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### Course: 4th grade foundations (Eureka Math/EngageNY) >Unit 3

Lesson 4: Topic E: Foundations

# 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 …
we just evaluate what’s in the parentheses first, then solve it:
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:
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
a)
b)
Tips
• 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?

• Can the distributive property work if there is multiplication or division inside the parentheses? Like in 9(3/3)?
• That's not a failure to distribute due to the fraction/division though, it fails because e it requires a minimum of 2 terms to distribute onto.
Say the problem is 9(3/3+3/3), then you just handle the multiplication inside just like any other fractions/divisions
9*3/3+9*3/3 -> 27/3+27/3 -> 9/1+9/1 = 18
• What if you have two parentheses? Such as (3x6) - (3x3)
• You can take out the 3 from both terms
3(6-3) = 18 - 9 = 9. This gives the same answer as multiplying the numbers in the brackets.
• why is this important for me to know in life
• 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
• 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.😊
• Sal wrote the 2 there, because he was signifying that when the positive 7 and the negative 5 were combined together, it would equal a positive 2. He then added this positive 2 to the 6+x in the rest of the expression and got 8+x. Did that help?
• In example c, what does the underneath 5+7 represent?
• 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?
• What if the expression does not have a operation inside?
Example: 18(26)
• Technically, `18(26)` does have an operation...

In this instance, the parentheses denote multiplication. Therefore,

`18(26) = 18*26`

Knowing this, you can now continue with the distributive property.
• Why do you use a parenthesis instead of a multiplication symbol?
• The parenthesis helps the problem more understandable rather than doing this 3*4-7
• 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
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.
• 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.
• What if the format is this
1/2(2a-6b+8)
• 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.