Math Antics - What Is Arithmetic? - By Mathantics
Transcript
00:03 | Oh hi welcome to Math Antics . In this video | |
00:08 | we're going to learn about arithmetic . Sometimes when people | |
00:12 | use the word arithmetic they just use it to mean | |
00:15 | the same thing as the word math or working with | |
00:17 | numbers . But often it's used more specifically to refer | |
00:21 | to four basic math operations . Addition , subtraction , | |
00:26 | multiplication and division . And that's how we're going to | |
00:29 | use the word in this video and we're going to | |
00:31 | spend the rest of the video talking about these four | |
00:34 | important math operations . But what does that mean ? | |
00:38 | Math operations , scalpel forceps ? Mhm . Yeah . | |
00:49 | Well there's your problem . Not exactly . Math involves | |
00:54 | both numbers and operations and the operations . Just tell | |
00:58 | you what to do with the numbers . For example | |
01:02 | the addition operation tells us to take two numbers and | |
01:05 | to combine their values . If we have the amount | |
01:07 | to and we add it to the amount three we | |
01:11 | end up with the amount five . That's addition . | |
01:14 | It combines two amounts . The subtraction operation tells us | |
01:18 | to take one number away from another number . In | |
01:21 | other words if we start with an amount like five | |
01:25 | and we subtract or take away the amount three from | |
01:28 | it , we have only two left over Subtraction takes | |
01:32 | an amount away from another amount . The multiplication operation | |
01:37 | tells us to take one number and then repeat it | |
01:40 | a certain number of times . It's basically just repeated | |
01:43 | addition . For example if we have the amount five | |
01:47 | and we multiply it by three . That means we | |
01:50 | combine three groups of five to get a total of | |
01:53 | 15 . So five times three is the same as | |
01:58 | five plus five plus five . See how it's just | |
02:01 | repeated addition , multiplication takes an amount and repeats it | |
02:05 | a number of times . And finally the division operation | |
02:10 | tells us to take a number and divide it into | |
02:12 | a certain number of equal groups . For example , | |
02:16 | if we start with the amount 15 and we divide | |
02:19 | that by three . That means we want to separate | |
02:22 | 15 into three groups that are the same size . | |
02:26 | In this case that would be three groups of five | |
02:29 | . So division takes an amount and separates it into | |
02:33 | a number of equally sized groups . If you think | |
02:36 | about it , you'll see that this is similar to | |
02:38 | repeated subtraction . To make arithmetic easier to write down | |
02:43 | each of these operations gets its own symbol and some | |
02:46 | of them even have more than one symbol for addition | |
02:49 | . We use this symbol called a plus sign to | |
02:52 | show that two numbers are being added . So when | |
02:55 | you see a math operation like this , you just | |
02:57 | say two plus one for subtraction . We use this | |
03:01 | symbol called a minus sign to show in a number | |
03:03 | is being subtracted from another . When reading this sign | |
03:07 | , you usually say to -1 or two . Take | |
03:11 | away one for multiplication . We use this symbol that | |
03:14 | looks a lot like an X . It's called the | |
03:16 | time symbol . So this problem would read three times | |
03:20 | 4 oh . And sometimes other symbols like a dot | |
03:24 | or an asterisk are also used to show multiplication . | |
03:27 | And finally for division we use this symbol which we | |
03:31 | usually just called the division sign . And we read | |
03:34 | it like this eight divided by two . And there's | |
03:37 | several other types of division science that are commonly used | |
03:40 | to this one is used to do long division and | |
03:43 | the fraction line is also a really useful way to | |
03:45 | show division and so is the slash like this . | |
03:49 | But in this video we're just going to focus on | |
03:51 | these four main symbols for our arithmetic operations plus minus | |
03:57 | times and divided by . But there's one other really | |
04:01 | important symbol that we use all the time in arithmetic | |
04:04 | , but it doesn't tell us what to do with | |
04:06 | numbers . Instead it tells us about them specifically . | |
