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Distributive property explained

The distributive property tells us how to solve expressions in the form of a(b + c).  The distributive property is sometimes called the distributive law of multiplication and division.
Normally when we see an expression like this …
distributive property format
we just evaluate what’s in the parentheses first, then solve it:
distributive property in practice
This is following the official “order of operations” rule that we’ve learned in the past.
With the distributive property, we multiply the ‘4’ first:
distributing values
We distribute the 4 to the 8, then to the 3.
Then we need to remember to multiply first, before doing the addition!
We got the same answer, 44, with both approaches!
Why did we do it differently when we could have easily worked out what was in the brackets first? 
This is preparation for when we have variables instead of numbers inside the parentheses.
Another example before we start to use variables:
Example of the distributive property using variables:
More examples
  • We usually use the distributive property because the two terms inside the parentheses can’t be added because they’re not like terms
  • Make sure you apply the outside number to all of the terms inside the parentheses/brackets
Try our stack of practice questions with useful hints and answers! Like this one:

Want to join the conversation?

  • male robot johnny style avatar for user youngtiaffay
    Can the distributive property work if there is multiplication or division inside the parentheses? Like in 9(3/3)?
    (37 votes)
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  • starky seedling style avatar for user Tyler Robles
    What if you have two parentheses? Such as (3x6) - (3x3)
    (12 votes)
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  • starky seed style avatar for user fraser-thiede, nicole
    why is this important for me to know in life
    (9 votes)
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    • blobby green style avatar for user Jessika Cavett
      i honestly think its for jobs that have to do with math, like welding and being a mechanic there are plenty of jobs that take complex equation's even animation it takes over hundreds of frames to even get a small clip think of how much algebra you'd have to do
      (5 votes)
  • duskpin seedling style avatar for user Cadence-Chan
    Im confused..... What does the 2 in example c mean? Does it mean to divide 12 by the answer of 5+2 by 2? Because that would be logical if it does.😊
    (6 votes)
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  • blobby green style avatar for user destinymabe
    In example c, what does the underneath 5+7 represent?
    (6 votes)
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    • duskpin ultimate style avatar for user GeekGamerGirl
      I think you may be talking about example b, in which there is a sort of wiggly line with a downward facing peak in the middle. This is just a symbol Sal uses to indicate a particular part of an expression. I'm not sure of its name, but does it look kind of like this } but lying flat on the ground?
      (3 votes)
  • primosaur seedling style avatar for user Uriel Velazquez
    What if the expression does not have a operation inside?
    Example: 18(26)
    (2 votes)
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  • female robot amelia style avatar for user Katelyn
    Why do you use a parenthesis instead of a multiplication symbol?
    (5 votes)
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  • blobby green style avatar for user kasandrajennings77
    What if the format is this
    (2 votes)
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    • stelly blue style avatar for user Kim Seidel
      Distribute the 1/2
      2a (1/2) -6b (1/2) + 8 (1/2)
      It may be easier if you change the other numbers into fractions.
      2a/1 (1/2) -6b/1 (1/2) + 8/1 (1/2)
      Finish the multiplication of each fraction pair and reduce them.
      For example: 2a/1 (1/2) = 2a/2 = a
      I'll let you finish the rest.
      Hope this helps.
      (5 votes)
  • blobby green style avatar for user wowjohnwow
    My concern was a viral math problem on social media, that seems to have really perplexed those who are familiar with distribution. 6 / 2(1+2).
    Should a person distribute, you are left with:
    6 / 2(1+2)
    6 / 2 + 4
    6 / 6
    answer would be 1
    However when done parenthesis first,
    6 / 2(1+2)
    6 / 2(3)
    * 6 / 2 * 3
    3 * 3
    answer in this case being 9
    I know you stated distribution is utilized when solving variables, however based on your two examples whether a person distributes or not, you would get the same answer. However this viral question online has posed an interesting dilemma here.
    One of two things, either distribution is strictly for algebra when solving variables, or US standardized testing isn't teaching our students this properly and the lines between the two are very blurred (Perhaps schools aren't keeping AMS books up to date, or schools don't care because the education system is simply regurgitating said provided information verbatim for a good grade). The process mathematically is not clearly being taught simultaneous across the American board, and it explains where something that should be so simple is almost fist fight debatable..... What's happening here, please help.
    (3 votes)
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    • mr pink green style avatar for user David Severin
      that just shows that trying to write an ambiguous problem will be an issue - people are purposefully being vague for the sake of confusion and debate on the internet. If you wrote it correctly either way, there would be no doubt about which of the two answers should be. So there is a big difference between 6/2*(1+2) which multiplies 6/2 times the sum of 1 and 2 and 6/(2(1+2)) which clearly puts all of the stuff in the denominator of the problem. If you see it in traditional fraction form (a vertical line with a numerator and denominator) it would be clear which one is meant rather than using a / for divide.
      (3 votes)
  • male robot donald style avatar for user ᴀɴᴅʀᴇɪɴɪ ᴅɪ𝐬ʜᴀʀᴛ, ʙʀᴀʏᴅᴇɴ✔️
    Here is the question Use the distrubitive property to rewrite this product below in two different ways. Simplify your anwsers. Should they still be equal? Why?


    (4 votes)
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