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### Course: 6th grade > Unit 6

Lesson 12: Distributive property with variables# 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.

## Want to join the conversation?

- What's the purpose of the distributive property if you just evaluate the same answer?(41 votes)
- its a another way to do it. it could be easy or hard depending(8 votes)

- 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)
- Actually, this is an easier and faster way. You'll find this helpful later in life.(13 votes)

- whats the definition of distributive,associative,and commutative?(9 votes)
- 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)=?(9 votes)

- this has taught me as much as my math teacher, nothing.(8 votes)
- dang that's depressing

but true tho lol(7 votes)

- How would I use this in real life?(11 votes)
- For example, in this problem:

4(8+3), using distributive property, would you write: (4 * 8) + (4 * 3), or 32+12

?(7 votes)- do 4x8=32 then 4x3=12, and finally, add 32 plus 12 which is 44. :)(6 votes)

- 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)- 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)

- 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)
- 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**! ('^*_^) /*:p )

Try applying this a few times and you'll get it in no time !

( in fact, I think my answer must already be late(8 votes)

- 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)
- 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)

- What happens if I don't know a number?(6 votes)
- 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.