WEBVTT
Kind: captions
Language: en

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fractions<00:00:00.840><c> represent</c><00:00:01.400><c> pieces</c><00:00:01.719><c> or</c><00:00:01.880><c> a</c><00:00:02.040><c> part</c><00:00:02.200><c> of</c>

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fractions represent pieces or a part of
 

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fractions represent pieces or a part of
something<00:00:03.560><c> in</c><00:00:03.679><c> a</c><00:00:03.840><c> picture</c><00:00:04.200><c> we</c><00:00:04.279><c> can</c><00:00:04.440><c> display</c>

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something in a picture we can display
 

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something in a picture we can display
this<00:00:05.040><c> by</c><00:00:05.200><c> taking</c><00:00:05.400><c> a</c><00:00:05.520><c> full</c><00:00:05.759><c> shape</c><00:00:06.080><c> like</c><00:00:06.200><c> a</c>

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this by taking a full shape like a
 

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this by taking a full shape like a
circle<00:00:06.919><c> and</c><00:00:07.080><c> splitting</c><00:00:07.439><c> it</c><00:00:07.560><c> up</c><00:00:07.720><c> into</c><00:00:08.000><c> equal</c>

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circle and splitting it up into equal
 

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circle and splitting it up into equal
parts<00:00:09.040><c> you</c><00:00:09.160><c> can</c><00:00:09.320><c> choose</c><00:00:09.639><c> how</c><00:00:09.760><c> many</c><00:00:10.000><c> parts</c><00:00:10.280><c> you</c>

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parts you can choose how many parts you
 

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parts you can choose how many parts you
want<00:00:10.559><c> to</c><00:00:10.719><c> split</c><00:00:11.000><c> it</c><00:00:11.120><c> up</c><00:00:11.240><c> into</c><00:00:11.559><c> in</c><00:00:11.679><c> this</c><00:00:11.840><c> case</c>

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want to split it up into in this case
 

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want to split it up into in this case
we're<00:00:12.160><c> looking</c><00:00:12.400><c> at</c><00:00:12.559><c> four</c><00:00:13.360><c> so</c><00:00:13.519><c> if</c><00:00:13.639><c> we</c><00:00:13.839><c> cut</c><00:00:14.040><c> the</c>

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we're looking at four so if we cut the
 

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we're looking at four so if we cut the
circle<00:00:14.559><c> into</c><00:00:14.799><c> four</c><00:00:15.120><c> equal</c><00:00:15.440><c> pieces</c><00:00:16.279><c> we'll</c><00:00:16.520><c> have</c>

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circle into four equal pieces we'll have
 

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circle into four equal pieces we'll have
four<00:00:17.160><c> out</c><00:00:17.320><c> of</c><00:00:17.439><c> four</c><00:00:17.960><c> or</c><00:00:18.520><c> still</c><00:00:18.760><c> the</c><00:00:18.880><c> whole</c><00:00:19.160><c> one</c>

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four out of four or still the whole one
 

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four out of four or still the whole one
in<00:00:20.279><c> the</c><00:00:20.400><c> orange</c><00:00:20.760><c> diagram</c><00:00:21.199><c> in</c><00:00:21.279><c> the</c><00:00:21.400><c> corner</c><00:00:21.800><c> you</c>

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in the orange diagram in the corner you
 

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in the orange diagram in the corner you
can<00:00:22.039><c> see</c><00:00:22.279><c> you</c><00:00:22.359><c> can</c><00:00:22.560><c> then</c><00:00:22.760><c> start</c><00:00:23.039><c> looking</c><00:00:23.279><c> at</c>

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can see you can then start looking at
 

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can see you can then start looking at
taking<00:00:23.880><c> pieces</c><00:00:24.880><c> of</c><00:00:25.000><c> the</c><00:00:25.160><c> hole</c><00:00:25.519><c> for</c><00:00:25.680><c> example</c>

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taking pieces of the hole for example
 

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taking pieces of the hole for example
you<00:00:26.240><c> can</c><00:00:26.400><c> take</c><00:00:26.640><c> one4</c><00:00:27.279><c> away</c><00:00:27.880><c> and</c><00:00:28.039><c> leave</c>

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you can take one4 away and leave
 

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you can take one4 away and leave
3/4<00:00:30.000><c> 1</c><00:00:30.119><c> over</c><00:00:30.320><c> 4</c><00:00:30.640><c> you</c><00:00:30.800><c> take</c><00:00:31.000><c> away</c><00:00:31.720><c> and</c><00:00:31.800><c> then</c><00:00:32.000><c> 3</c>

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3/4 1 over 4 you take away and then 3
 

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3/4 1 over 4 you take away and then 3
over<00:00:32.480><c> 4</c><00:00:33.000><c> you</c><00:00:33.160><c> leave</c>

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over 4 you leave
 

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over 4 you leave
behind<00:00:35.920><c> when</c><00:00:36.120><c> representing</c><00:00:36.559><c> a</c><00:00:36.719><c> fraction</c><00:00:37.120><c> you</c>

