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Distributive property over subtraction

Learn how to apply the distributive property of multiplication over subtraction and why it works. This is sometimes just called the distributive property or distributive law. Created by Sal Khan and Monterey Institute for Technology and Education.

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  • winston baby style avatar for user Khan Artist
    What's the purpose of the distributive property if you just evaluate the same answer?
    (41 votes)
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  • aqualine ultimate style avatar for user edwardduong21
    why should i use this law if the other procedure is faster and easier? is it commonly used in algebra in the future? I'm sorry just a Grade 8 Canadian boy.
    (16 votes)
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  • piceratops ultimate style avatar for user poopshady
    whats the definition of distributive,associative,and commutative?
    (9 votes)
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  • blobby green style avatar for user Jackson Enerson
    this has taught me as much as my math teacher, nothing.
    (8 votes)
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  • starky sapling style avatar for user Nebula
    How would I use this in real life?
    (11 votes)
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  • purple pi purple style avatar for user Emily Hur
    For example, in this problem:
    4(8+3), using distributive property, would you write: (4 * 8) + (4 * 3), or 32+12
    ?
    (7 votes)
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  • winston baby style avatar for user Bella
    Um i am having a lot of trouble with the "Distributive Law"
    and my brain is going haywire. i can't seem to collect my thoughts.
    If anyone thinks they can made it somewhat clearer i would appreciate it.
    (6 votes)
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    • duskpin ultimate style avatar for user ✟lilac pineapple✟
      Hello, sorry if this is too late to answer.

      The 'Distributive Law', or as some call it, 'Distributive Property', is where you find the GCF, or G reatest C ommon F actor of two numbers in an equation or expression. Take, for example, 27x x 99y

      27x x 99y - Both numbers share a factor or 9. This is the GCF

      3x x 11y - This is the equation after dividing both numbers by the GCF

      9(3x x 11y) - This is the finished expression. Some people choose to put a multiplication sign after the 9 {9x(3x x 11y)}, but it is okay to leave the multiplication sign out.

      Thank you for your time and have a nice day! :)
      (8 votes)
  • mr pink red style avatar for user baileyvines1
    When using the distributive property on a problem like 2(4+b), would your answer be 8+2b or would it be 6b?
    (6 votes)
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    • leafers tree style avatar for user Peter S. ^^'
      The correct way of applying the distributive property, would be multiplying each item in the brackets (4 + b) by the number preceding these parentheses: 2 ( ).

      2 * 4 + 2 * b
      = 8 + 2b

      ...aaand we need to leave + 2b like this, since it's a variable.

      So yes, your first assumption was indeed correct! ('^_^) /
      Try applying this a few times and you'll get it in no time !
      ( in fact, I think my answer must already be late
      :p )
      (8 votes)
  • piceratops seed style avatar for user jbroadhurst
    Why when using the distributive law we have to multiply vs any of the other concepts? I mean, I know it's statistically correct but why? :)
    (9 votes)
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    • leaf green style avatar for user weroarforareason
      The reason we multiply in the distributive law instead of using other operations is due to the hierarchical nature of mathematical operations, often remembered by the acronym PEMDAS (Parentheses, Exponents, Multiplication and Division, Addition and Subtraction). Multiplication and division are one level above addition and subtraction. This hierarchy is why you can distribute a multiply or divide over an add or subtract.

      For example, consider the expression 7 * (x + y). According to the distributive law, this can be rewritten as 7 * x + 7 * y3. Here, the multiplication operation (represented by *) is distributed over the addition operation (represented by +), resulting in two separate terms.

      The distributive law is particularly useful when dealing with expressions that contain variables1. For instance, if you have an expression like 5 * (x + 3), you can’t simplify the terms inside the parentheses because they’re not like terms1. By applying the distributive law, you can simplify this expression to 5 * x + 5 * 3, or 5x + 15.

      In conclusion, the distributive law is a fundamental property of numbers that allows us to simplify and solve mathematical expressions. It’s an essential tool in algebra and other areas of mathematics.
      (2 votes)
  • marcimus purple style avatar for user Camille
    What happens if I don't know a number?
    (6 votes)
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    • leaf green style avatar for user dmpuni
      Credit where credit is due, this comment is from Bellaart. If you don't know a number, it's the same as having a 'variable' (calling that variable or 'unknown number' for p in this case).

      "if you are solving the problem and there is a variable with nothing to be substituted with then you would solve the problem with variable. EXAMPLE: 5(p + 3) [nothing is substituted for the variable because they don't tell you to and the directions say to use the distributive law or property] it becomes: 5 * p + 5*3 { * will stand for multiplication} then 5p + 15. so the answer is 5p+ 15" - Bellaart
      (7 votes)

Video transcript

Rewrite the expression five times 9 minus 4-- that's in parentheses-- using the distributive law of multiplication over subtraction. Then simplify. So let me just rewrite it. This is going to be 5 times 9 minus 4, just like that. Now, if we want to use the distributive property, well, you don't have to. You could just evaluate 9 minus 4 and then multiply that times 5. But if you want to use the distributive property, you distribute the 5. You multiply the 5 times the 9 and the 4, so you end up with 5 times 9 minus 5 times 4. Notice, we distributed the 5. We multiplied it times both the 9 and the 4. In the first distributive property video, we gave you an idea of why you have to distribute the 5, why it makes sense, why you don't just multiply it by the 9. And we're going to verify that it gives us the same answer as if we just evaluated the 9 minus 4 first. But anyway, what are these things? So 5 times 9, that is 45. So we have 45 minus-- what's 5 times 4? Well, that's 20. 45 minus 20, and that is equal to 25, so this is using the distributive property right here. If we didn't want to use the distributive property, if we just wanted to evaluate what's in the parentheses first, we would have gotten-- let's go in this direction-- 5 times-- what's 9 minus 4? 9 minus 4 is 5. Let me do that in a different color. 5 times 9 minus 4. So it's 5 times 5. 5 times 5 is just 25, so we get the same answer either way. This is using the distributive law of multiplication over subtraction, usually just referred to as the distributive property. This is evaluating the inside of the parentheses first and then multiplying by 5.