Sometimes when people use the word “arithmetic” they just use it to mean the same thing as the word “math” or “working with numbers”.

But often, it's used more specifically to refer to four basic math operations: addition, subtraction, multiplication and division.

And that's how we're gonna use the word in this video

and we're gonna spend the rest of the video talking about these four important math operations.

But what does that mean, “math operations”?

…scalpel…

…forceps…

Well there's your problem!

Uh… not exactly.

Math involves both numbers and operations and the operations just tell you what to DO with the numbers.

For example, the addition operation tells us to take two numbers and to combine their values.

If we have the amount 2 and we add it to the amount 3, we end up with the amount 5.

That's addition… it combines two amounts.

The subtraction operation tells us to take one number away from another number.

In other words, if we start with an amount (like 5) and we subtract (or take away) the amount 3 from it, we have only 2 left over.

Subtraction takes an amount away from another amount.

The multiplication operation tells us to take one number and then repeat it a certain number of times.

It's basically just repeated addition.

For example, if we have the amount 5 and we multiply it by 3, that mean we combine 3 groups of 5 to get a total of 15.

So 5 times 3 is the same as 5 + 5 + 5 …see how it's just repeated addition?

Multiplication takes an amount and repeats it a number of times.

And finally, the division operation tells us to take a number and divide it into a certain number of equal groups.

For example, if we start with the amount 15 and we divide that by 3, that means we want to separate 15 into 3 groups that are the same size.

In this case that would be 3 groups of 5. So division takes an amount and separates it into a number of equally sized groups.

If you think about it, you'll see that this is similar to repeated subtraction.

To make arithmetic easier to write down, each of these operation gets its own symbol, and some of them even have more than one symbol.

For addition, we use this symbol (called a 'plus' sign) to show that two numbers are being added.

So when you see a math operation like this, you just say “2 plus 1”.

For subtraction, we use this symbol (called a 'minus' sign) to show when a number is being subtracted from another.

When reading this sign, you usually say “2 minus 1” or “2 take away 1”.

For multiplication, we use this symbol that looks a lot like an 'x'. It's called the 'times' symbol.

So this problem would read, “3 times 4”.

Oh, and sometimes other symbols like a dot or an asterisk are also used to show multiplication.

And finally, for division we use this symbol, which we usually just call 'the division sign'.

And we read it like this… “8 divided by 2”.

And there are several other types of division signs that are commonly used too.

This one is used to do long division.

And the fraction line is also a really useful way to show division and so is a slash like this.

But in this video, we're just going to focus on these four main symbols for our arithmetic operations:

'plus', 'minus', 'times', and 'divided by'

Oh… but there's one other really important symbol that we use all the time in arithmetic,

but it doesn't tell us what to DO with numbers. Instead, it tells us about them.

Specifically, it tells us that two amounts are equal, which is why it's called “the equal sign”.

In arithmetic, the equal sign is used to show what the answer is to an operation or a set of operations.

On one side of the equal sign, you show the math operations that need to be done,

and on the other side, you show the answer you get once they have been done.

And speaking of answers, did you know that the answers for each of the four arithmetic operations gets a different name?

And it's important to learn those names because they'll help you when you need to read math instructions or when you're solving word problems.

The answer to an addition problem is called a “sum”.

The answer to a subtraction problem is called a “difference”.

The answer to a multiplication problem is called a “product”.

and the answer to a division problem is called a “quotient”.

Try to memorize these so that if someone asks you, “What's the product of 4 and 5?”

You'll know that they're really asking, “What answer do you get if you multiply 4 and 5?”

And speaking of memorization, in a minute we'll see why it's so important to memorize the answers

to some basic arithmetic problems (the ones involving the numbers 1 thru 10).

But first, I want to tell you two more important things about these arithmetic operations.

The first thing you need to know is that for two of these operations, the order of the numbers doesn't matter,

but for the other two operations it does matter.

With addition, you can switch the order of the numbers you're adding and you'll still get the same answer.

1 + 2 is equal to 2 + 1.

No matter which number comes first, the answer will still be 3.

And it's the same with multiplication.

You can switch the order of the numbers in a multiplication problem and you'll still get the same answer.

