Math Antics - Finding A Percent Of A Number - Free Educational videos for Students in K-12

Math Antics - Finding A Percent Of A Number - By mathantics

Transcript


00:03	Uh huh . Hi and welcome to Math Antics .
00:08	In today's video , we're going to learn how to
00:09	do one of the most common calculations with percentages .
00:12	We're going to learn how to find a percent of
00:14	a number . But what does that even mean ?
00:17	Do numbers have Percents that they hide somewhere ? And
00:20	then we have to go looking for them like a
00:22	game of hide and seek . Uh huh . Gotcha
00:28	not exactly finding a percent of a number makes more
00:33	sense if you remember that a number just represents an
00:36	amount and that percent is really just a fraction .
00:39	So finding a percent of a number really means finding
00:42	a fraction of an amount . Think about it this
00:45	way let's say the number 20 represents an amount .
00:48	Like the amount of ladybugs that you found at the
00:50	park one day . And let's also imagine that you
00:53	agreed to give 25 of all the lady bugs you
00:56	found to your little sister . Okay then . So
00:59	how many is that if you have 20 ladybugs ,
01:02	how many is 25 of that amount ? That's what
01:05	it means to find the percent of a number .
01:08	You're finding out how much that percent or fraction of
01:11	the total is In this case . Since our total
01:14	is 20 , we need to know what 25 of
01:17	20 is . So how do we figure that out
01:20	? Well , it's really easy if you remember back
01:23	to one of our fractions videos . The one about
01:25	multiplying fractions in that video . We learned that when
01:29	dealing with fractions sometimes the word of is used instead
01:33	of the multiplication symbol . When they say find one
01:36	half of 16 . They really mean fined one half
01:39	times 16 . Well , guess what ? Since the
01:43	percent is just a special fraction of means the exact
01:47	same thing with Percents . That it did with fractions
01:49	when we have 25% of 20 that means the same
01:54	as 25% times 20 . Great . So all we
01:58	have to do to find a percent of a number
02:00	is to multiply but how do we multiply a percent
02:03	and a number together ? Do we just forget about
02:05	the percent sign and multiply the numbers together ? No
02:09	, if we did it that way our number would
02:11	be way too big . 25 should be a smaller
02:15	part or a fraction of 20 ladybugs . But if
02:18	we did 25 times 20 we would get 500 ladybugs
02:22	. Clearly that's not the right answer . Here's what
02:26	we have to do . Instead remember that when you
02:28	see a percent written like this with the percent sign
02:30	, it's an abbreviation for a fraction in this case
02:33	25 over 100 . So we need to use that
02:36	fraction form when we multiply . Since we're really multiplying
02:39	by a fraction now , some of you may also
02:42	remember that presents . Have a decimal form , we'll
02:44	get to that in just a minute . Okay then
02:47	if we use the fraction form of our percent ,
02:49	then our problem becomes 25 over 100 times 20 .
02:53	Now that's a problem . We know how to do
02:56	to multiply fractions . We just multiply the top numbers
02:59	and then we multiply the bottom numbers to get the
03:01	answer And we can just write 20 as a fraction
03:04	by putting one as the bottom number because 20/1 is
03:08	the exact same value as 20 . So let's go
03:11	ahead and multiply it on the top , we have
03:14	25 times 20 which gives us 500 And on the
03:18	bottom we have 100 times one which is just 100
03:22	. So our answer is 500 over 100 Now 500
03:26	over 100 might seem like a strange answer , but
03:29	that's just because we still need to simplify it .
03:31	500 over 100 simplifies to 5/1 and 5/1 is just
03:37	five . That's much better . So 25 of 20
03:42	is fine . All right . So to find a
03:45	percent of a number , we just need to multiply
03:47	the fraction form of the percent by the number and
03:50	we have our answer . But there's another slightly different
03:54	method that you can use that works especially well if
03:57	you're allowed to use a calculator in our first percentages
04:00	video , we learned that Percents have both a fraction
04:03	form and a decimal form . We've already seen how
04:06	we can use the fraction form to find a percent
04:07	of a number but we can also use the decimal
04:10	form if we want to . Instead , the procedure
04:13	starts the same . If you need to find 25
04:16	of 20 , you first replace the word of with
04:19	the multiplication symbol . Next we'll replace the percent but
04:22	with its decimal form this time 25 is the same
04:26	as the decimal 0.25 . Then all we have to
04:30	do is multiply . And although I could easily do
04:33	the decimal multiplication by hand I happen to have a
04:36	calculator so I'm going to use it . I just
04:39	enter 0.25 times 20 it equals . And I get
04:44	five , yep that's the same answer we got when
04:47	we use the fraction form of 25% . Oh yeah
04:50	So that's how you find a percent of a number
04:53	. You just multiply the number by either the fraction
04:55	form or the decimal form of the 1% . Either
04:58	way we'll give you the right answer . So you
05:00	can choose whichever will be easier for you to do
05:03	. Let's see a couple more examples before you practice
05:05	on your own . This next one involves money ,
05:09	pretend that your best friend has a job walking dogs
05:11	and offers to give you 35 of whatever he earns
05:15	. If you help them walk some of the dogs
05:17	, If your friend earns $80 that week , how
05:19	much of the money will you get in ? Other
05:21	words ? You need to figure out what 35 of
05:24	80 is . Okay then let's start by replacing the
05:29	of with the time symbol . And next we have
05:31	to decide if we want to replace the percent with
05:33	its fraction form or its decimal form . I think
05:36	I'll use the decimal form for this one which means
05:38	I'll replace the 35 with 0.35 . Now all we
05:43	have to do is multiply 0.35 times 80 . And
05:46	that's 28 . That means you'll get $28 if you
05:49	help your friend walk those dogs ching . Okay then
05:54	in the last two problems we found a percent of
05:56	a number which like we learned at the beginning of
05:58	the video just means finding a fraction of an amount
06:02	. And like you'd expect when finding a fraction of
06:04	something . The answer was smaller than the amount we
06:06	started with . But remember fractions can be improper to
06:10	which means that their value is greater than one And
06:13	in the same way%s can be greater than 100% .
06:17	So you might come across situations like this , suppose
06:20	that last year your school had 400 students but this
06:24	year it has 120 of that amount . Well 100%
06:28	. Would mean the exact same number of students is
06:30	last year . So 120 must mean that there's more
06:33	students now . But how many students to find out
06:37	? We need to calculate what 120 of 400 is
06:41	great . We know just how to do that .
06:43	We just multiply 400 by the fraction form or the
06:46	decimal form of 120% . Let's use the decimal form
06:51	again to get the decimal form of 120% . We
06:54	move the decimal point over two places to the left
06:57	and we get 1.20 . So we multiply 1.20 times
07:03	400 , which gives us 480 . So this year
07:07	there's 480 students at school . All right then that's
07:11	how you find the percent of a number and it's
07:13	a really useful mask . You'll , that has a
07:15	lot of real life applications , so it's important to
07:18	learn how to do it right ? As always ,
07:21	the best way to learn math is to practice on
07:24	your own . Thanks for watching Math Antics and I'll
07:26	see you next time .

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