Math Antics - Fractions and Decimals - Free Educational videos for Students in K-12

Math Antics - Fractions and Decimals - By mathantics

Transcript


00:03	Uh huh . Okay . In the last section we
00:07	learned one of the most important things about fractions .
00:10	We learned that their numbers that are written like division
00:12	problems . We also know that fractions can be used
00:15	to represent smaller parts of things now , since a
00:18	fraction is just a division problem if we wanted to
00:21	we could go ahead and do the division and get
00:22	an answer and that answer would be a regular number
00:25	. That's the value of the fraction . Let's look
00:28	at this fraction facing 15th . That's the same as
00:31	the division problem . 10 divided by five . Now
00:34	we know that 10 divided by five is to .
00:36	So the value of this fraction is too . So
00:39	what's the deal The value to doesn't seem like a
00:41	smaller part of something . In fact it seems like
00:43	two of something . I mean aren't fractions supposed to
00:46	have a value smaller than one . Here's the deal
00:49	. If the top number of a fraction is bigger
00:51	than the bottom number then the value of the fraction
00:54	will be greater than one . But if the top
00:56	number is smaller than the bottom number then the value
00:59	of the fraction will be smaller than one . But
01:02	if we divide a smaller number by a bigger number
01:04	and get a value that's smaller than one , then
01:07	how are we going to write that down ? Like
01:08	a regular number isn't one the smallest number we can
01:11	right beside zero . Luckily the answer is no .
01:15	You see , we can write values that are smaller
01:17	than one by using something called decimal numbers . To
01:21	understand how decimal numbers work . Let's first review how
01:24	we write down regular numbers that don't involve fractions .
01:27	We call those numbers hold numbers we use whole numbers
01:30	when we count things and counting things is very important
01:33	in math . The system that we count things with
01:37	is based on the number 10 . In fact it's
01:39	called base 10 and it uses what we call powers
01:42	of 10 as the groups or building blocks that we
01:45	count with . It's probably no surprise that our first
01:48	building block is one and we can get bigger building
01:51	blocks just by multiplying by 10 . So our next
01:54	building block is one times 10 or 10 and the
01:58	one after that is 10 times 10 or 100 .
02:01	And the one after that is 100 times 10 ,
02:03	which is 1000 . I could keep on multiplying by
02:07	10 to get bigger and bigger building blocks . But
02:09	I think I'm going to stop at 1000 for now
02:11	. So what am I gonna do with all these
02:13	powers of 10 ? Well like I said , they're
02:16	the building blocks of our counting system . So I'm
02:18	going to count with them . But before I do
02:20	that I should mention two more things that are number
02:23	system needs . Besides these building blocks . And those
02:25	two things are digits and number of places , digits
02:29	are just the 10 different symbols we use for counting
02:31	, you know , 012345678 and nine . Number of
02:36	places are like little imaginary boxes that can hold just
02:39	one digit at a time and they're used like counters
02:42	. You know to count things , we use one
02:45	number of place for each of our building blocks to
02:47	count how many of each of them we have .
02:50	For example , let's say I have 200's . Well
02:52	then I just put a two in the number of
02:54	place that counts how many hundreds I have . And
02:57	let's say I have five tens . Well then I
02:59	put a five in the number of place that counts
03:01	tents . And I also have three ones . So
03:04	I put a three and the number of place that
03:05	counts ones . Each number place is named for the
03:09	building block accounts . For example , this number places
03:12	called the ones place because it counts once . This
03:15	is the tens place because it counts tins and the
03:18	hundreds place counts hundreds and so on . Of course
03:22	most of you aren't used to seeing numbers written like
03:24	this . So let's rearrange our number of places to
03:26	make it look more like we're used to there .
03:29	Now you can see that the two in the hundreds
03:30	place , the five in the tens place and the
03:33	three in the ones place all combined to make 253
03:36	. Oh and most of the time we don't actually
03:39	show the number of places they're invisible there . That's
03:42	better . Okay , so that's how we use our
03:45	building blocks , number of places and digits to write
03:48	any whole number we want to . But this video
03:50	is about fractions , right ? So how are we
03:52	gonna write fractions with this system ? A lot of
03:55	fractions have value smaller than one . But right now
03:57	our smallest building block is one . It looks like
04:00	we're gonna need some smaller building blocks . You remember
04:03	how we got our other based in building blocks ?
04:05	We started with one and kept multiplying by 10 to
04:08	get bigger and bigger building blocks . Well , to
04:10	get smaller building blocks , all we have to do
04:13	is start with one and keep dividing by 10 .
04:15	Wait a minute , divide a smaller number like one
04:18	by a bigger number like 10 . Well that sounds
04:20	like a fraction to me exactly . If we do
04:23	that , the building block we get will be a
04:25	fraction and its value will be one part out of
04:27	10 or 1/10 . And we can use that to
04:30	write values that are smaller than one . A good
04:33	way to see how this new building block fits in
