A Beginning Look at Basic Algebra – Lesson 1
by Elaine Ernst Schneider
Objective(s): By the end of this lesson the student will be able to:
Define these terms: variable; algebraic expression; signs of operation; order of operations.
Algebra provides the basics for all higher math. You will work with numbers and letters (variables) to form sentences (expressions) that you can solve. The best way to learn math is by practicing it, so each lesson will include exercises using the skills learned.
A place to begin:
Letters in math are called variables. They can stand for different numbers at different times.
A mathematical sentence is called an expression. It can include numbers, variables, signs of operation, and symbols of inclusion.
Signs of operation tell you what to do to the sentence. The four operations are addition, subtraction, multiplication, and division.
Symbols of inclusion are parentheses ( ) and brackets [ ].
An important caution:
Be very neat in your calculations. Many an algebra problem is missed because the student misread what he or she had written or did not “line up” the column correctly for subtraction or division. Always double check operations. You don’t want to miss a problem because you added incorrectly.
Let’s Get Started:
To “evaluate” an expression means to find its value, or to solve it. The first rule to learn about algebra is “what to do when.” The order in which an expression’s operations are done can completely change the answer.
When evaluating an algebraic expression, first look for the symbols which show the innermost work. That can be expressed by use of parentheses or brackets. If BOTH parentheses and brackets are present, the parentheses are usually the innermost and should be worked first.
Here is an example:
24 + [46 – (2 X 11)]
24 + [46 – 22]
24 + 24
Now it’s time for you to try a few.
9 – (4 X 2)
(9 – 4) X 2
(9 – 4) X (2 X 1)
48 – [42 – (3 X 9)]
63 – [8/2 + (14 – 10)]
(Note: 8/2 is the same as 8 divided by 2, just like in fractions.)
[800/ (200 X 4)]
28 + [ 10 – (4 + 2) ]
(11-5) X (10 + 14)
125 / ( 5 X 5) (Remember from number 5? / = divided by.)
[28 – (4 X 5)] – 4