Math Antics - Subtracting Mixed Numbers - Free Educational videos for Students in K-12

Math Antics - Subtracting Mixed Numbers - By Mathantics

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00:03	Uh huh . Hi I'm rob . Welcome to Math
00:07	Antics . In our previous lesson we learned how to
00:10	add mixed numbers and in this lesson we're going to
00:12	learn how to subtract them . Subtraction is always a
00:15	little trickier than addition because subtraction does not have the
00:19	community of property . That means that the order of
00:21	the numbers you're subtracting matters and you can't switch it
00:24	like you can with addition subtraction is also tricky because
00:28	if you try subtracting a number from a smaller number
00:30	like 1 -5 you get a negative answer . Fortunately
00:34	we're not going to cover any problems that give negative
00:36	answers in this video . But as you'll see in
00:38	a few minutes there are cases where it seems like
00:41	you need to subtract a bigger number from a smaller
00:43	one at first all of this means that subtracting mixed
00:47	numbers can be quite a bit more complicated than adding
00:50	them . But don't worry we'll take it one step
00:52	at a time and it will help a lot if
00:54	you make sure that you have a good understanding of
00:56	topics like adding mixed numbers , subtracting fractions , order
01:00	of operations and multi digit subtraction . Because this lesson
01:03	built on all of those concepts . Okay to see
01:07	why subtracting mixed numbers is trickier than adding them .
01:10	Let's have a look at two problems side by side
01:12	. Five plus two and one third and five minus
01:15	two and one third . We learned how to do
01:17	problems like the first one in the previous video about
01:20	adding mixed numbers since two and one third just means
01:23	two plus one third . We learned that we could
01:25	rewrite the problem like this and simply add up the
01:28	whole number of parts to get the whole number part
01:30	of the answer . Five plus two is seven so
01:33	the answer is seven and one third . But if
01:36	we try to do the same thing with subtraction we're
01:38	going to get the wrong answer . If we rewrite
01:41	two and one third as two plus one third ,
01:43	it looks like we could just subtract the whole numbers
01:46	five minus two is three which leaves three plus one
01:48	third or three and one third as the answer .
01:51	But it turns out that's not correct . So what
01:54	did we do wrong ? Well when we subtract a
01:56	mixed number , we need to subtract the entire mixed
01:59	number . We need to subtract the whole number part
02:01	and we need to subtract the fraction part But we
02:04	didn't subtract the 1/3 , we added it . That's
02:07	because when we rewrote the mixed number as a sum
02:10	of a whole number and a fraction we forgot or
02:13	we didn't realize that they form a group , we
02:16	just put the two plus one third , right after
02:19	the minus sign . And it made it look like
02:21	we should subtract the two and add the one third
02:24	. But we actually should have subtracted both of them
02:26	. One way to avoid that mistake is to use
02:29	parentheses around the mixed number you're subtracting so you remember
02:32	that its parts form a group and you need to
02:34	apply the minus sign to the whole group and you
02:37	can only get rid of the parentheses after you apply
02:40	or distribute the subtraction to each member of the group
02:43	like this minus two minus one third . Now that
02:47	we have the problem written correctly , we'll get the
02:49	right answer . If we do these math operations going
02:52	from left to right , we have 5 -2 which
02:55	is three . But then for the last step we
02:57	need to subtract one third from three . That might
03:01	seem hard to do unless you remember what we learned
03:03	about whole fractions . In the last video when adding
03:06	mixed numbers , sometimes we'd get an answer like this
03:09	two and three thirds , but since three thirds is
03:12	what I call a whole fraction , its value is
03:14	just one . And we learned that we could simplify
03:17	an answer like that . Two and three thirds is
03:19	two plus one which is three . Well , how
03:22	about if we just do that same process in reverse
03:25	instead of simplifying let's unseen cliff . I we're trying
03:29	to take one third away from three . Right ?
03:31	So let's rewrite three as two plus one and then
03:34	let's rewrite two plus one is two plus 3/3 .
03:37	Does the problem look easier to do . Now we
03:40	converted part of the whole number into the whole fraction
03:43	3/3 . And we already know how to subtract fractions
03:46	3/3 minus 1/3 is to over three . So that
03:50	means our final answer is 2.2/3 . So as you
03:54	can see , subtracting mixed numbers can be a little
03:56	complicated . But not all problems are that hard .
03:59	Some are pretty easy like this . one , six
04:02	and 4/5 minus one and 3/5 . We still need
04:05	to remember that the mixed numbers form groups . So
04:08	we have to subtract both parts , but that's where
04:11	the stacked format that we learned about in the last
04:13	video can really help us out . Since the order
04:16	of a subtraction problem is important . We need to
04:18	be sure to put the mixed number that we're starting
04:20	with on top and the mixed number that we're taking
04:23	away on the bottom and doing that helps us remember