04:10 | It tells us that two amounts are equal . Which | |
04:12 | is why it's called the equal sign in arithmetic . | |
04:16 | The equal sign is used to show what the answer | |
04:18 | is to an operation or a set of operations . | |
04:21 | On one side of the equal sign , you show | |
04:23 | the math operations that need to be done and on | |
04:26 | the other side you show the answer you get once | |
04:28 | they have been done . And speaking of answers , | |
04:32 | did you know that the answers for each of the | |
04:34 | four arithmetic operations gets a different name And it's important | |
04:37 | to learn those names because they'll help you when you | |
04:40 | need to read math instructions or when you're solving word | |
04:43 | problems . The answer to an addition problem is called | |
04:47 | a some . The answer to a subtraction problem is | |
04:50 | called a difference . The answer to a multiplication problem | |
04:53 | is called a product , and the answer to a | |
04:55 | division problem is called a quotient . Try to memorize | |
04:59 | these so that if someone asks you what's the product | |
05:02 | of four and five , you'll know that they're really | |
05:04 | asking what answer do you get if you multiply four | |
05:07 | and five And speaking of memorization in a minute we'll | |
05:11 | see why . It's so important to memorize the answers | |
05:14 | to some basic arithmetic problems , the ones involving the | |
05:17 | numbers one through 10 . But first I want to | |
05:19 | tell you to more important things about these arithmetic operations | |
05:24 | . The first thing you need to know is that | |
05:26 | for two of these operations , the order of the | |
05:28 | numbers doesn't matter . But for the other two operations | |
05:31 | it does matter with addition , you can switch the | |
05:35 | order of the numbers you're adding and you'll still get | |
05:37 | the same answer . One plus two is equal to | |
05:40 | two plus one , no matter which number comes first | |
05:43 | . The answer will still be three . And it's | |
05:46 | the same with multiplication . You can switch the order | |
05:49 | of the numbers in a multiplication problem and you'll still | |
05:51 | get the same answer . Two times five is the | |
05:54 | same as five times 2 . In both cases , | |
05:58 | the answer will be 10 When you can switch the | |
06:01 | order of the numbers and operations like that and still | |
06:04 | get the same answer . The technical math term is | |
06:07 | to say that the operations commute or that they have | |
06:10 | the communicative property . Try saying that 10 times fast | |
06:13 | . Community property . Community property . Community of property | |
06:16 | . Community property don't . On the other hand , | |
06:19 | subtraction and division don't have the community of property . | |
06:23 | If you switch the order of the numbers , it's | |
06:25 | not the same problem . And you'll get a different | |
06:28 | answer . That means you have to pay close attention | |
06:31 | to the order of the numbers and a subtraction or | |
06:33 | division problem to make sure you're working the right problem | |
06:37 | . For example , taking one away from 10 is | |
06:40 | not the same as taking 10 away from one And | |
06:43 | dividing six into two groups is not the same as | |
06:47 | dividing two into 6 groups . Another important thing you | |
06:51 | need to know about these arithmetic operations is that they | |
06:54 | form pairs that are called inverse operations . A good | |
06:58 | way to understand what an inverse operation is . Is | |
07:00 | to think of the undo feature on a computer . | |
07:03 | If you do something on a computer , there's usually | |
07:06 | a way to undo it or to go back the | |
07:08 | way it was before . In math , inverse operations | |
07:11 | are like that . Addition and subtraction are inverse operations | |
07:16 | . What one does the other un does . If | |
07:19 | you add 5-10 to get 15 you can undo that | |
07:23 | operation by taking 15 and then subtracting five from it | |
07:27 | to get back to the original 10 . It's like | |
07:30 | give and take edition gives and subtraction takes Likewise multiplication | |
07:36 | and division are inverse operations . If you multiply four | |
07:39 | times 10 that means to combine four groups of 10 | |
07:43 | for a total of 40 . But then you can | |
07:45 | undo that by dividing You could take that 40 and | |
