If you're seeing this message, it means we're having trouble loading external resources on our website.

If you're behind a web filter, please make sure that the domains *.kastatic.org and *.kasandbox.org are unblocked.

Main content

Writing basic expressions with variables

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, 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"
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 eight and k"
can be written as
8, k.

Let's take a look at a trickier example

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

Let's try some practice problems!

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

Want to join the conversation?

  • starky seedling style avatar for user ~panda boy jickle~
    why does the square over the square mean divided? Why cant we have an actual division sign?
    (56 votes)
    Default Khan Academy avatar avatar for user
    • duskpin tree style avatar for user Nicholas
      That is a common way to represent division in algebra, the division sign is not really used there. Have you noticed that the division sign is a fraction line with two dots representing the numerator and denominator? It evolved from the fraction idea to make it a simpler concept in arithmetic.
      (48 votes)
  • piceratops seed style avatar for user jacob_tolle
    How could algebraic expression be used in everyday life?
    (42 votes)
    Default Khan Academy avatar avatar for user
    • primosaur ultimate style avatar for user E
      That's a great question! There are lots of different ways algebraic expressions are used in everyday life. For instance: computer programming/computer science. Take a look at the CS tutorials on Khan Academy and you'll see what I mean. Also, Algebra is a useful, logical way to help explain things. Just the other day my mom used math to help teach a group of girls how to make a beaded ring. You can even use algebraic expressions to provide situations, like when giving the rules to a game.
      Hopefully this helped, and you'll look into the hundreds of other ways that algebraic expressions are used every day.
      (59 votes)
  • marcimus pink style avatar for user Olivia S.
    Can their be more than 1 variable like 3xp
    (19 votes)
    Default Khan Academy avatar avatar for user
  • duskpin ultimate style avatar for user Michelle Hoeks
    So I’ve got a math question but can’t understand the second part.
    Here’s the problem, I’ve got the first half figured out.

    If the sum of twice a number and -7 is increased by 8, the result is 16 greater than the opposite of the number. What is the number?
    ( how do I write 16 greater than?)
    (5 votes)
    Default Khan Academy avatar avatar for user
    • duskpin ultimate style avatar for user SherlockHolmes.42
      Saying that n is the number:
      - Come up with a formula.
      2n + (-7) + 8 = -n + 16
      - 16 greater than the opposite of the number is the same as saying -n (opposite of number) + 16 (16 greater than). Tip: When someone says "greater than" they are typically talking about addition, and when someone says "less than" they are typically talking about subtraction.
      - Next, simplify.
      2n + 1 = -n + 16
      - Subtract 1 and add n to both sides.
      2n + n = 16 - 1
      - Simplify.
      3n = 15
      - Divide both sides by 3.
      n = 5 <-- answer!

      I hope this answer helps you out, and have a great day!
      (10 votes)
  • mr pink red style avatar for user BoQuizard:📚🧙
    Is't 'of' a multiplication word?
    (4 votes)
    Default Khan Academy avatar avatar for user
  • blobby green style avatar for user 403824
    why is fraction considered as a division?
    (6 votes)
    Default Khan Academy avatar avatar for user
    • blobby green style avatar for user Archer8888
      I like to think of fractions as segments of a pie or cake. Lets say you & I split (divide) a cake, we take the 1 whole cake & slice it down the middle. On the plate is still 1 whole cake or we could say there are two halves (2/2), if we divide 2 by 2 we get 1 or a whole cake (2/2). You take your half (1/2), now I have one half (1/2). If we divide 1 by 2 (1/2) we get 0.5 or a half! Hope that helps!
      (3 votes)
  • blobby green style avatar for user andrea
    So we had an expression about division, and it's usually not as sweet and straightforward with obvious words like these. My questions is, what are other ways to say 'divided by' and can you give me examples?
    (5 votes)
    Default Khan Academy avatar avatar for user
    • piceratops ultimate style avatar for user Davis
      You can say 'divided by' like this:
      /,
      The division sign,
      and in fraction form.

      Unfortunately, you can't really do the division sign or fraction form on a computer, so you have to stick to the /.
      (4 votes)
  • blobby green style avatar for user Da'shyne Green
    There should be a timer to see if you know it and you can do it fast enough.
    (4 votes)
    Default Khan Academy avatar avatar for user
  • leafers sapling style avatar for user Scyth Of Jewel
    why dose p+p-p+p+p work in the answers but some thing like 2 1/2 not work
    (3 votes)
    Default Khan Academy avatar avatar for user
  • winston baby style avatar for user LayLay12
    when it said six minus b it said b-6 is wrong which is not true because b can be bigger than six thats why im asking someone to fix it
    (2 votes)
    Default Khan Academy avatar avatar for user