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### Course: Arithmetic > Unit 1

Lesson 1: Multiplication as equal groups# Introduction to multiplication

Let's dive into the concept of multiplication using the example of a squirrel collecting acorns. Together, we'll see that multiplication is all about adding equal groups together. We'll find that 5 groups of 3 acorns each can be represented as 5 times 3, which equals 15 acorns.

## Want to join the conversation?

- Is it hard to multiply with decimals?(28 votes)
- Multiplying with decimals is the same as regular multiplication, except you need to be extra careful with the decimal points.

Multiplying with decimals can be tricky, but it's not really hard - there are just more steps. The key is to practice until you get the hang of it.

You can watch this video to get a better idea of the process:

https://www.khanacademy.org/math/algebra-basics/basic-alg-foundations/alg-basics-operations-with-decimals/v/multiplying-decimals

Hope this helps answer your question!(19 votes)

- why do you need to say 3+3+3+3+3 instead of counting in 3s(19 votes)
- It's just a clear way to show it, to make sure that you understand that multiplication is really repeated addition (2+2+2, or something)(16 votes)

- I don't understand why you say 5 threes, can you explain that for me?(9 votes)
- The squirrel has collected 3 acorns every day for 5 days, so there are 5 groups of acorns with 3 acorns in each group.

If you wanted to find the total number of acorns, that is 3 x 5 or 3 + 3 + 3 + 3 + 3 = 15(9 votes)

- why did they make the multiplication symbol × ?(9 votes)
- If you were to make it five groups every day how many would there be?(9 votes)
- If there were 5 acorns collected every day, then there would be 5 groups of 5.

The total number of acorns would be 5 x 5 = 5 + 5 + 5 + 5 + 5 = 25.(9 votes)

- Is division and multiplication the same thing?(4 votes)
- Division is the opposite of multiplication, so they are related.(15 votes)

- is there history behind the multiplication symbol ?(8 votes)
- X was used by William Oughtred (1574-1660) in the Clavis Mathematicae (Key to Mathematics), composed about 1628 and published in London in 1631 (Smith).(1 vote)

- why can he write so nicely on a computer?(6 votes)
- He's probably writing on a tablet with a stylus I assume(3 votes)

- Why is there a squirrel in the video!(5 votes)
- to help David explain better(4 votes)

- can i add odd numbers like this?(6 votes)
- I do not see the numbers.(1 vote)

## 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.