07:49 | then divide it back into four separate groups of 10 | |
07:52 | . So multiplying groups things . But dividing um groups | |
07:56 | them . All right . We've learned a lot about | |
07:59 | arithmetic so far . But when it comes to actually | |
08:02 | doing arithmetic it's really helpful to start off by memorizing | |
08:06 | some of the basic arithmetic facts That usually involves memorizing | |
08:11 | the answers to all the arithmetic problems . That can | |
08:14 | be made from the numbers one through 10 like two | |
08:17 | plus two equals four or three times four equals 12 | |
08:21 | . You may be thinking that sounds like a lot | |
08:24 | of facts to memorize and you're right . But fortunately | |
08:28 | because of the two things we just learned about arithmetic | |
08:31 | , it's not as bad as it sounds . Thanks | |
08:34 | to inverse operations . You really only have to memorize | |
08:37 | the facts for addition and multiplication because if you know | |
08:40 | them , you can easily figure out the subtraction and | |
08:43 | division facts from them . For example , with addition | |
08:47 | , if you memorize the fact three plus seven equals | |
08:50 | 10 , Then you'll also know two different subtraction facts | |
08:54 | . You'll know that 10 -3 is seven and you'll | |
08:57 | also know that 10 -7 is three . This group | |
09:01 | is sometimes called a fact family because the facts are | |
09:04 | related . Here's me and my fact family at the | |
09:07 | Grand Canyon . Here's me and my fact family climbing | |
09:11 | Mount Everest And here's me and my fact family on | |
09:15 | the surface of the moon . Likewise with multiplication . | |
09:20 | If you memorize the fact three times eight equals 24 | |
09:24 | , then you'll also know two different division facts . | |
09:26 | You'll know that 24 divided by three is 8 And | |
09:30 | that 24 divided by eight is 3 . This is | |
09:33 | another fact family . Okay great . So we just | |
09:37 | need to memorize the addition and multiplication facts . But | |
09:40 | there's still a lot of them . Ah But there's | |
09:42 | only half as many as you might think . And | |
09:45 | that's because addition and multiplication had the community of property | |
09:49 | . Remember you can switch the order of the problem | |
09:51 | and get the same answer . That means if you | |
09:54 | know the addition fact four plus seven equals 11 . | |
09:58 | You also know that seven plus four equals 11 . | |
10:01 | So you don't need to memorize both of them . | |
10:04 | And the same is true for multiplication . If you | |
10:07 | know the fact four times nine equals 36 Then you | |
10:10 | also know that nine times 4 equals 36 . Pretty | |
10:14 | handy , Huh ? Lots of times these math facts | |
10:17 | are organized into tables that help you memorize them . | |
10:20 | This is especially true for the multiplication facts with an | |
10:23 | invention called the Times Table . This table shows you | |
10:27 | the answer you'd get . If you multiply the number | |
10:29 | along the top row with the number along the side | |
10:32 | row . That's a lot of answers to memorize . | |
10:35 | But if you remember the rule about switching the order | |
10:38 | , then you only have to memorize about half of | |
10:40 | the chart because for example , you get the same | |
10:43 | answer for two times four and four times two . | |
10:47 | All right . That's a lot of information about arithmetic | |
10:50 | . So , you might want to re watch this | |
10:51 | video if you didn't get it all the first time | |
10:54 | , most of the exercises for this section focus on | |
10:57 | helping you memorize these basic addition and multiplication facts . | |
11:00 | The more you practice them , the sooner you'll have | |
11:03 | them memorized . Once you know some of the basic | |
11:05 | arithmetic facts , you'll be ready to move on to | |
11:08 | other arithmetic topics like order of operations and multi digit | |
11:12 | arithmetic as always . Thanks for watching Math Antics and | |
11:15 | I'll see you next time . Learn more at Math | |
11:19 | Antics dot com . |
Summarizer
DESCRIPTION:
OVERVIEW:
Math Antics - What Is Arithmetic? is a free educational video by Mathantics.
This page not only allows students and teachers view Math Antics - What Is Arithmetic? videos but also find engaging Sample Questions, Apps, Pins, Worksheets, Books related to the following topics.