04:35	with the other ones is to look at a number
04:37	line Oh look a number line And it goes from
04:40	0 to 10 . And it shows our first two
04:43	building blocks one and 10 . If we take 10
04:46	and divided into 10 equal parts , each of those
04:49	parts is equal to one and if we take one
04:52	and divide it into 10 equal parts , then each
04:54	of those parts is a 10th . Now our number
04:57	line shows three building blocks 10 , 1 and a
05:00	10th . A 10th is a small number . We
05:03	can get even smaller building blocks if we keep dividing
05:06	by 10 . So let's take 1/10 and divide it
05:09	into 10 equal parts . This even smaller fraction is
05:13	called 1/100 which is one out of 100 . And
05:16	since it's one over 100 it would take 100 of
05:18	them to equal one . We can see this by
05:22	taking all 10 of our 10th and dividing each of
05:24	them into 10 parts . Now if we count up
05:27	all of those smaller parts , we'll find that there
05:29	are 100 of them . We could keep on dividing
05:32	with our number line to get smaller and smaller building
05:34	blocks , but I'll show you an even easier way
05:36	to find them . Let's list the building blocks we
05:39	have so far . Notice that on this side of
05:41	the one the first building block is 10 and on
05:44	the other side of the one the first building block
05:46	is 1/10 And back on this side are next building
05:50	block is 100 . And on the other side it's
05:52	one over 100 . Well then if the next building
05:55	block on this side is 1000 what do you suppose
05:57	the next building block on the other side will be
06:00	, yep , you guessed it ? One over 1000
06:03	or 2000 . Of course I could keep on going
06:07	in either direction . Getting powers of 10 that are
06:09	bigger and bigger . Whole numbers or smaller and smaller
06:12	fractions . But I think these are enough for now
06:15	. All right now that we have all these new
06:17	smaller or fractional building blocks it means that we can
06:20	count smaller and smaller parts of things . But to
06:23	do that we're going to need a new number place
06:25	for each of them . This will be called the
06:27	10th place because it counts 10ths and this will be
06:30	the hundreds place because it counts hundreds and this will
06:33	be the 1000th place because it counts thousands . To
06:36	see how the new number places work . Let's bring
06:38	back our last example digits to hundreds , five tens
06:41	and three ones . But this time let's add 6/10
06:45	by putting a six and the 10th place and 4/100
06:48	by putting a four in the hundreds place . Now
06:50	let's put our number of places back . Like we
06:52	used to seeing them . Oh it looks like there's
06:55	a problem . This number looks like 25,364 but we
07:00	only added tiny little fractions to R 253 . It
07:03	can't be that big . Here's our problem . We
07:06	can't tell which number of places which because they all
07:09	look the same . What we need is a kind
07:11	of marker that will help us tell them apart .
07:13	And that marker is called a decimal point . The
07:16	decimal point is just a dot that we always put
07:19	right here between the ones place and the 10th place
07:22	. That way we always know that the ones places
07:24	on the left of the decimal point and the 10th
07:26	places on the right there . That's better now .
07:30	Our number reads 253.64 That's how you read the decimal
07:34	point . When you get to it , you just
07:35	say point . So the decimal point is really just
07:39	a separator between the number of places that count whole
07:41	numbers on this side from the number of places that
07:44	count fractions on this side , these amounts are greater
07:47	than one and these amounts are smaller than one .
07:49	We call numbers that use the decimal point decimal numbers
07:53	or decimals for short . So that's how decimal numbers
07:56	work . And they're important because we use them to
07:58	convert a fraction from a division problem into a regular
08:01	number . In the next section we'll learn how to
08:04	convert some special fractions into decimals . But before that
08:07	let's do a quick review . If we take a
08:10	fraction and do the division will get an answer and
08:13	that answer is called the value of the fraction .
08:16	Our number system is called Base 10 . It uses
08:20	powers of 10 is building blocks for counting as well
08:23	as 10 different digits . Number of places are like
08:26	counters that hold one digit at a time and help
08:29	us count how many of each . Based in building
08:31	block a number is made of . There are based
08:34	in building blocks like 1 10 , 101,000 that help
08:38	us make really big numbers . There are also very
08:42	small based in building blocks for actions that are smaller
08:45	than one that help us make really small numbers .
08:48	These building blocks have names like 10th , hundreds and
08:52	thousands . The decimal point is a separator that goes
08:56	between the number of places that count values of one
08:58	or greater from the number of places that count values
09:01	smaller than one . To make sure you understand how
09:04	decimals work and how they relate to fractions . Be
09:06	sure to do those exercises , but you didn't see
09:09	that coming , did you ? Yeah , learn more
09:12	at math antics dot com .

Summarizer

DESCRIPTION:

OVERVIEW:

Math Antics - Fractions and Decimals is a free educational video by mathantics.

This page not only allows students and teachers view Math Antics - Fractions and Decimals videos but also find engaging Sample Questions, Apps, Pins, Worksheets, Books related to the following topics.