Learn to write algebraic expressions in and out of word problems.

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

Sometimes in math we describe an expression with a phrase. For example, the phrase
"22 more than 55"
can be written as the expression
2+52 + 5.
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,
"33 more than xx"
can be written as the algebraic expression
x+3x+ 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:
OperationWordsExample algebraic expression
Additionplus, sum, more than, increased byx+3x + 3
Subtractionsubtracted, minus, difference, less than, decreased byp6p - 6
Multiplicationtimes, product8k8k
Divisiondivided, quotienta÷9a \div 9
For example, the word "product" tells us to use multiplication. So, the phrase
"the product of 88 and kk"
can be written as
8k8k.

Let's take a look at a trickier example

Write an expression for "mm decreased by 77".
Notice that the phrase "decreased by" tells us to use subtraction.
So the expression is m7m - 7.

Let's try some practice problems!

Basic expressions

More complicated expressions

Word problems