Subtracting Rational Numbers - By Anywhere Math
Transcript
| 00:0-1 | College these days is getting more and more expensive . | |
| 00:03 | Many students bank accounts hover right around zero . When | |
| 00:07 | I was going to school . I even had a | |
| 00:09 | few times when I over drew my bank account which | |
| 00:13 | meant my balance was actually negative . So let's say | |
| 00:17 | for example my account balance was negative $5.70 . And | |
| 00:22 | without knowing it , uh I went and just bought | |
| 00:25 | a candy bar for a dollar 15 . What would | |
| 00:28 | be my bank balance ? My account balance Now , | |
| 00:50 | Welcome to anywhere . Math . I'm Jeff Jacobson . | |
| 00:52 | And today we are talking about subtracting rational numbers . | |
| 00:57 | Here we go . Just So my account balance was | |
| 01:02 | negative $5.70 . So I'm spending more money than I | |
| 01:07 | actually had in this case , which is why it's | |
| 01:09 | negative . Uh and then maybe I didn't know I | |
| 01:12 | withdrew or over drew and I just went and bought | |
| 01:16 | a candy bar like normal for a dollar 15 . | |
| 01:19 | So the question is , what is my new balance | |
| 01:22 | ? Well when we buy something , we're actually taking | |
| 01:26 | money out of our bank account , were withdrawing money | |
| 01:30 | . Uh So that's like subtracting . So the problem | |
| 01:34 | we're gonna set up is I'm starting with negative $5.70 | |
| 01:41 | in my bank account . I bought a candy bar | |
| 01:44 | for $1.15 , which means my bank account is not | |
| 01:49 | gonna increase , it's actually going to get more negative | |
| 01:53 | , right ? I'm gonna owe more money . So | |
| 01:56 | I'm going to subtract $1.15 . So that's essentially what's | |
| 02:02 | happening and we know when we're subtracting integers , we've | |
| 02:07 | done that before . The subtracting an integer is the | |
| 02:10 | same thing as adding its opposite . The same rules | |
| 02:14 | apply when we're subtracting rational numbers , whether it's decimals | |
| 02:19 | or fractions or mixed numbers , the same rules apply | |
| 02:24 | . So subtracting an integer or a rational number in | |
| 02:28 | this case is the same as adding its opposite . | |
| 02:32 | So I'm gonna rewrite this As negative $5.70 plus adding | |
| 02:38 | the opposite . This was a positive $1.15 . So | |
| 02:43 | I'm gonna add a negative $1.15 . All we're doing | |
| 02:48 | is just changing it to an addition problem . And | |
| 02:52 | now we're adding two negatives right there , the same | |
| 02:55 | signs . So when we add them , I'm going | |
| 02:57 | to add these basically just look at just look at | |
| 03:02 | the absolute value of them , add them together . | |
| 03:05 | And then my answer is going to be negative . | |
| 03:07 | So adding that together 5 70 plus 1 15 lined | |
| 03:13 | up the decimals right ? 1 15 And I get | |
| 03:17 | 586 . And then I got to remember these were | |
| 03:23 | negative . So my answer is gonna be negative . | |
| 03:25 | So my new balance now is negative $6.85 . Okay | |
| 03:36 | . And the bank would not be very happy with | |
| 03:38 | me . Okay let's try an example . Yeah . | |
| 03:42 | Example one negative four and 1/7 minus a negative 6/7 | |
| 03:48 | same thing we talked about before . Subtracting a rational | |
| 03:52 | number or an integer . It doesn't matter . Is | |
| 03:54 | the same thing as adding its opposite . So my | |
| 03:57 | first step is I'm gonna changes to an addition problem | |
| 04:01 | . So negative four and 1/7 doesn't change subtraction becomes | |
| 04:07 | addition . Mhm . The -6 7th . The opposite | |
| 04:11 | of that is 6/7 . Mhm . Okay . Now | |
| 04:17 | I gotta think . Okay I've got a mixed number | |
| 04:21 | plus a fraction . There's multiple ways to do this | |
| 04:25 | . If you're really comfortable with fractions and mixed numbers | |
| 04:28 | you could probably do this in your head and think | |
| 04:31 | well especially because they have common denominators already . But | |
| 04:35 | if not an easy way to do this is to | |
| 04:38 | just change them , change the mixed number to an | |
| 04:40 | improper fraction . So that's what we're gonna do . | |
| 04:44 | So to change it to an improper fraction I'm gonna | |
| 04:47 | do the denominator times a whole number . So seven | |
| 04:49 | times four is 28 plus one is 29 . So | |
| 04:52 | I have negative 29 over seven . Denominator stays the | |
| 04:57 | same plus Since that's positive . I don't really need | |
| 05:01 | the parentheses anymore . So 6/7s denominators are the same | |
| 05:07 | , which is great . So all I need to | |
| 05:08 | do is add the enumerators . Mm So denominator does | |
| 05:13 | not change negative 29 plus six is -23/7 which is | |
| 05:23 | an improper fraction . So I'm going to convert it | |
| 05:25 | back to a mixed number Seven into 23 goes three | |
| 05:30 | times and I would have to seven's left over and | |
| 05:34 | I have to remember it's negative so that is negative | |
| 05:38 | three And to 7th . Let's try another example . | |
| 05:45 | Okay , example to 12.8 -21.6 . This is gonna | |
| 05:49 | be our last example . If you want to give | |
| 05:51 | this a shot on your own positive video and go | |
| 05:53 | for it . Here we go . Same thing subtracting | |
| 05:57 | a rational number . I'm going to change it to | |
| 05:59 | an addition problem first . So that's going to become | |
| 06:02 | 12.8 plus a negative 21.6 . Now adding rational numbers | |
| 06:13 | , we've already done that . If you still need | |
| 06:14 | some practice , look at the previous video . But | |
| 06:17 | here we've got different signs . We're adding a positive | |
| 06:21 | with a negative , which means some things are canceling | |
| 06:24 | out and to figure out what's left over . We | |
| 06:28 | need to subtract . So I'm gonna take the absolute | |
| 06:30 | value of these , right ? The absolute value of | |
| 06:35 | 12.8 is just 12.8 . Absolute value of negative . | |
| 06:38 | 21.6 is 21.6 Which means I'm gonna subtract the greater | |
| 06:45 | number . 21.6 -12.8 . Yeah 21.6 -12.8 . I'm | |
| 06:54 | lining the decimals up again . I'm subtracting 12.8 . | |
| 07:00 | You need to borrow zero . That becomes 16 . | |
| 07:03 | subtract I get eight Decimal points . Stay in line | |
| 07:08 | . Got to borrow again . That becomes 10 eight | |
| 07:11 | and that zero now I need to remember . Last | |
| 07:15 | step is I gotta look which one had the greater | |
| 07:18 | absolute value And that's the 21.6 . And because that | |
| 07:23 | was negative Well I'm gonna have negative 8.8 left over | |
| 07:29 | because basically this negative cancels out all that 12.8 And | |
| 07:34 | then there's still negative 8.8 left over . Okay here's | |
| 07:43 | some to try on your own . Thank you so | |
| 07:55 | much for watching and as always if you like this | |
| 07:57 | video please subscribe . Mhm . |
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