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### Unit 6: Lesson 12

Distributive property with variables

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

## Want to join the conversation?

• I remember using this in Algebra but why were we forced to use this law to calculate instead of using the traditional way of solving whats in the parentheses first, since both ways gives the same answer. •   This is preparation for later, when you might have variables instead of numbers. Sure 4(8+3) is needlessly complex when written as (4*8)+(4*3)=44 but soon it will be 4(8+x)=44 and you'll have to solve for x.

At that point, it is easier to go:
(4*8)+(4x) =44
32 + 4x =44
4x =12
x = 3

Working with numbers first helps you to understand how the above solution works. Hope this helps.
• Okay, so I understand the distributive property just fine but when I went to take the practice for it, it wanted me to find the greatest common factor and none of the videos talked about HOW to find the greatest common factor. Can any one help me out? • one question i had when he said 4times(8+3) but the equation is actually like 4(8+3) and i don't get how are you supposed to know if there's a times table there.its on 19-39 on video. • • • why is the distributive property important in math? how can it help you? isn't just doing 4x(8+3) easier than breaking it up and do 4x8+4x3? • • Ok so what this section is trying to say is this equation 4(2+4r) is the same as this equation 8+16r. The reason why they are the same is because in the parentheses you add them together right? That would make a total of those two numbers. Those two numbers are then multiplied by the number outside the parentheses. So in doing so it would mean the same if you would multiply them all by the same number first. You would get the same answer, and it would be helpful for different occasions! This is a choppy reply that barely makes sense so you can always make a simpler and better explanation. Hope this helps!
• • • Help me with the distributive property. Please? If you add numbers to add other numbers, isn't that the communitiave property? I can't get it. It's so confusing for me, and I want to scream sometimes....In a problem at school, it really "tugged" at me, and I couldn't get it! May y'all help me? PLEASE! PLEASĖ? PLEAS-!" • The commutative property means when the order of the values switched (still using the same operations) then the same result will be obtained. For example, 1+2=3 while 2+1=3 as well. 2*5=10 while 5*2=10 as well.

The literal definition of the distributive property is that multiplying a value by its sum or difference, you will get the same result.

Let's take 7*6 for an example, which equals 42.
If we split the 6 into two values, one added by another, we can get 7(2+4). 7*2=14, and 7*4=28. 14+28=42

There is of course more to why this works than of what I am showing, but the main thing is this: multiplication is repeated addition. You can think of 7*6 as adding 7 six times (7+7+7+7+7+7). Having 7(2+4) is just a different way to express it: we are adding 7 six times, except we first add the 7 two times, then add the 7 four times for a total of six 7s.

With variables, the distributive property provides an extra method in rewriting some annoying expressions, especially when more than 1 variable may be involved.

For example, if we have b*(c+d). c and d are not equal so we cannot combine them (in ways of adding like-variables and placing a coefficient to represent "how many times the variable was added". However, the distributive property lets us change b*(c+d) into bc+bd. Even if we do not really know the values of the variables, the notion is that c is being added by d, but you "add c b times more than before", and "add d b times more than before".
Experiment with different values (but make sure whatever are marked as a same variable are equal values).