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behind when representing a fraction you
 

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behind when representing a fraction you
always<00:00:37.520><c> need</c><00:00:37.680><c> two</c><00:00:37.960><c> numbers</c><00:00:38.280><c> you</c><00:00:38.360><c> need</c><00:00:38.520><c> a</c><00:00:38.719><c> top</c>

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always need two numbers you need a top
 

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always need two numbers you need a top
and<00:00:39.200><c> a</c><00:00:39.399><c> bottom</c><00:00:40.399><c> technically</c><00:00:40.920><c> the</c><00:00:41.079><c> top</c><00:00:41.280><c> is</c>

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and a bottom technically the top is
 

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and a bottom technically the top is
called<00:00:41.640><c> the</c><00:00:41.760><c> numerator</c><00:00:42.440><c> and</c><00:00:42.600><c> the</c><00:00:42.760><c> bottom</c><00:00:43.039><c> is</c>

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called the numerator and the bottom is
 

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called the numerator and the bottom is
called<00:00:43.399><c> the</c><00:00:43.600><c> denominator</c><00:00:44.600><c> however</c><00:00:44.840><c> in</c><00:00:45.039><c> most</c>

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called the denominator however in most
 

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called the denominator however in most
math<00:00:45.600><c> classes</c><00:00:46.120><c> if</c><00:00:46.199><c> you</c><00:00:46.320><c> just</c><00:00:46.480><c> talk</c><00:00:46.640><c> about</c><00:00:46.840><c> the</c>

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math classes if you just talk about the
 

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math classes if you just talk about the
top<00:00:47.199><c> and</c><00:00:47.320><c> the</c><00:00:47.440><c> bottom</c><00:00:47.920><c> people</c><00:00:48.160><c> won't</c><00:00:48.440><c> usually</c>

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top and the bottom people won't usually
 

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top and the bottom people won't usually
correct<00:00:49.120><c> you</c><00:00:49.879><c> so</c><00:00:50.079><c> here</c><00:00:50.239><c> you</c><00:00:50.320><c> can</c><00:00:50.440><c> see</c><00:00:50.640><c> an</c>

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correct you so here you can see an
 

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correct you so here you can see an
example<00:00:51.199><c> of</c><00:00:51.399><c> 1</c><00:00:51.640><c> over</c><00:00:51.879><c> two</c><00:00:52.280><c> we've</c><00:00:52.480><c> got</c><00:00:52.559><c> a</c><00:00:52.680><c> circle</c>

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example of 1 over two we've got a circle
 

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example of 1 over two we've got a circle
cut<00:00:53.199><c> in</c><00:00:53.440><c> half</c><00:00:54.280><c> and</c><00:00:54.399><c> then</c><00:00:54.760><c> in</c><00:00:54.960><c> purple</c><00:00:55.359><c> we</c><00:00:55.559><c> have</c>

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cut in half and then in purple we have
 

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cut in half and then in purple we have
10<00:00:56.280><c> over</c><00:00:56.600><c> 15</c><00:00:57.160><c> so</c><00:00:57.320><c> we</c><00:00:57.480><c> have</c><00:00:57.680><c> 10</c><00:00:58.120><c> purple</c><00:00:58.480><c> Parts</c>

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10 over 15 so we have 10 purple Parts
 

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10 over 15 so we have 10 purple Parts
out<00:00:58.920><c> of</c><00:00:59.120><c> 15</c><00:00:59.680><c> total</c><00:01:00.199><c> pieces</c><00:01:01.160><c> a</c><00:01:01.320><c> fraction</c><00:01:01.840><c> also</c>

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out of 15 total pieces a fraction also
 

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out of 15 total pieces a fraction also
represents<00:01:02.719><c> a</c><00:01:03.080><c> division</c><00:01:04.080><c> the</c><00:01:04.239><c> notation</c><00:01:04.640><c> for</c><00:01:04.799><c> a</c>

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represents a division the notation for a
 

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represents a division the notation for a
fraction<00:01:05.479><c> also</c><00:01:05.880><c> represents</c><00:01:06.400><c> a</c><00:01:06.560><c> division</c>

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fraction also represents a division
 

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fraction also represents a division
because<00:01:07.560><c> a</c><00:01:07.720><c> fraction</c><00:01:08.119><c> and</c><00:01:08.280><c> division</c><00:01:08.759><c> actually</c>

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because a fraction and division actually
 

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because a fraction and division actually
works<00:01:09.320><c> the</c><00:01:09.439><c> same</c><00:01:09.720><c> way</c><00:01:10.560><c> so</c><00:01:10.799><c> anytime</c><00:01:11.119><c> you</c><00:01:11.240><c> see</c>

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works the same way so anytime you see
 

