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Lesson 7: Distributive property

# Distributive property when multiplying

Sal uses the distributive property to break up 4x7 into smaller numbers.

## Want to join the conversation?

• why did he meow and why did he say yup there still mad • what is 7 times 7 • can you use angry cats more often? • i don't understand Distributive property. • i think the problem is that they dont teach people a definition, i am a bit late to answer but heres my try.

if i am incorrect anywhere, please flag this answer as i am rarely active and comment where did i go wrong so other people do not make the same mistake, thank you so much 8)

Firstly, this is my definition.
Distributive property lets us distribute any value of mathematics into a combination of operations. It is helpful in creating or solving problems. All questions are just either simple or complex distributions of the final answer. You just have to find out how the value got distributed into the question and what that real value is.

then the weird long story explanation.

so every mathematical number or group of numbers, they all can be obtained by more than one possible ways, for example, you can get 3 by so so so so many ways, think of some ways you can get the number 3 in maths. let me start. if you take away 24 candies out of 27 candies from your sisters candy jar, she will have 3 candies left. so 27 - 24 = 3. Now think of some more of the other ways you can get a 3.

like 6-3 or 5+20+13+2-37.

Now here is the most amazing part. when you see a three anywhere in school or at home, you could 'DISTRIBUTE' that 3 in so many different ways too, you could literally write the long operations or terms we used above to express a 3, like 100-97 or 1+2 or 1+1+1. SO intead of that one simple three, you can write all the different ways in which you could distribute the value of 3. The number 3 is nothing but a value, do not focus too much on the symbol.

This 7-4 could also be written in place of 3 anywhere in the world, 3 is just a value, a reality. A value in my opinion is a reality that we see, acknowledge and try to communicate it to the people around us. So we assign a symbol to it for easier communication. 3 isnt just this symbol, neither is any other maths value. It could be anything, three could be this iii or this hhh or yyy or brickbrickbrick or ballballball.

But when it comes to multiple mathematical operations, like 3 + 7 x 5. In this maths operation, you can still substitute the value of three with lets say 80-77, but now in this case of " 3 '+' 7 x 5 " you will have to put this 'DISTRIBUTED VALUE OF 3' in brackets or parenthesis. Because otherwise you might end up 'commutating' (means moving around) the multiplication to one of these 'DISTRIBUTIONS of 3' and get to the wrong answer. That is why the order of operations exists, or the order of solutions exists where we always solve the parenthesis first, because that way we could identify what is the real value of whatever is inside that parenthesis and then we could just use that real value and add/subtract/multiply/divide it with other real values to finally get to our real answer.

in simple terms lets say we distributed 3 into 5+6-40+26,

now lets put this into our example above of 3 + 7 x 5.

if we just use 5 + 6 - 40 + 26 + 7 x 5, we wouldnt know which numbers are the combined distribution of the real value, obviously here we know which are because we have already specified that for the sake of understanding. if we solve it as is we get 32, if my calculations are right haha. But in reality thats not the answer. if we solve 3 + 7 x 10 we would get 38. SO we have to specify it in brackets/parenthesis which are the terms that we distributed 3 into. like (5 + 6 - 40 + 26) + 7 x 5. Here we first solve the parenthesis as per the rules which exist so that we dont stray away from the real answer and then get the answer 38.

everything in maths, it might look all big and scary but it already has an answer. An answer from which it was distributed into this long scary thing. the same thing goes for almost every mathematical equation or operation in higher classes too. They are all just one term blown up into this big complex terms. just focus on finding the real value of it all.

Pay attention to the wording here. most of science and maths is just very easy if you learn and know the literal meanings of the names of things and focus on that. Because most namers try to put everything that is in the explanation of that thing, into one or two words which could tell any reader the general sense of what is in that topic.
• Give this a ton of votes. • hi can you help me with multipacaitoion • i need help on a question its 8 x 4 but the first problem you did • I don't understand the distributive property. • I got the achivement of seingthis video for an hour omggg :D • What is the easiest way to learn my 7 times table? This is very hard. • Many kids have difficulty with 7’s, but this does not have to be you if you use a strategy.

There are multiple strategies. Here are three of them. These strategies come from the idea that multiplication is the same as counting groups of objects (distributive property).

1) If you’re good with 2’s and 5’s, a possible way to multiply a number by 7 is to multiply it by 2, multiply it by 5, then add the results. This is based on the fact that 2 + 5 = 7.

Example: let’s do 8 x 7.
8 x 2 = 16
8 x 5 = 40
16 + 40 = 56, the answer.

2) If you’re good with 10’s and 3’s, a possible way to multiply a number by 7 is to multiply it by 10, multiply it by 3, then subtract the results. This is based on the fact that 10 - 3 = 7.

Example: let’s do 8 x 7 again.
8 x 10 = 80
8 x 3 = 24
80 - 24 = 56, the answer.

3) lf you’re good with 6’s, a possible way to multiply a number by 7 is to multiply it by 6 and add the original number. This is based on the fact that 6 + 1 = 7.

Example: let’s do 8 x 7 again.
8 x 6 = 48
original number = 8
48 + 8 = 56, the answer.

These are not the only strategies. From looking at the ideas in the three strategies l wrote, you might even come up with your own strategy that you like better.

Have a blessed, wonderful day!