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 term can be a number, a variable, or a number and variable combined by multiplication or division.
Some examples of terms are:
x, 8, 4y,
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:
Expression
Number of Terms
Description
6x
1
A number multiplied by a variable. The number is always written first followed by the variable(s).
3w – 8
2
Terms separated by –
7b + 5t – 6
3
Terms separated by + and –
1
All multiplication and division, no + or – symbol
Example:
Determine the number of terms in the following expressions:
a) 5xyz
b) 3x + 2y – 2x + 6
Solution:
a) 5xyz has one term
b) 3x + 2y – 2x + 6 has four terms
Coefficients Of Algebraic Terms
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)
Videos
Algebraic expressions -
Professor Edward Burger explains algebraic expressions