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works the same way so anytime you see
one<00:01:11.680><c> number</c><00:01:12.159><c> over</c><00:01:12.479><c> top</c><00:01:12.680><c> of</c><00:01:12.759><c> the</c><00:01:12.880><c> other</c><00:01:13.119><c> you</c><00:01:13.240><c> can</c>

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one number over top of the other you can
 

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one number over top of the other you can
actually<00:01:13.720><c> replace</c><00:01:14.040><c> it</c><00:01:14.280><c> with</c><00:01:14.520><c> any</c><00:01:14.799><c> of</c><00:01:15.000><c> the</c>

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actually replace it with any of the
 

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actually replace it with any of the
following<00:01:15.720><c> kinds</c><00:01:15.960><c> of</c><00:01:16.119><c> notation</c><00:01:16.680><c> you</c><00:01:16.759><c> could</c>

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following kinds of notation you could
 

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following kinds of notation you could
have<00:01:17.119><c> 3</c><00:01:17.439><c> /</c><00:01:18.080><c> 5</c><00:01:18.600><c> using</c><00:01:18.880><c> the</c><00:01:19.040><c> line</c><00:01:19.280><c> with</c><00:01:19.439><c> two</c><00:01:19.680><c> dots</c>

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have 3 / 5 using the line with two dots
 

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have 3 / 5 using the line with two dots
in<00:01:20.079><c> the</c><00:01:20.200><c> top</c><00:01:20.360><c> and</c><00:01:20.560><c> bottom</c><00:01:21.560><c> you</c><00:01:21.680><c> could</c><00:01:21.920><c> have</c><00:01:22.240><c> 3</c>

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in the top and bottom you could have 3
 

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in the top and bottom you could have 3
ID<00:01:23.119><c> 5</c><00:01:23.600><c> using</c><00:01:24.000><c> the</c><00:01:24.119><c> long</c><00:01:24.400><c> division</c><00:01:25.119><c> notation</c>

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ID 5 using the long division notation
 

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ID 5 using the long division notation
you<00:01:26.280><c> could</c><00:01:26.520><c> have</c><00:01:26.799><c> 3</c><00:01:27.360><c> over</c><00:01:27.759><c> five</c><00:01:28.159><c> but</c><00:01:28.280><c> written</c>

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you could have 3 over five but written
 

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you could have 3 over five but written
with<00:01:28.759><c> just</c><00:01:28.880><c> a</c><00:01:29.079><c> slash</c><00:01:30.000><c> and</c><00:01:30.119><c> you</c><00:01:30.200><c> can</c><00:01:30.360><c> have</c><00:01:30.479><c> the</c>

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with just a slash and you can have the
 

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with just a slash and you can have the
notation<00:01:31.079><c> we</c><00:01:31.200><c> were</c><00:01:31.360><c> using</c><00:01:31.759><c> of</c><00:01:31.920><c> three</c><00:01:32.280><c> ID</c><00:01:32.799><c> 5</c><00:01:33.119><c> 3</c>

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notation we were using of three ID 5 3
 

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notation we were using of three ID 5 3
over<00:01:33.720><c> five</c><00:01:34.600><c> these</c><00:01:34.720><c> are</c><00:01:34.920><c> all</c><00:01:35.159><c> different</c>

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over five these are all different
 

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over five these are all different
notations<00:01:35.920><c> for</c><00:01:36.159><c> division</c><00:01:36.720><c> and</c><00:01:36.799><c> you</c><00:01:36.880><c> should</c>

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notations for division and you should
 

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notations for division and you should
try<00:01:37.200><c> to</c><00:01:37.320><c> get</c><00:01:37.479><c> comfortable</c><00:01:38.000><c> with</c><00:01:38.159><c> all</c><00:01:38.280><c> of</c><00:01:38.840><c> them</c>

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try to get comfortable with all of them
 

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try to get comfortable with all of them
now<00:01:39.960><c> whenever</c><00:01:40.240><c> you</c><00:01:40.360><c> have</c><00:01:40.439><c> a</c><00:01:40.600><c> fraction</c><00:01:41.079><c> you</c>

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now whenever you have a fraction you
 

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now whenever you have a fraction you
must<00:01:41.640><c> have</c><00:01:42.280><c> equal</c><00:01:42.680><c> parts</c><00:01:43.680><c> you</c><00:01:43.840><c> cannot</c><00:01:44.200><c> have</c>

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must have equal parts you cannot have
 

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must have equal parts you cannot have
someone's<00:01:44.799><c> half</c><00:01:45.040><c> being</c><00:01:45.280><c> bigger</c><00:01:45.600><c> than</c><00:01:45.920><c> the</c>

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someone's half being bigger than the
 

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someone's half being bigger than the
other<00:01:46.240><c> person's</c><00:01:47.159><c> half</c><00:01:48.159><c> you</c><00:01:48.320><c> also</c><00:01:48.520><c> don't</c><00:01:48.719><c> have</c>

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other person's half you also don't have
 

