by applying arithmetic operations such as addition, subtraction, multiplication, and division on them.
Simplifying monomials follows a sequence of operations involving rules for handling exponents, multiplying, and dividing. Learning this requires a basic understanding of monomials and rules to simplify them. Here are some rules to simplify monomials:
- The power of a power rule says that when evaluating the power of a power, multiply the exponents of base variables.
- The multiply monomials rule says that when you multiply monomial expressions, add the exponents of like bases.
- The dividing monomials rule says that when you divide monomials, subtract the exponents of like bases.