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Writing expressions

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
"2 more than 5"
can be written as the expression
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,
"3 more than x"
can be written as the algebraic expression
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+3
Subtractionsubtracted, minus, difference, less than, decreased byp6
Multiplicationtimes, product8k
Divisiondivided, quotienta÷9
For example, the word "product" tells us to use multiplication. So, the phrase
"the product of 8 and k"
can be written as

Let's take a look at a trickier example

Write an expression for "m decreased by 7".
Notice that the phrase "decreased by" tells us to use subtraction.
So the expression is m7.

Let's try some practice problems!

Basic expressions

Write an expression for "y more than 7".

Write an expression for "6 minus b".

Write an expression for "x divided by 9".

Write an expression for "2 multiplied by t".

Write an expression for "the sum of a and 4".

More complicated expressions

Write an expression for "8 less than the product of 7 and x".

Write an expression for "the sum of 6 and the product of 3 and d".

Word problems

Daniel makes 100 dollars each week. He worked for x weeks this summer.
How much money did Daniel make this summer?
Write your answer as an expression.

Sebastian has 12 more trophies than Megan. Megan has t trophies.
How many trophies does Sebastian have?
Write your answer as an expression.

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