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other person's half you also don't have
to<00:01:48.960><c> use</c><00:01:49.159><c> circles</c><00:01:49.560><c> as</c><00:01:49.680><c> the</c><00:01:49.799><c> only</c><00:01:50.040><c> shape</c><00:01:50.399><c> you</c>

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to use circles as the only shape you
 

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to use circles as the only shape you
could<00:01:50.640><c> use</c><00:01:50.880><c> rectangles</c><00:01:51.479><c> you</c><00:01:51.600><c> could</c><00:01:51.759><c> use</c>

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could use rectangles you could use
 

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could use rectangles you could use
triangles<00:01:52.960><c> you</c><00:01:53.079><c> could</c><00:01:53.240><c> use</c><00:01:53.399><c> a</c><00:01:53.640><c> square</c>

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triangles you could use a square
 

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triangles you could use a square
anything<00:01:54.960><c> will</c><00:01:55.159><c> work</c><00:01:55.439><c> as</c><00:01:55.560><c> long</c><00:01:55.680><c> as</c><00:01:55.799><c> you</c>

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anything will work as long as you
 

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anything will work as long as you
subdivide<00:01:56.439><c> it</c><00:01:56.640><c> into</c><00:01:56.880><c> equal</c><00:01:57.240><c> pieces</c><00:01:58.240><c> you</c><00:01:58.360><c> can</c>

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subdivide it into equal pieces you can
 

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subdivide it into equal pieces you can
use<00:01:58.719><c> fractions</c><00:01:59.159><c> to</c><00:01:59.280><c> represent</c><00:02:00.079><c> of</c><00:02:00.240><c> anything</c>

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use fractions to represent of anything
 

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use fractions to represent of anything
what<00:02:01.360><c> we'll</c><00:02:01.520><c> see</c><00:02:01.719><c> later</c><00:02:02.079><c> is</c><00:02:02.200><c> that</c><00:02:02.399><c> fraction</c>

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what we'll see later is that fraction
 

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what we'll see later is that fraction
notation<00:02:03.360><c> can</c><00:02:03.520><c> also</c><00:02:03.719><c> be</c><00:02:03.840><c> used</c><00:02:04.039><c> to</c><00:02:04.200><c> describe</c><00:02:04.520><c> a</c>

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notation can also be used to describe a
 

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notation can also be used to describe a
ratio<00:02:05.880><c> let's</c><00:02:06.079><c> take</c><00:02:06.200><c> a</c><00:02:06.320><c> look</c><00:02:06.439><c> at</c><00:02:06.600><c> this</c><00:02:06.799><c> example</c>

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ratio let's take a look at this example
 

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ratio let's take a look at this example
let's<00:02:07.399><c> say</c><00:02:07.520><c> in</c><00:02:07.680><c> total</c><00:02:08.039><c> we</c><00:02:08.160><c> have</c><00:02:08.360><c> nine</c><00:02:08.640><c> pets</c><00:02:09.479><c> but</c>

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let's say in total we have nine pets but
 

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let's say in total we have nine pets but
those<00:02:09.879><c> nine</c><00:02:10.200><c> pets</c><00:02:10.759><c> are</c><00:02:10.959><c> made</c><00:02:11.120><c> up</c><00:02:11.280><c> of</c><00:02:11.440><c> three</c>

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those nine pets are made up of three
 

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those nine pets are made up of three
dogs<00:02:12.160><c> four</c><00:02:12.520><c> cats</c><00:02:12.959><c> and</c><00:02:13.080><c> two</c><00:02:13.360><c> pigs</c><00:02:14.239><c> you</c><00:02:14.360><c> could</c>

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dogs four cats and two pigs you could
 

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dogs four cats and two pigs you could
then<00:02:14.800><c> have</c><00:02:15.000><c> these</c><00:02:15.200><c> three</c><00:02:15.440><c> fractions</c><00:02:16.360><c> three</c>

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then have these three fractions three
 

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then have these three fractions three
dogs<00:02:16.920><c> out</c><00:02:17.080><c> of</c><00:02:17.200><c> nine</c><00:02:17.480><c> pets</c><00:02:18.080><c> four</c><00:02:18.400><c> over</c><00:02:18.680><c> n</c><00:02:19.120><c> four</c>

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dogs out of nine pets four over n four
 

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dogs out of nine pets four over n four
cats<00:02:20.400><c> out</c><00:02:20.560><c> of</c><00:02:20.680><c> nine</c><00:02:21.000><c> pets</c><00:02:21.640><c> or</c><00:02:21.840><c> two</c><00:02:22.080><c> pigs</c><00:02:22.360><c> out</c><00:02:22.480><c> of</c>

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cats out of nine pets or two pigs out of
 

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cats out of nine pets or two pigs out of
nine<00:02:23.319><c> pets</c><00:02:24.319><c> you</c><00:02:24.400><c> could</c><00:02:24.560><c> also</c><00:02:24.840><c> have</c><00:02:24.959><c> a</c><00:02:25.120><c> test</c>

