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

 

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$5, plus, 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 $x$x"

can be written as the algebraic expression

$x+ 3$x, plus, 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	$x + 3$x, plus, 3
Subtraction	Subtracted, minus, difference, less than, decreased by	$p - 6$p, minus, 6
Multiplication	Times, product	$8k$8, k
Division	Divided, quotient	$a \div 9$a, divided by, 9

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

"the product of eight and $k$k"

can be written as

$8k$8, k.

Let's take a look at a trickier example

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

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

So, the expression is $m - 7$m, minus, 7.

[Hide explanation.]

The word decreased is used, which means we should subtract, but we still need to be careful about which order to put the numbers in.

For example, "$m$m decreased by seven" tells us to start at $m$m and decrease by seven which can be written as the expression $m - 7$m, minus, 7.

On the other hand, the expression $7 - m$7, minus, m is "seven decreased by $m$m".