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# Constructing numerical expressions

Sometimes, we don't need to solve an equation right away. Instead, we can use the information in a given word problem to construct a numerical expression that represents the information. Created by Sal Khan.

## Want to join the conversation?

- There are no videos explaining the use of brackets? It can be quite confusing to anyone learning for the first time when they try to solve any problem that includes braces and parenthesis.(53 votes)
- brackets and perentheses are the same thing you just want to do the parentheses before the brackets like the teacher taught you parentheses first.(38 votes)

- I just lost my marbles trying to understand this. Pun intended. :)))) It's easy tho(33 votes)
- addition is an opperation so why did Sal say that he solved the problem without using operations even though he used addition?(14 votes)
- So, he didn't really use the operation. He just wrote down what they were asking for. If he had actually performed the operation, he would have come up with 27, which is a number, not a numerical expression.

Hope this helps.(8 votes)

- I just wanted to know that is it important that the factor we are multiplying with, in this case 3, goes on the left side instead of the right side of the parenthesis?(7 votes)
- When Sal made the expression 3(4+5), there are more ways to do this, right? The way he did it was adding 4 and 5 which makes 9, and multiplying it to make 27. The way I thought of doing it was this:

3(4+5)

(12+15)

x = 27 (don't know why I added x there :/)

Hmmm... I wonder if there are MORE ways to do this...(6 votes)- No, those are the 2 possible ways of doing the problem.(0 votes)

- At0:56, tripling is multiplying by three. What is it called when you multiply by five?(0 votes)
- Actually, there
**is**a known name for multiplying by 5. Here are all of them:`Multiplying by two is called doubling`

`

Multiplying by three is called tripling

Multiplying by four is called quadrupling

Multiplying by five is called quintupling

Multiplying by 6 is called (this is weird) sextupling

Multiplying by seven is septupling

Multiplying by eight is octupling

I think I know the rest, but I am*not sure*, so it doesn't matter.

I hope you were helped by this information. Thanks!(8 votes)

- What do you do with 7 [3 (6-2)]-64(3 votes)
- PEMDAS and the blank is multiplication right after the bracket(2 votes)

- thanks this helped me do it(2 votes)
- 3(3x+7)+4(5x-2)(2 votes)
- Why did Sal not write a operation for the number 3? What do we do with it?(3 votes)
- He did cut the video a bit short. Basically after he did what he showed, you then have to multiply each number inside the bracket by the number outside the bracket.

So Sal wrote 3(4+5) so next you multiply 4 by the 3 3x4=12, and the 5 by the 3 3x5=15. Finally you just add the two answers together 12+15=27.

This works because you're just distributing 3 over to 4 and over to 5, you're moving it over to it, which gets you the same answer as you'd get if you just added the group in the parenthesis first then multiplied it by 3 (4+5)=9x3=27.

But you don't start with adding what's in the parenthesis with Distributive Property because it won't help you with more complex Algebra equations.(0 votes)

## Video transcript

Alan found 4 marbles
to add to his 5 marbles currently in his pocket. He then had a competition
with his friends and tripled his marbles. Write a numerical expression
to model the situation without performing
any operations. So let's think about
what's going on. So he already had 5
marbles in his pocket. And then he found 4 more
marbles to add to that. So we can add the 4
marbles to the 5 marbles. So 4 marbles plus the 5 marbles. So that's what happens
after the first sentence. He found 4 marbles to
add to his 5 marbles currently in his pocket. He then had a competition
with his friends and tripled his marbles. So this is how many marbles
he had before tripling. And now he's
tripling his marbles. So we want to multiply 3 times
the total number of marbles he has now-- times 4 plus 5. So this right over here is
the numerical expression that models the situation
without performing any operations. We, of course, could then
actually calculate this. He has 9 marbles
before tripling. And then you multiply
it by 3 and he has 27. But this is what
they're asking for. They want us to write
this expression.