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nine pets you could also have a test
 

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nine pets you could also have a test
example<00:02:25.840><c> where</c><00:02:26.000><c> you</c><00:02:26.120><c> wrote</c><00:02:26.360><c> a</c><00:02:26.519><c> test</c><00:02:26.879><c> and</c><00:02:26.959><c> you</c>

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example where you wrote a test and you
 

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example where you wrote a test and you
answered<00:02:27.519><c> 16</c><00:02:27.879><c> of</c><00:02:27.959><c> the</c><00:02:28.080><c> 20</c><00:02:28.400><c> questions</c>

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answered 16 of the 20 questions
 

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answered 16 of the 20 questions
correctly<00:02:29.440><c> so</c><00:02:29.560><c> you're</c><00:02:29.920><c> overall</c><00:02:30.160><c> grade</c><00:02:30.400><c> of</c><00:02:30.480><c> the</c>

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correctly so you're overall grade of the
 

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correctly so you're overall grade of the
test<00:02:30.840><c> is</c><00:02:31.000><c> 16</c><00:02:31.360><c> out</c><00:02:31.519><c> of</c><00:02:31.680><c> 20</c><00:02:32.160><c> or</c><00:02:32.360><c> 16</c><00:02:32.800><c> over</c><00:02:33.040><c> 20</c><00:02:33.720><c> or</c>

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test is 16 out of 20 or 16 over 20 or
 

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test is 16 out of 20 or 16 over 20 or
you<00:02:34.000><c> could</c><00:02:34.160><c> convert</c><00:02:34.480><c> this</c><00:02:34.599><c> to</c><00:02:34.760><c> a</c><00:02:34.920><c> percent</c>

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you could convert this to a percent
 

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you could convert this to a percent
which<00:02:35.400><c> we'll</c><00:02:35.560><c> see</c><00:02:35.760><c> in</c><00:02:35.840><c> a</c><00:02:35.959><c> later</c>

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which we'll see in a later
 

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which we'll see in a later
unit<00:02:38.040><c> now</c><00:02:38.160><c> there's</c><00:02:38.360><c> a</c><00:02:38.480><c> few</c><00:02:38.800><c> different</c><00:02:39.080><c> kinds</c>

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unit now there's a few different kinds
 

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unit now there's a few different kinds
of<00:02:39.519><c> fractions</c><00:02:40.440><c> even</c><00:02:40.640><c> though</c><00:02:40.840><c> these</c><00:02:41.000><c> different</c>

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of fractions even though these different
 

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of fractions even though these different
definitions<00:02:41.840><c> do</c><00:02:42.120><c> exist</c><00:02:42.519><c> you</c><00:02:42.640><c> don't</c><00:02:42.800><c> have</c><00:02:42.920><c> to</c>

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definitions do exist you don't have to
 

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definitions do exist you don't have to
let<00:02:43.239><c> that</c><00:02:43.400><c> scare</c><00:02:43.720><c> you</c><00:02:43.920><c> because</c><00:02:44.159><c> once</c><00:02:44.319><c> we</c><00:02:44.480><c> start</c>

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let that scare you because once we start
 

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let that scare you because once we start
doing<00:02:44.959><c> the</c><00:02:45.200><c> math</c><00:02:46.000><c> all</c><00:02:46.200><c> of</c><00:02:46.400><c> these</c><00:02:46.599><c> different</c>

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doing the math all of these different
 

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doing the math all of these different
fractions<00:02:47.360><c> will</c><00:02:47.560><c> behave</c><00:02:48.080><c> in</c><00:02:48.239><c> the</c><00:02:48.360><c> same</c><00:02:48.680><c> way</c><00:02:49.480><c> so</c>

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fractions will behave in the same way so
 

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fractions will behave in the same way so
we<00:02:49.760><c> do</c><00:02:49.920><c> have</c><00:02:50.040><c> a</c><00:02:50.239><c> zero</c><00:02:50.599><c> fraction</c><00:02:51.200><c> a</c><00:02:51.360><c> zero</c>

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we do have a zero fraction a zero
 

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we do have a zero fraction a zero
fraction<00:02:52.000><c> is</c><00:02:52.159><c> the</c><00:02:52.319><c> first</c><00:02:52.680><c> example</c><00:02:53.360><c> and</c><00:02:53.480><c> that's</c>

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fraction is the first example and that's
 

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fraction is the first example and that's
when<00:02:53.959><c> the</c><00:02:54.120><c> numerator</c><00:02:54.720><c> or</c><00:02:54.879><c> the</c><00:02:55.080><c> top</c><00:02:55.440><c> is</c><00:02:55.640><c> zero</c><00:02:56.159><c> if</c>

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when the numerator or the top is zero if
 

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when the numerator or the top is zero if
the<00:02:56.400><c> numerator</c><00:02:56.879><c> is</c><00:02:57.080><c> zero</c><00:02:57.879><c> then</c><00:02:58.000><c> the</c><00:02:58.159><c> fraction</c>

