Practice English Speaking&Listening with: Math Antics - Percents Missing Total

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Hi! Welcome to Math Antics. In our last lesson about percents,

we learned that therere three main types of percent problems because theres three different numbers that could be missing.

Those three numbers are thepart’, thetotal’, and thepercent’.

Theyre just the three variable (or changeable numbers) in the percentage equation.

The forth number is always 100, since thats what percent means: per 100.

In the last two videos, we learned how to solve problems where thepartwas unknown and where thepercentwas unknown.

In this video, were gonna learn how to solve problems where thetotalis unknown or missing.

With this type of problem, youll be told what the percent is,

and youll be told what part of the total you have.

But youll need to figure out what that total itself is.

Heres an example of a problem like that:

Your friend has a bag of marbles, and he tells you that 20% of the marbles are red.

If theres 7 red marbles,

how many marbles does he have altogether?

Okay, so how do you know that its the total thats missing in this problem?

Well, the wordaltogetheris a big clue because it means almost the same thing astotal”.

So, if the question has words like, “altogether”, orin all”, ortotal”, orwhole”, orentire

those can help you know that you need to find the total.

And another way that we can tell is by the numbers that we ARE given.

In this problem, we know that the percent is 20, and were also told that PART of the marbles are red,

so we know that the PART is 7.

So that means that it must be the total thats missing!

Alright then, so how do we figure out what the total is?

Well, using a little algebra (which you dont need to know how to do right here)

we can re-arrange our percent equation like this:

What this new form of the equation tells us is that,

if we take thepartand multiply it by 100, and then we divide that by thepercent’, well get thetotal’.

That seems simple enough. Its just two steps!

Lets try it out on our word problem about the marbles.

We know that thepart’ (that are red) is 7,

so step one is to just multiply that part by 100.

7 × 100 is 700.

And in step two, we take that 700 and divide it by thepercent’, which were told is 20.

Okay, 700 divided by 20…. hmmm….

Well, we could use a calculator to divide, but this doesnt seem too hard,

so Ill just do the division the long way.

20 is to big to divide into the first digit (7) so well need to include the digit next to it as well.

Now we ask, “How many20s does it take to make 70 or almost 70”.

That would be 3 because 3 × 20 is 60.

70 minus 60 leaves 10 as the remainder.

And then we bring down the zero and then we ask, “How many20s will divide into 100?”

Ah-ha5, because 5 × 20 is 100, so that leaves no remainder.

So 700 divided by 20 is 35.

And that means that the total number of marbles is 35.

And in a problem like this, you can always check your answer

by making sure that the fraction of thepartover thetotalwould give you the correct percent.

For example, in this case, you could make sure that the fraction 7 over 35 would really be 20%.

Now that wasnt so tough, was it?

Lets see one more example to make sure youve got the procedure down before you try some on your own.

The next problem says:

A high school marching band has 12 flute players.

[frantic flute music]

If 8% of the band members play the flute,

then how many members are in the entire band?

Okay, so the smallerpartin this problem is 12 since theres 12 flute players.

And were told that they make up 8 percent of the band, so thepercentis 8.

Again, its thetotalthats missing,

and to find it, we just need to follow our 2-step procedure.

For step one, we multiply thepartby 100:

12 × 100 = 1,200

For step two, we divide that 1,200 by the percent, which is 8.

(This time I think Ill use a calculator to divide.)

1,200 divided by 8 equals 150.

Greatthat means that the total number of band members is 150.

And again, you can always check your answer the way we did in the last example.

Alrightthat does it for this lesson.

Rememberthe key to getting really good at math is to do it yourself.

Doing practice problems on your own will help you become a great problem solver.

Good luck! Thanks for watching Math Antics and Ill see ya next time.

Learn more at www.mathantics.com

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