2.1 Use the language of algebra  (Page 3/8)

Grouping symbols in algebra are much like the commas, colons, and other punctuation marks in written language. They indicate which expressions are to be kept together and separate from other expressions. [link] lists three of the most commonly used grouping symbols in algebra.

Here are some examples of expressions that include grouping symbols. We will simplify expressions like these later in this section.

Identify expressions and equations

What is the difference in English between a phrase and a sentence? A phrase expresses a single thought that is incomplete by itself, but a sentence makes a complete statement. “Running very fast” is a phrase, but “The football player was running very fast” is a sentence. A sentence has a subject and a verb.

In algebra, we have expressions and equations . An expression is like a phrase. Here are some examples of expressions and how they relate to word phrases:

Notice that the phrases do not form a complete sentence because the phrase does not have a verb. An equation    is two expressions linked with an equal sign. When you read the words the symbols represent in an equation, you have a complete sentence in English. The equal sign gives the verb. Here are some examples of equations:

Simplify expressions with exponents

To simplify a numerical expression means to do all the math possible. For example, to simplify $4·2+1$ we’d first multiply $4·2$ to get $8$ and then add the $1$ to get $9.$ A good habit to develop is to work down the page, writing each step of the process below the previous step. The example just described would look like this:

Suppose we have the expression $2·2·2·2·2·2·2·2·2.$ We could write this more compactly using exponential notation. Exponential notation is used in algebra to represent a quantity multiplied by itself several times. We write $2·2·2$ as $2^3$ and $2·2·2·2·2·2·2·2·2$ as $2^9.$ In expressions such as $2^3,$ the $2$ is called the base and the $3$ is called the exponent. The exponent tells us how many factors of the base we have to multiply.