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the numerator is zero then the fraction
 

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the numerator is zero then the fraction
always<00:02:58.879><c> represents</c><00:02:59.400><c> zero</c><00:02:59.879><c> no</c><00:03:00.000><c> matter</c><00:03:00.239><c> what</c>

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always represents zero no matter what
 

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always represents zero no matter what
the<00:03:00.480><c> denominator</c><00:03:01.080><c> is</c><00:03:01.599><c> unless</c><00:03:01.959><c> you</c><00:03:02.159><c> have</c><00:03:02.560><c> zero</c>

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the denominator is unless you have zero
 

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the denominator is unless you have zero
as<00:03:03.239><c> both</c><00:03:03.440><c> the</c><00:03:03.599><c> numerator</c><00:03:04.080><c> and</c><00:03:04.239><c> the</c>

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as both the numerator and the
 

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as both the numerator and the
denominator<00:03:05.120><c> then</c><00:03:05.280><c> that's</c><00:03:05.519><c> technically</c>

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denominator then that's technically
 

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denominator then that's technically
undefined<00:03:06.760><c> and</c><00:03:06.959><c> something</c><00:03:07.200><c> you</c><00:03:07.280><c> would</c><00:03:07.480><c> cover</c>

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undefined and something you would cover
 

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undefined and something you would cover
in<00:03:07.879><c> a</c><00:03:08.000><c> later</c><00:03:08.319><c> Math</c>

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in a later Math
 

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in a later Math
course<00:03:10.120><c> the</c><00:03:10.280><c> next</c><00:03:10.440><c> one</c><00:03:10.599><c> is</c><00:03:10.799><c> proper</c><00:03:11.319><c> fractions</c>

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course the next one is proper fractions
 

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course the next one is proper fractions
so<00:03:12.519><c> a</c><00:03:12.680><c> fraction</c><00:03:12.959><c> is</c><00:03:13.080><c> supposed</c><00:03:13.319><c> to</c><00:03:13.480><c> represent</c>

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so a fraction is supposed to represent
 

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so a fraction is supposed to represent
part<00:03:14.080><c> of</c><00:03:14.159><c> a</c><00:03:14.319><c> whole</c><00:03:14.720><c> and</c><00:03:14.840><c> that's</c><00:03:15.040><c> why</c><00:03:15.200><c> this</c><00:03:15.319><c> is</c>

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part of a whole and that's why this is
 

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part of a whole and that's why this is
the<00:03:15.640><c> proper</c><00:03:16.000><c> fraction</c><00:03:16.599><c> when</c><00:03:16.760><c> the</c><00:03:16.879><c> numerator</c>

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the proper fraction when the numerator
 

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the proper fraction when the numerator
the<00:03:17.680><c> top</c><00:03:18.000><c> is</c><00:03:18.159><c> smaller</c><00:03:18.599><c> than</c><00:03:18.720><c> the</c><00:03:18.879><c> bottom</c><00:03:19.280><c> the</c>

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the top is smaller than the bottom the
 

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the top is smaller than the bottom the
denominator<00:03:20.440><c> any</c><00:03:20.680><c> fraction</c><00:03:21.200><c> like</c><00:03:21.440><c> that</c><00:03:21.840><c> will</c>

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denominator any fraction like that will
 

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denominator any fraction like that will
always<00:03:22.280><c> be</c><00:03:22.440><c> a</c><00:03:22.599><c> proper</c><00:03:22.920><c> fraction</c><00:03:23.319><c> and</c><00:03:23.440><c> it's</c>

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always be a proper fraction and it's
 

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always be a proper fraction and it's
smaller<00:03:24.080><c> than</c>

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smaller than
 

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smaller than
one<00:03:26.440><c> next</c><00:03:26.680><c> is</c><00:03:26.799><c> a</c><00:03:26.920><c> whole</c><00:03:27.200><c> fraction</c><00:03:28.000><c> when</c><00:03:28.159><c> the</c>

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one next is a whole fraction when the
 

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one next is a whole fraction when the
number<00:03:28.599><c> in</c><00:03:28.760><c> the</c><00:03:28.959><c> top</c><00:03:29.200><c> or</c><00:03:29.319><c> the</c><00:03:29.400><c> numerator</c><00:03:30.040><c> is</c>

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number in the top or the numerator is
 

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number in the top or the numerator is
equal<00:03:30.480><c> to</c><00:03:30.640><c> the</c><00:03:30.760><c> number</c><00:03:31.000><c> in</c><00:03:31.120><c> the</c><00:03:31.280><c> bottom</c><00:03:31.560><c> or</c><00:03:31.760><c> the</c>

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equal to the number in the bottom or the
 

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equal to the number in the bottom or the
denominator<00:03:32.599><c> then</c><00:03:32.720><c> that</c><00:03:32.840><c> is</c><00:03:32.959><c> a</c><00:03:33.080><c> whole</c>

