# Why do we have math if we can describe things in words?

Algebraic expressions are useful because they represent the value of an expression for all of the values a variable can take on.

Sometimes in math, we describe an expression with a phrase. For example, the phrase

"two more than five"

can be written as the expression

$5+2$.

Similarly, when we describe an expression in words that includes a variable, we're describing an algebraic expression, an expression with a variable.

For example,

"three more than $x$"

can be written as the algebraic expression

$x+ 3$.

But why? Why use math if we can describe things in words? One of the many reasons is that math is more precise and easier to work with than words are. This is a question you should keep thinking about as we dig deeper into algebra.

# Different words for addition, subtraction, multiplication, and division

Here is a table that summarizes common words for each operation:

Operation | Words | Example algebraic expression |
---|---|---|

Addition | Plus, sum, more than, increased by | $x + 3$ |

Subtraction | Subtracted, minus, difference, less than, decreased by | $p - 6$ |

Multiplication | Times, product | $8k$ |

Division | Divided, quotient | $a \div 9$ |

For example, the word product tells us to use multiplication. So, the phrase

"the product of eight and $k$"

can be written as

$8k$.

# Let's take a look at a trickier example

**Write an expression for "$m$ decreased by seven".**

Notice that the phrase "decreased by" tells us to use subtraction.

So, the expression is $m - 7$.