Math Antics - What Is Arithmetic? - Free Educational videos for Students in K-12 | Lumos Learning

Math Antics - What Is Arithmetic? - Free Educational videos for Students in k-12


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 .
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