What's the purpose of the distributive property if you just evaluate the same answer?

its a another way to do it. it could be easy or hard depending

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.

Actually, this is an easier and faster way. You'll find this helpful later in life.

whats the definition of distributive,associative,and commutative?

PEMDAS tells us what order we can do certain math operations in - Parentheses, Exponents, Multiplication/Division, and Addition/Subtraction: 5(2+3)=5(5)=25 In this case, PEMDAS was sufficient. But we're not always dealing with numbers, as we see below: 5x(2x+3)=?

this has taught me as much as my math teacher, nothing.

dang that's depressing but true tho lol

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.

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! :)

What happens if I don't know a number?

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

For example, in this problem: 4(8+3), using distributive property, would you write: (4 * 8) + (4 * 3), or 32+12 ?

do 4x8=32 then 4x3=12, and finally, add 32 plus 12 which is 44. :)

When using the distributive property on a problem like 2(4+b), would your answer be 8+2b or would it be 6b?

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 )

Main content

Course: 6th grade foundations (Eureka Math/EngageNY) > Unit 4

Lesson 1: Topic A & D: Foundations

Distributive property over subtraction

Name: Distributive property over subtraction
Uploaded: 2011-02-20T16:39:05Z
Description: 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.

Google Classroom

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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Khan Artist
Posted 9 years ago. Direct link to Khan Artist's post “What's the purpose of the...”
What's the purpose of the distributive property if you just evaluate the same answer?
Button navigates to signup pageComment on Khan Artist's post “What's the purpose of the...”
(40 votes)
Answer
- Screeper
  Posted 4 years ago. Direct link to Screeper's post “its a another way to do i...”
  its a another way to do it. it could be easy or hard depending
  Comment on Screeper's post “its a another way to do i...”
  (7 votes)
edwardduong21
Posted 9 years ago. Direct link to edwardduong21's post “why should i use this law...”
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.
Button navigates to signup pageComment on edwardduong21's post “why should i use this law...”
(15 votes)
Answer
- Vicky Lee
  Posted 5 years ago. Direct link to Vicky Lee's post “Actually, this is an easi...”
  Actually, this is an easier and faster way. You'll find this helpful later in life.
  Comment on Vicky Lee's post “Actually, this is an easi...”
  (12 votes)
poopshady
Posted 12 years ago. Direct link to poopshady's post “whats the definition of d...”
whats the definition of distributive,associative,and commutative?
Button navigates to signup pageComment on poopshady's post “whats the definition of d...”
(10 votes)
Answer
- Johnnathantan2003
  Posted 11 years ago. Direct link to Johnnathantan2003's post “PEMDAS tells us what orde...”
  PEMDAS tells us what order we can do certain math operations in - Parentheses, Exponents, Multiplication/Division, and Addition/Subtraction:
  
  5(2+3)=5(5)=25
  
  In this case, PEMDAS was sufficient. But we're not always dealing with numbers, as we see below:
  
  5x(2x+3)=?
  Button navigates to signup page
  (8 votes)
Jackson Enerson
Posted a year ago. Direct link to Jackson Enerson's post “this has taught me as muc...”
this has taught me as much as my math teacher, nothing.
Button navigates to signup pageComment on Jackson Enerson's post “this has taught me as muc...”
(9 votes)
Answer
- MarxMischief
  Posted a year ago. Direct link to MarxMischief's post “dang that's depressing bu...”
  dang that's depressing
  but true tho lol
  Button navigates to signup page
  (6 votes)
Bella
Posted 6 years ago. Direct link to Bella's post “Um i am having a lot of t...”
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.
Button navigates to signup pageButton navigates to signup page
(7 votes)
Answer
- ✟ ~Lilac Pineapple~ ✟
  Posted a year ago. Direct link to ✟ ~Lilac Pineapple~ ✟'s post “Hello, sorry if this is t...”
  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! :)
  Button navigates to signup page
  (6 votes)
Camille
Posted 11 years ago. Direct link to Camille's post “What happens if I don't k...”
What happens if I don't know a number?
Button navigates to signup pageComment on Camille's post “What happens if I don't k...”
(7 votes)
Answer
- dmpuni
  Posted 11 years ago. Direct link to dmpuni's post “Credit where credit is du...”
  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
  Button navigates to signup page
  (6 votes)
Emily Hur
Posted 11 years ago. Direct link to Emily Hur's post “For example, in this prob...”
For example, in this problem:
4(8+3), using distributive property, would you write: (4 * 8) + (4 * 3), or 32+12
?
Button navigates to signup pageComment on Emily Hur's post “For example, in this prob...”
(6 votes)
Answer
- jugugalu
  Posted 4 years ago. Direct link to jugugalu's post “do 4x8=32 then 4x3=12, an...”
  do 4x8=32 then 4x3=12, and finally, add 32 plus 12 which is 44. :)
  Button navigates to signup page
  (5 votes)
Nebula
Posted a year ago. Direct link to Nebula's post “How would I use this in r...”
How would I use this in real life?
Button navigates to signup pageComment on Nebula's post “How would I use this in r...”
(9 votes)
Answer
jbroadhurst
Posted 9 years ago. Direct link to jbroadhurst's post “Why when using the distri...”
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? :)
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(9 votes)
Answer
- weroarforareason
  Posted 16 hours ago. Direct link to weroarforareason's post “The reason we multiply in...”
  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.
  Button navigates to signup page
  (1 vote)
baileyvines1
Posted 10 years ago. Direct link to baileyvines1's post “When using the distributi...”
When using the distributive property on a problem like 2(4+b), would your answer be 8+2b or would it be 6b?
Button navigates to signup pageComment on baileyvines1's post “When using the distributi...”
(5 votes)
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- Peter S. ^^'
  Posted 10 years ago. Direct link to Peter S. ^^''s post “The correct way of applyi...”
  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 )
  Button navigates to signup page
  (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.