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denominator then that is a whole
 

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denominator then that is a whole
fraction<00:03:33.920><c> because</c><00:03:34.159><c> whenever</c><00:03:34.400><c> you</c><00:03:34.599><c> divide</c>

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fraction because whenever you divide
 

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fraction because whenever you divide
something<00:03:35.319><c> by</c><00:03:35.480><c> itself</c><00:03:36.040><c> you</c><00:03:36.239><c> get</c><00:03:36.400><c> one</c><00:03:36.760><c> and</c><00:03:36.840><c> you</c>

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something by itself you get one and you
 

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something by itself you get one and you
have<00:03:37.159><c> the</c><00:03:37.280><c> whole</c><00:03:37.599><c> part</c><00:03:38.000><c> back</c><00:03:38.720><c> and</c><00:03:38.920><c> lastly</c><00:03:39.360><c> we</c>

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have the whole part back and lastly we
 

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have the whole part back and lastly we
have<00:03:39.599><c> an</c><00:03:39.760><c> improper</c><00:03:40.280><c> fraction</c><00:03:41.120><c> sometimes</c><00:03:41.360><c> the</c>

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have an improper fraction sometimes the
 

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have an improper fraction sometimes the
numerator<00:03:41.959><c> or</c><00:03:42.120><c> the</c><00:03:42.280><c> top</c><00:03:42.480><c> is</c><00:03:42.599><c> bigger</c><00:03:42.879><c> than</c><00:03:43.040><c> the</c>

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numerator or the top is bigger than the
 

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numerator or the top is bigger than the
bottom<00:03:43.480><c> and</c><00:03:43.599><c> that</c><00:03:43.799><c> fraction</c><00:03:44.159><c> represents</c>

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bottom and that fraction represents
 

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bottom and that fraction represents
something<00:03:45.040><c> bigger</c><00:03:45.280><c> than</c><00:03:45.439><c> one</c><00:03:46.200><c> so</c><00:03:46.360><c> if</c><00:03:46.439><c> you</c><00:03:46.599><c> have</c>

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something bigger than one so if you have
 

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something bigger than one so if you have
7<00:03:47.080><c> over</c><00:03:47.360><c> 5</c><00:03:47.599><c> for</c><00:03:47.760><c> example</c><00:03:48.360><c> you</c><00:03:48.560><c> actually</c><00:03:48.840><c> have</c>

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7 over 5 for example you actually have
 

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7 over 5 for example you actually have
one<00:03:49.319><c> whole</c><00:03:49.799><c> piece</c><00:03:50.519><c> plus</c><00:03:51.000><c> two</c><00:03:51.280><c> pieces</c><00:03:51.640><c> more</c><00:03:51.920><c> in</c>

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one whole piece plus two pieces more in
 

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one whole piece plus two pieces more in
the<00:03:52.239><c> next</c><00:03:52.560><c> hole</c><00:03:53.439><c> with</c><00:03:53.640><c> those</c><00:03:53.879><c> definitions</c><00:03:54.360><c> in</c>

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the next hole with those definitions in
 

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the next hole with those definitions in
mind<00:03:55.040><c> we</c><00:03:55.159><c> can</c><00:03:55.360><c> place</c><00:03:55.680><c> each</c><00:03:55.840><c> of</c><00:03:56.040><c> these</c><00:03:56.239><c> kinds</c><00:03:56.439><c> of</c>

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mind we can place each of these kinds of
 

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mind we can place each of these kinds of
fractions<00:03:57.079><c> on</c><00:03:57.200><c> the</c><00:03:57.360><c> number</c><00:03:57.640><c> line</c><00:03:58.239><c> maybe</c><00:03:58.519><c> this</c>

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fractions on the number line maybe this
 

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fractions on the number line maybe this
illustration<00:03:59.200><c> will</c><00:03:59.360><c> help</c><00:03:59.519><c> make</c><00:03:59.920><c> these</c>

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illustration will help make these
 

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illustration will help make these
definitions<00:04:00.560><c> more</c><00:04:00.799><c> clear</c><00:04:01.760><c> first</c><00:04:02.360><c> we</c><00:04:02.519><c> have</c><00:04:02.640><c> the</c>

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definitions more clear first we have the
 

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definitions more clear first we have the
zero<00:04:03.120><c> fraction</c><00:04:03.799><c> so</c><00:04:04.000><c> on</c><00:04:04.120><c> the</c><00:04:04.360><c> left</c><00:04:04.560><c> of</c><00:04:04.640><c> the</c>

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zero fraction so on the left of the
 

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zero fraction so on the left of the
number<00:04:05.000><c> line</c><00:04:05.280><c> without</c><00:04:05.519><c> getting</c><00:04:05.799><c> into</c><00:04:06.200><c> the</c>

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number line without getting into the
 

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number line without getting into the
negatives<00:04:07.200><c> we</c><00:04:07.360><c> see</c><00:04:07.560><c> the</c><00:04:07.760><c> zero</c><00:04:08.000><c> fraction</c><00:04:08.480><c> right</c>

