Learn to write expressions for phrases like "3 more than x."

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+25+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 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 eight and kk"
can be written as
8k8k.

Let's take a look at a trickier example

Write an expression for "mm decreased by seven".
Notice that the phrase "decreased by" tells us to use subtraction.
So, the expression is m7m - 7.
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, "mm decreased by seven" tells us to start at mm and decrease by seven which can be written as the expression m7m - 7.
On the other hand, the expression 7m7 - m is "seven decreased by mm".

Let's try some practice problems!

Question 1
Write an expression for "yy more than seven".