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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
2, plus, 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,
"3 more than x"
can be written as the algebraic expression
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:
OperationWordsExample algebraic expression
Additionplus, sum, more than, increased byx, plus, 3
Subtractionsubtracted, minus, difference, less than, decreased byp, minus, 6
Multiplicationtimes, product8, k
Divisiondivided, quotienta, divided by, 9
For example, the word "product" tells us to use multiplication. So, the phrase
"the product of 8 and k"
can be written as
8, k.

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 m, minus, 7.

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.

Want to join the conversation?

  • duskpin ultimate style avatar for user jennifer
    Why do you talk in this ducument that 3 more than x is x+3? It should be3+x
    (2 votes)
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  • leaf green style avatar for user David Bacon
    I have a problem with sentence problem like this:Write an expression for "
    8
    less than the product of
    7
    and
    x
    ". and I wrote 8-7x but they gave me wrong how I can answer that ?
    (2 votes)
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  • aqualine ultimate style avatar for user sicspi
    How do I solve this problem 8 squared
    (2 votes)
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  • blobby green style avatar for user asgal
    I have a weird problem, when I practiced on khan on subtraction with algebra it showed something like this p - 6 I use that example to do my subtraction problem on IXL but it said it was wrong I had to put the number then the letter.
    (1 vote)
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    • stelly blue style avatar for user Kim Seidel
      "p - 6" and "-6 + p" are equivalent and it shouldn't matter which term comes first. The commutative property of addition tells use the 2 expressions are identical. However, you may have been given some explicit directions in IXL that asked you to write the terms in a certain order. If you didn't follow their instructions, that could have caused it to be wrong.

      The other possibility is that you confused "p - 6" with "-6p". The first one is subtraction. The second one is multiplication. These are different.

      Hope this helps.
      (2 votes)
  • marcimus purple style avatar for user fatimakassim287
    These were some pretty easy questions. The problem is that its very confusing for which order I should put the problem in.
    (1 vote)
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  • primosaur tree style avatar for user britton.jet
    why are theas from like 4or5 years ago
    (1 vote)
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    • stelly blue style avatar for user Kim Seidel
      The site defaults to show you to top rated questions and answers. These are generally older because it takes time for votes to accumulate. They also might be very relevant to what you are looking for. If you want to see the more recent questions & answers, change the sort sequence to "recent".
      (1 vote)
  • primosaur tree style avatar for user britton.jet
    ok kim
    (1 vote)
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  • primosaur tree style avatar for user britton.jet
    im stuck
    (1 vote)
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  • male robot johnny style avatar for user kharris
    What is this? Is this in High School. I've got 3 years till High School
    (1 vote)
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  • aqualine ultimate style avatar for user Mmesoma Nwabuwa
    This stuff is pretty easy but i can never be too sure. That is why i'm going back to the basics of it to learn it again and improve my skills
    (1 vote)
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