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Welcome to our Math lesson on What are (Algebraic) Expressions, this is the first lesson of our suite of math lessons covering the topic of The Meaning of Expressions. Simplifying Expressions, you can find links to the other lessons within this tutorial and access additional Math learning resources below this lesson.
In the first chapter of this course - more specifically, in tutorial 1.4 - we explained the meaning of arithmetic expressions, which consists of several numbers combined through a series of basic operations (including raising in a power) that eventually (after making all the necessary operations) result in a single numerical value.
For example,
is an arithmetic expression as when using the PEMDAS (or BEDMAS) rule to make the operations, we obtain
i.e. a single number that is equivalent to the value of the original expression.
On the other hand, there are other types of expressions that contain not only numbers but they also include certain letters. Obviously, such letters are used to replace numbers that may be known or not. Such expressions are known as "algebraic expressions".
By definition, algebraic expressions are those expressions in which numbers are expressed using letters or alphabets without specifying their actual values.
In scientific terminology, the letters that are used to substitute numbers are known as 'variables' as their value may vary depending on the conditions presented in the exercise.
Algebraic expressions are different from equations (which we explain in more specific detail in chapter 9) as unlike in equations, in algebraic expressions all terms are written on the same side without any equal symbol ( = ) in-between.
Obviously, if the expression contains at least one letter (variable), it is classified as algebraic, not arithmetic. For example,
are all algebraic expressions, as they contain at least one letter alongside numbers.
Remark! You will often see a letter written directly after a number, or two letters one after another without any operation symbol in-between. In such cases, we will assume the corresponding operation as multiplication. For example, 3ab is equivalent to 3·a·b (3 × a × b); -4mn is equivalent to -4·m·n (-4 × m × n), etc. This occurs only in multiplication; other operations need to have their corresponding symbol clearly written in the expression.
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