04:26	that both parts of a mixed numbers are being subtracted
04:29	. Even if we don't put parentheses around them .
04:31	To remind us that's because we'll subtract the parts column
04:34	by column , just like we would and multi digit
04:37	subtraction , we'll subtract the fraction on the bottom from
04:40	the fraction on the top and then we'll subtract the
04:42	whole number on the bottom from the whole number on
04:44	the top . 4/5 minus 3/5 is 1/5 And 6
04:49	-1 is five . So the answer is just five
04:53	and 1/5 . See that really was easy and that's
04:56	why I recommend using stack form whenever you can for
04:59	subtracting mixed numbers . It will help you remember that
05:01	both parts of a mixed numbers are being subtracted without
05:04	having to worry about groups or parentheses . But even
05:08	though the stack form is a great way to keep
05:10	from getting confused about groups , it doesn't make every
05:12	problem quite that simple . For example . Let's try
05:15	the problem . Five and 1/7 minus two and 3/7
05:19	. Unless you stack form again , we're starting out
05:22	with five and 1/7 . So it goes on top
05:24	and two and 3/7 goes on the bottom . But
05:27	when we try to subtract the fractions column you'll see
05:29	that we have a little problem . 1/7 is less
05:32	than 3/7 so we can't subtract it without getting a
05:35	negative number which we'd really like to avoid . So
05:38	what do we do now ? Well do you remember
05:41	what you do in multi digit subtraction ? When you
05:43	have to subtract a bigger digit from a smaller one
05:45	, yep you borrow or regroup from the column to
05:49	the left . And we can do something really similar
05:51	to that with mixed numbers . We can make the
05:54	fraction part of a mixed number bigger by borrowing from
05:57	the whole number part . In the video about adding
06:00	mixed numbers . We learned that a mixed number with
06:03	a fraction part . That's improper is bad form because
06:06	you can simplify out a whole fraction and then add
06:08	it to the whole number part . Well we can
06:11	do that process in reverse also . We can subtract
06:14	out one as a whole fraction from the whole number
06:17	part and add it to the fraction part to get
06:19	an improper fraction . And even though that's considered bad
06:22	form , it's ok because it's not our final answer
06:25	and it helps us subtract the fraction column without getting
06:28	a negative fraction . In this example we do that
06:31	by changing the whole number part five into four plus
06:34	one and then changing four plus one into four plus
06:37	7/7 . And finally we can combine that 7/7 with
06:42	the 1/7 to get 8/7 . now the fraction on
06:45	top is big enough to subtract 3/7 from 8/7 minus
06:50	3/7 is 5/7 . And then we just need to
06:53	subtract the whole number of parts . The top hole
06:56	number used to be five but we borrowed from it
06:59	. So now it's 44 minus two equals two .
07:02	So our answer is two and 5/7 . Let's try
07:05	another example to make sure you've got it . And
07:07	let's make it a story problem this time . Suppose
07:10	there's this guy who's a builder named rob and suppose
07:13	he needs to fix something by subtracting the mixed number
07:16	one and 5/8 from six and 1/8 . Can you
07:18	fix it ? Yes , I can . Well ,
07:22	at least with the help of my trusty cat ,
07:23	Richard , where did that rascal runoff to Richard ?
07:27	Richard ? Oh well the first thing we need to
07:30	do is put these in stacked form with the number
07:33	I'm taken away on the bottom . Then I need
07:36	to subtract the fractions . But I notice that the
07:38	fraction on top is less than the fraction on the
07:41	bottom . So I need to make the fraction on
07:43	top bigger by borrowing from the whole number part .
07:46	I can replace the six with five plus one and
07:49	I can replace five plus one with five plus 8/8
07:53	. To get the whole fraction I need to add
07:55	to the top fraction 8/8 plus 1/8 is 9/8 .
08:00	So now I can subtract the fraction column because the
08:02	fraction on top is bigger . 9/8 minus 5/8 is
08:07	4/8 . And then I can subtract the whole numbers
08:10	five minus one is four . So the answer is
08:13	four and 4/8 . Does that look right to you
08:15	? Richard ? You're right . Four eights can simplify
08:19	to one half . So my final answer is four
08:22	and one half . Thanks for your help . Richard
08:25	. Good job rob the builder . So now you
08:27	know how to subtract mixed numbers . Some problems will
08:30	be easy . Like our second example where you can
08:32	just subtract the fraction parts and the whole number parts
08:35	. But in other problems you may need to borrow
08:37	or regroup using that unseen cliff eyeing procedure . And
08:41	remember that the stacked form is a great way to
08:44	keep everything straight . Of course you may also need
08:47	to solve problems where the mixed numbers have unlike fractions
08:50	and you'll need to change them into like fractions before
08:52	you can subtract . But that works the same way
08:55	as you saw in the last video so you already
08:57	know how to handle that . I know I'm always
08:59	saying it , but that's because it's true . The
09:01	way to really learn math is to practice by doing
09:04	some problems on your own . As always . Thanks
09:06	for watching Math Antics and I'll see you next time
09:09	, learn more at Math antics dot com

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