Math Antics - Factoring - By mathantics
Transcript
00:03 | Uh huh Hi and welcome to Math antics . In | |
00:08 | today's lesson , we're going to learn all about factoring | |
00:11 | . Factoring is a math operation . It's something you | |
00:14 | do to a number now with the other math operations | |
00:17 | you've done so far , you're given two or more | |
00:19 | numbers to work with . But with factoring you only | |
00:22 | get one number . That's because factoring is like being | |
00:25 | given the answer to a multiplication problem and then having | |
00:28 | to figure out what that problem was . So you | |
00:30 | can think of factoring as unm multiplying When you multiply | |
00:34 | , you take two numbers and multiply them together to | |
00:37 | get one number . And when you factor you take | |
00:39 | one number and figure out what two numbers you can | |
00:42 | multiply together to get that number . For example , | |
00:45 | let's say you're asked to factor the number 10 . | |
00:48 | Now that means that you need to figure out what | |
00:49 | numbers you can multiply together to get 10 . If | |
00:53 | you know your multiplication table , you'll remember that two | |
00:55 | times five equals 10 . That means that two and | |
00:58 | five are factors of 10 . So factors are just | |
01:01 | the parts of a multiplication problem . And factoring is | |
01:04 | figuring out what those parts are . I'm sure some | |
01:07 | of you are wondering why would I ever want to | |
01:09 | factor a number now ? That's a good question and | |
01:12 | I have a good answer . Factoring can make solving | |
01:15 | some math problems easier . For example , factoring is | |
01:19 | really useful for simplifying fractions . By breaking a number | |
01:22 | up into its factors you can sometimes cancel out factors | |
01:25 | that aren't really needed for now though , you just | |
01:28 | need to learn what factoring is and how to do | |
01:30 | it . So let's see another example . Let's factor | |
01:33 | the number 24 for this one . I think I'll | |
01:35 | use my multiplication table . Let's see here . Alright | |
01:39 | , well four times six is 24 . So that | |
01:41 | means that four and six are factors of 24 . | |
01:44 | Now , hold on , I'm sure some of you | |
01:46 | have seen that three times eight is also 24 that's | |
01:49 | true . We could have decided to factor 24 in | |
01:52 | 23 times eight instead . So which of the factories | |
01:54 | is right , Is it four and six or three | |
01:57 | and eight ? Actually they're both right . There can | |
02:00 | be more than one way to factor a number . | |
02:02 | That's one of the things that might make factory in | |
02:04 | a little confusing . At first you're used to having | |
02:06 | just one right answer because when you add subtract multiply | |
02:10 | or divide there is just one right answer . But | |
02:12 | when you factor or a new multiply a number , | |
02:15 | you might find that there's more than one correct way | |
02:17 | you can do it . So we can see that | |
02:19 | the number 24 has quite a few factors for is | |
02:22 | a factor six is a factor three is a factor | |
02:25 | and eight is a factor . The fact that each | |
02:28 | of these numbers is a factor of 24 means that | |
02:30 | each of them can divide evenly into 24 and when | |
02:33 | I say divide evenly , I mean that it will | |
02:35 | divide in without a remainder . For example , if | |
02:38 | we take our first factor four and divide it into | |
02:41 | 24 using a calculator , our answer will be 64 | |
02:45 | divides into 24 6 times with no remainder . But | |
02:49 | what if we try to divide 24 by a number | |
02:51 | that isn't one of our factors like the number seven | |
02:54 | , If we try 24 divided by seven on a | |
02:56 | calculator , we get 3.42857 , Blah Blah Blah . | |
03:02 | A long decimal number that didn't divide it evenly because | |
03:05 | there's a big remainder . What we just did is | |
03:08 | called testing for the visibility Testing for the visibility is | |
03:11 | a way to find out if a number is a | |
03:12 | factor of another number with the test we just did | |
03:16 | . We confirmed that four is a factor of 24 | |
03:18 | , but seven is not . Sometimes you may be | |
03:21 | asked to find all the factors of the number . | |
03:23 | If that happens , you can use testing for the | |
03:25 | visibility to solve the problem , To see how it | |
03:28 | works . Let's try to find all the factors of | |
03:30 | 24 . We already know four of them . But | |
03:33 | there's a lot more numbers we can test , fortunately | |
03:35 | , we only need to test numbers that are less | |
03:37 | than half of the number we're testing and since half | |
03:40 | of 24 is 12 , we just need to test | |
03:42 | the numbers one through 12 to keep things organized . | |
03:46 | Let's list the numbers we're going to test and we'll | |
03:48 | circle the factors that we already know 346 and eight | |
03:52 | . We can also cross out the seven since we | |
03:55 | already tested it and found out it wasn't a factor | |
03:58 | . Okay . Now for the numbers we haven't tested | |
04:00 | yet . Let's start with one . Well , of | |
04:02 | course one is a factor because one will divide evenly | |
04:05 | into any whole number . So one is always a | |
04:08 | factor . And since one is a factor then that | |
04:10 | means that 24 is also a factor because one times | |
04:14 | 24 equals 24 . It might seem weird that a | |
04:17 | number is always a factor of itself . But it's | |
04:19 | true knowing that helps you get started listening the factors | |
04:23 | because you can always include one and the number itself | |
04:27 | . Now let's move on and test too . If | |
04:29 | we divide 24 x two , we get 12 . | |
04:32 | So yes , two is a factor because it divided | |
04:35 | evenly . You can factor 24 into two times 12 | |
04:39 | . That means that we can also circle 12 as | |
04:41 | a factor of 24 . So any time you do | |
04:44 | a visibility test and the number you're checking passes the | |
04:47 | test then the answer you get from dividing will also | |
04:50 | pass the test . It will also be a factor | |
04:53 | That will speed things up because we know we don't | |
04:55 | have to test 12 . Okay , let's move on | |
04:58 | to the next number . We haven't checked . 5 | |
05:01 | 24 divided by five equals 4.8 . Well that didn't | |
05:05 | divide evenly because our answer is a decimal number . | |
05:07 | That means that five is not a factor of 24 | |
05:11 | . Next we'll try 9 , 24 divided by nine | |
05:14 | equals 2.66666 . That's definitely not a factor . Okay | |
05:19 | , how about 10 24 divided by 10 equals 2.4 | |
05:23 | , Nope . That's a decimal number . So 10 | |
05:26 | is not a factor . It looks like the last | |
05:28 | one we have to try is 1124 , divided by | |
05:31 | 11 equals 2.181818 . That's not a factor either . | |
05:36 | All right . Since we've tested all the numbers that | |
05:39 | are less than half of 24 , we found all | |
05:41 | of its possible factors and they are 123468 12 and | |
05:48 | 24 . Now I know that might seem like a | |
05:51 | lot of work but fortunately you probably won't have to | |
05:54 | do many of those problems . The important thing is | |
05:56 | just to know what factoring is and how you can | |
05:59 | use testing for the visibility to help you find factors | |
06:02 | . Alright , that wraps up this lesson but since | |
06:05 | actually doing math is the best way to learn it | |
06:07 | . Be sure to try the exercise problems for this | |
06:09 | section . Thanks for watching and I'll see you next | |
06:12 | time learn more at math . Antics dot com . |
Summarizer
DESCRIPTION:
OVERVIEW:
Math Antics - Factoring is a free educational video by mathantics.
This page not only allows students and teachers view Math Antics - Factoring videos but also find engaging Sample Questions, Apps, Pins, Worksheets, Books related to the following topics.