2 × 5 is the same as 5 × 2.

In both cases, the answer will be 10.

When you can switch the order of the numbers in operations like that and still get the same answer,

the technical math term is to say that the operations “commute” or that they have the “commutative property”.

…try saying that ten times fast!

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D'oh!

On the other hand, subtraction and division don't have the commutative property.

If you switch the order of the numbers, it's not the same problem and you'll get a different answer.

That means you have to pay close attention to the order of the numbers in a subtraction or a division problem

to make sure you're working the right problem.

For example, taking 1 away from 10 is NOT the same as taking 10 away from 1.

And dividing 6 into 2 groups is NOT the same as dividing 2 into 6 groups.

Another thing important you need to know about these arithmetic operations is that they form pairs that are called “inverse operations”.

A good way to understand what an inverse operation is, is to think of the “undo” feature on a computer.

If you do something on a computer, there's usually a way to undo it or to go back to the way it was before.

In math, inverse operations are like that.

Addition and subtraction are inverse operations. What one does, the other un-does.

If you add 5 to 10 to get 15, you can undo that operation by taking 15 and then subtracting 5 from it to get back to the original 10.

It's like give and take… addition gives, subtraction takes.

Likewise, multiplication and division are inverse operations.

If you multiply 4 times 10, that means to combine 4 groups of 10 for a total of 40.

But then you could undo that by dividing.

You could take that 40 and then divide it back into 4 separate groups of 10.

So multiplying groups things, but dividing un-groups them.

Alright, we've learned a lot about arithmetic so far, but when it comes to actually doing arithmetic,

it's really helpful to start off by memorizing some of the basic arithmetic facts.

That usually involves memorizing the answers to all the arithmetic problems that can be made from the numbers 1 thru 10,

like 2 + 2 = 4 or 3 × 4 = 12

You may be thinking, “That sounds like a LOT of facts to memorize!” And you're right.

But fortunately, because of the two things we just learned about arithmetic, it's not as bad as it sounds.

Thanks to inverse operations, you really only have to memorize the facts for addition and multiplication,

because if you know them, you can easily figure out the subtraction and division facts from them.

For example, with addition, if you memorize the fact: 3 + 7 = 10. Then you'll also know two different subtraction facts.

You'll know that 10 minus 3 is 7. And you'll also know that 10 minus 7 is 3.

This group is sometimes called a 'fact family' because the facts are related.

Here's me and my fact family at the Grand Canyon.

Here's me and my fact family climbing Mount Everest.

And here's me and my fact family on the surface of the Moon.

Likewise, with multiplication, if you memorize the fact: 3 × 8 = 24, then you'll also know two different division facts.

You'll know that 24 divided by 3 is 8 and that 24 divided by 8 is 3.

This is another fact family.

Okay, great, so we just need to memorize the addition and multiplication facts, but there's still a lot of them.

Ah… but there's only half as many as you might think. That's because addition and multiplication have the commutative property.

Remember?… You can switch the order of the problem and get the same answer.

That means if you know the addition fact: 4 + 7 = 11 you also know that 7 + 4 = 11. So you don't need to memorize both of them.

And the same is true for multiplication. If you know the fact: 4 × 9 = 36, then you also know that 9 × 4 = 36. Pretty handy, huh?

Lots of times, these math facts are organized into tables that help you memorize them.

This is especially true for the multiplication facts with an invention called the “times table”.

This table shows you the answer you'd get if you multiplied a number along the top row with a number along the side row.

That's a LOT of answers to memorize, but if you remember the rule about switching the order,

then you only have to memorize about half of the chart because… for example… you get the same answer for 2 × 4 and 4 × 2.

Alright… that's a lot of information about arithmetic, so you might want to re-watch this video if you didn't get it all the first time.

Most of the exercises for this section focus on helping you memorize these basic addition and multiplication facts.

The more you practice them, the sooner you'll have them memorized.

Once you know some of the basic arithmetic facts,

you'll be ready to move on to other arithmetic topics like Order of Operations and Multi-Digit Arithmetic.

As always, thanks for watching Math Antics and I'll see ya next time.

Learn more at www.mathantics.com