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## Arithmetic

### Course: Arithmetic > Unit 1

Lesson 1: Multiplication as equal groups# Introduction to multiplication

CCSS.Math:

Sal introduces multiplication as equal groups. He relates multiplication to skip counting and repeated addition.

## Want to join the conversation?

- Is 150 divide by 0.25 equal 600(14 votes)
- Yes, because 0.25 is 1/4, and 150 divided by (1/4) = 150 x 4 = 600.

Have a blessed, wonderful day!(20 votes)

- I can't do multiplecation(7 votes)
- That’s ok,a lot of people don’t know it.(5 votes)

- what is the toltel of 9 groups of 8(4 votes)
- 9 groups of 8 are the same as
**9 x 8**.**9 x 8**is qual to**9 + 9 + 9 + 9 + 9 + 9 + 9 + 9**

That is equal to**72**.(9 votes)

- and im new from third grade in khan academy(5 votes)
- i like that very much(5 votes)

- how old is this?(6 votes)
- No matter how old the video is, the information remains relevant, but it was made three years ago.(1 vote)

- i love acorns(5 votes)
- what is the square root of 2964?(3 votes)
- This is the beginning of most people's mathematical journey. After this you (a person that knows a lot of mathematics, like proofs, elementary analysis, elementary algebra, probability and stats) can learn advanced arithmetic also called Number Theory.

BTW, Why do we not use the sexagesimal system?(1 vote)- Using a high number for the base has the advantage of often producing numbers with small numbers of digits, but has the disadvantage of requiring knowledge of a large number of basic addition, subtraction, multiplication, and division facts to perform calculations.

Using a low number as the base has the advantage of requiring knowledge of a small number of basic addition, subtraction, multiplication, and division facts to perform calculations, but has the disadvantage of often producing numbers with high numbers of digits.

So a base such as 10 strikes a good balance.

Have a blessed, wonderful day!(8 votes)

- how do we do the 8s(4 votes)
- I do not know(2 votes)

## Video transcript

- [Instructor] Our
squirrel friend here likes to collect acorns, because, really, that's how he is able to live. And let's say everyday, he
collects exactly three acorns. And so what I'm curious
about is how many acorns will he have after doing
this for five days? So one way to think about
it is every day he is able to collect a group of three acorns. So you could view this
as maybe what he's able to collect in day one. And then in day two, he's
able to collect a second group of three acorns. In day three, he's able
to collect another group of three acorns. And every day it's a
equal number of acorns that he's collecting. On the fourth day, another three. On the fifth day, another three. And so if you were curious
how many total acorns he's collected, well, you
could just count them up, or you could think about, well, he's got five
groups of three acorns. Five equal groups of three acorns. So you could say five groups of three acorns, three acorns. And so the total amount would be five, we could view this as five threes. Now, five threes, you could view this as five threes added together. Three plus three, plus three,
plus three, plus three. And if you wanted to calculate this, you could skip count by three. So this would be three, six, nine, 12, 15, because we add three, we get to six, we add another three, we get to nine, we add another three, we get to 12, we add another three, we get to 15. And so this would be a way of recognizing that you have 15 acorns, but we're starting to touch
on one of the most fundamental ideas in all of mathematics. In fact, we actually are applying it, we just haven't used the world, and that's, we are multiplying. We are using multiplication. All multiplication is is this notion of multiple
equal groups of something. So, here, one way to
express what we just did, is we just, when we said five threes, that's the same thing as five, and I'm going to introduce
a new symbol to you, five times three. So all of these things are equivalent. You're already used to seeing equal groups and multiple equal groups, and you're used to adding
something multiple times, and you're used to skip counting, and all of that is, in
some way shape or form, you have been doing multiplication. So when someone says five times three, you could view that is
five groups of three, or you could view that as five threes, or you could view that
as three plus three, plus three, plus three, or you could view that as 15. I'll leave ya there. There's a lot of practice on Khan Academy to work through this and make sure you get the underlying idea. But as you'll see, this is
perhaps one of the most useful concepts that you might
learn in your entire lives.