Workplace Math and PLAR Prep
Introduction to Algebra
Algebraic Expression
An algebraic expression is a combination of numbers, variables, and operations.
Some examples are:
4 – 2t 3n + 1 2x – x2 + 4 2n t + (t – 1)
Some things to know about algebraic expressions:
When a number (coefficient) sits right next to a variable, you assume those values are multiplied. For example, 2n means two n’s; that is 2 multiplied by n. ( 2 x n)
Sometimes the coefficient 1 is not written. For example, in the expression x – 3, the coefficient of x is 1.
Algebraic expressions allow you to describe what to do with a number quickly.
Algebraic Equation
An algebraic equation is a statement where two expressions, at least one of which is an algebraic expression, have the same value.
There are 3 kinds of equations:
Ones where you figure out an unknown value
For example: 3n + 1 = 4 --> This means the value of n helps 3n + 1 equal 4.
3n + 1 = 2n + 5 -->This means the value of n is the same for 3n +1 and 2n +5
Ones which are always true
For example: 2t + t = 3t -->This means the equation shows two ways of saying the same thing. ( 2t = t is the same thing as 3t)
Ones describing relationships
For example: y = 2x + 3 -->There is a relationship between the two variables x and y and you can calculate y if you know x.
A = lw -->There is a relationship between the length (l), width(w) and area (A)of a rectangle.
Give these a try...
Match each algebraic expression, on the right, with an equivalent phrase in words.
a) five more than a number 5 – n
b) a number is multiplied by five and four is added 4 + t + 5
c) a number is multiplied by four and five is added n – 5
d) four more than a number and then five more 4n + 5
e) a number is subtracted from five n + 5
f) five less than a number 5n+4
You can check your answers by clicking on the arrow here---------->
a) n+5
b) 5n+4
c) 4n+5
d) 4+t+5
e) 5-n
f) n-5
Now see if you can right your own algebraic expressions using these clues:
Write an equation to describe each situation.
a) Three more than a number is equal to eighteen.
b) Four more than double a number is equal to three times the same number.
c) One number is always double another.
d) If a number is subtracted from 10, the result is four times the original number.
You can check your answers by clicking on the arrow here---------->
a) 3 + m = 18
b) 4 + 2m = 3m
c) d = 2n
d) 10 – n = 4n