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negatives we see the zero fraction right
 

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negatives we see the zero fraction right
at

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at
 

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at
zero<00:04:10.920><c> next</c><00:04:11.120><c> is</c><00:04:11.239><c> a</c><00:04:11.439><c> proper</c><00:04:11.799><c> fraction</c><00:04:12.680><c> anytime</c>

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zero next is a proper fraction anytime
 

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zero next is a proper fraction anytime
you<00:04:13.280><c> have</c><00:04:13.400><c> a</c><00:04:13.560><c> fraction</c><00:04:13.959><c> that</c><00:04:14.120><c> is</c><00:04:14.400><c> part</c><00:04:14.560><c> of</c><00:04:14.680><c> the</c>

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you have a fraction that is part of the
 

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you have a fraction that is part of the
whole<00:04:15.239><c> just</c><00:04:15.400><c> like</c><00:04:15.560><c> the</c><00:04:15.760><c> original</c><00:04:16.160><c> definition</c>

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whole just like the original definition
 

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whole just like the original definition
that<00:04:17.199><c> is</c><00:04:17.359><c> where</c><00:04:17.519><c> you</c><00:04:17.639><c> have</c><00:04:17.759><c> a</c><00:04:17.959><c> proper</c><00:04:18.479><c> fraction</c>

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that is where you have a proper fraction
 

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that is where you have a proper fraction
then<00:04:19.720><c> right</c><00:04:19.880><c> at</c><00:04:20.079><c> the</c><00:04:20.199><c> one</c><00:04:20.639><c> you</c><00:04:20.799><c> have</c><00:04:21.000><c> the</c><00:04:21.160><c> whole</c>

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then right at the one you have the whole
 

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then right at the one you have the whole
fraction<00:04:22.079><c> so</c><00:04:22.360><c> if</c><00:04:22.560><c> the</c><00:04:22.759><c> top</c><00:04:23.040><c> is</c><00:04:23.199><c> equal</c><00:04:23.479><c> to</c><00:04:23.600><c> the</c>

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fraction so if the top is equal to the
 

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fraction so if the top is equal to the
bottom<00:04:24.360><c> then</c><00:04:24.479><c> you</c><00:04:24.600><c> have</c><00:04:24.840><c> the</c><00:04:25.000><c> whole</c>

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bottom then you have the whole
 

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bottom then you have the whole
piece<00:04:27.360><c> lastly</c><00:04:27.840><c> improper</c><00:04:28.360><c> fractions</c><00:04:28.680><c> are</c>

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piece lastly improper fractions are
 

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piece lastly improper fractions are
anywhere<00:04:29.360><c> greater</c><00:04:29.919><c> than</c><00:04:30.080><c> one</c><00:04:30.680><c> so</c><00:04:30.919><c> anytime</c><00:04:31.400><c> you</c>

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anywhere greater than one so anytime you
 

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anywhere greater than one so anytime you
have<00:04:32.000><c> a</c><00:04:32.320><c> larger</c><00:04:32.919><c> numerator</c><00:04:33.400><c> than</c><00:04:33.600><c> denominator</c>

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have a larger numerator than denominator
 

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have a larger numerator than denominator
you<00:04:34.479><c> have</c><00:04:34.680><c> an</c><00:04:34.960><c> improper</c><00:04:35.759><c> fraction</c><00:04:36.759><c> and</c><00:04:36.960><c> as</c><00:04:37.039><c> you</c>

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you have an improper fraction and as you
 

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you have an improper fraction and as you
can<00:04:37.280><c> see</c><00:04:37.479><c> going</c><00:04:37.759><c> from</c><00:04:37.919><c> left</c><00:04:38.080><c> to</c><00:04:38.280><c> right</c><00:04:38.479><c> a</c><00:04:38.639><c> zero</c>

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can see going from left to right a zero
 

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can see going from left to right a zero
fraction<00:04:39.479><c> is</c><00:04:39.680><c> less</c><00:04:39.880><c> than</c><00:04:40.000><c> a</c><00:04:40.120><c> proper</c><00:04:40.479><c> fraction</c>

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fraction is less than a proper fraction
 

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fraction is less than a proper fraction
which<00:04:41.560><c> then</c><00:04:41.720><c> is</c><00:04:41.919><c> less</c><00:04:42.120><c> than</c><00:04:42.199><c> a</c><00:04:42.320><c> whole</c><00:04:42.600><c> fraction</c>

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which then is less than a whole fraction
 

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which then is less than a whole fraction
and<00:04:43.600><c> those</c><00:04:43.759><c> are</c><00:04:43.919><c> all</c><00:04:44.160><c> less</c><00:04:44.400><c> than</c><00:04:44.680><c> an</c><00:04:44.840><c> improper</c>

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and those are all less than an improper
 

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and those are all less than an improper
fraction