Related Pages
Combining Like Terms
Adding And Subtracting Algebraic Expressions
Solving Equations
More Algebra Lessons
In these lessons, we will learn what are meant by variables, constants, terms, expressions and coefficients are in Algebra.
An algebraic expression is a combination of variables, constants, and algebraic operations (such as addition, subtraction, multiplication, division, and exponentiation with rational exponents). It does not contain an equals sign (=).
The following diagrams give two examples of algebraic expressions. Scroll down the page for more examples.
Printable & Online Algebra Worksheets
In mathematics, often the value of a certain number may be unknown. A
variable is a symbol, usually a letter, which is used to
represent an unknown number.
Some examples of variables are:
x, a, t, y, b
A constant is a fixed numerical value (e.g., 2, -5, \( \frac{1}{3}, \pi \).
A term can be a constant, a variable, or a product of constants and variables raised to powers. These are the individual parts of an algebraic expression separated by addition or subtraction.
Some examples of terms are:
\( x, 8, 4y, \frac{t}{2} \)
An expression can be term or a collection of terms separated by addition or subtraction operators. Some examples of expressions, with the numbers of terms, are listed below:
Example:
Determine the number of terms in the following expressions:
a) 5xyz
b) 3x + 2y – 2x + 6
Solution:
a) 5xyz has one term
The number (positive or negative) in the algebraic term is called the coefficient.
For example:
For the term 4x, 4 is the coefficient.
For the term –7y, –7 is the coefficient.
The coefficient of 1 in an algebraic term is usually not written.
For example:
1y can be written as simply y. So, 1y and y are the same.
Example:
Find the coefficient and variable of each of the following terms:
a) 0.2m
b) –3p
c) q
d) z
e)
Solution:
a) 0.2m (The coefficient is 0.2 and the variable is m)
b) –3p (The coefficient is –3 and the variable is p)
c) q (The coefficient is
and the variable is q)
d) z (The coefficient is 1 and the variable is z)
e) (The coefficient is
and the variable is x)
A presentation of the terms of an algebraic expression.
The number and types of terms are presented.
Constants, variables and numerical coefficients, terms and expressions are discussed.
This video shows the parts of an expression (terms, coefficients and variables) then explains about evaluating expressions using some examples.
What is a Term?
A term is any coefficient and its variable.
Identify the term in the expression:
4x - 2y + 5
Identify the coefficient and variable in the term:
7xy
Example:
Expressions are put into their simplest form so as not to be confusing or too complex. One way of simplifying expressions is to combine like terms. By combining terms we can shorten and simplify our expressions, making them easier to read. Like terms often contain the same variable or variables.
This video shows how to simplify algebraic expressions by using the distributive property and
combine like terms.
Example:
In this video, you’ll learn how to identify the parts of an expression in Algebra. You’ll learn about expressions, terms, coefficients, and more.
Try out our new and fun Fraction Concoction Game.
Add and subtract fractions to make exciting fraction concoctions following a recipe. There are four levels of difficulty: Easy, medium, hard and insane. Practice the basics of fraction addition and subtraction or challenge yourself with the insane level.
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