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Lecture Comments (2)

0 answers

Post by sherman boey on July 28, 2014

why 2 numbers need ()? cant i just replace it with X?

0 answers

Post by CW Burnette on February 8, 2013

i get it but is there another short cut

Finding a Percent of a Number

Related Links

  • To find the percent of a number, translate the sentence into an equation
    • “of” means times
    • “what” means unknown variable

Finding a Percent of a Number

50% of 30 is ?
  • 50% = .50
  • .50 ×30
15
12% of 26 is ?
  • 12% = .12
  • .12 ×26
3.12
What is 25% of 40
  • 25% = .25
  • .25 ×40
10
What number is 13% of 10?
  • 13% = .13
  • .13 ×10
1.3
What number is 30% of 90
  • 30% =.30
  • .30 ×90
27
Find 5 percent of 60
  • 5% = .05
  • .05 ×60
3
Find 100% of 37
  • 100% = 1
  • 1 ×37
37
Find 1% of 2500
  • 1% = 0.01
  • 0.01 ×2500
25
A bag of candy contains 35 pieces. If Susana ate 40% of the candy, how many pieces did she eat?
  • 40% = .40
  • .40 ×35
14
A bag of candy contains 15 pieces. If John ate 20% of the candy, how many piecees did she eat?
  • 20% = 0.2
  • 0.2 ×15
3

*These practice questions are only helpful when you work on them offline on a piece of paper and then use the solution steps function to check your answer.

Answer

Finding a Percent of a Number

Lecture Slides are screen-captured images of important points in the lecture. Students can download and print out these lecture slide images to do practice problems as well as take notes while watching the lecture.

  • Intro 0:00
  • Percent of a Number 0:06
    • Translate Sentence into an Equation
    • Example: 30% of 100 is What Number?
  • Extra Example 1: Finding a Percent of a Number 7:12
  • Extra Example 2: Finding a Percent of a Number 15:56
  • Extra Example 3: Finding a Percent of a Number 19:14
  • Extra Example 4: Finding a Percent of a Number 24:26

Transcription: Finding a Percent of a Number

Welcome back to Educator.com.0000

For the next lesson, we are going to be finding percents of a number.0002

When we are finding a percent of a number, that means we are finding a portion of a number, some part of a number.0008

Whenever we have a percent of a number, let's translate the sentence into an equation.0016

Of means times; whenever you see the word of in the sentence, it means times.0024

Of like this is times.0034

When you see the word what, what means the unknown.0036

What is what we are looking for; that is going to be the variable.0042

What is the variable.0045

Whenever you see the word is, is means equal.0048

Whenever you see the word is, you are going to write that symbol.0059

Whenever you are finding a percent of a number, you are always going to be0067

multiplying the percent with the number because of is times.0071

Here what is a variable X; you can use whatever variable you would like.0080

You can use A; you can use B; you can use Z; it doesn't matter.0085

X is; is means equals; 30 percent.0089

30 percent, whenever we solve with percents, we have to change it to a decimal.0097

Remember we can't solve with a percent number.0104

Remember to change percents into a decimal, you are going to start from the end of the number.0108

If you don't see the decimal point, then it always belongs at the end of a number.0122

You are going to move two spaces to the left.0128

You know it is going to be to the left when you change it to a decimal because decimals are small.0132

Think of decimals as smaller than percents.0136

To change from a percent to a decimal, we are going to move the decimal point0140

over to the left because that is going to make the number smaller.0144

Two spaces; it is going to go one, two.0147

That is where the decimal point is going to go.0152

Here it is going to be 0.30; this is going to change to 0.30.0156

Of always means times.0164

Here I want to show that I am going to multiply this number to this number.0171

Be careful because we don't want to use X for times anymore because here we have X as a variable.0176

Instead of using X, use parentheses.0184

You also probably know about the dot as times; sometimes that is OK.0190

But between two numbers, you don't want to use dot because that looks like a decimal also.0195

Maybe if you write it a little bit too low, it might look like a decimal.0201

Whenever you are going to multiply two numbers together, it is always best to just use parentheses.0207

Writing the number in parentheses like that between two numbers,0215

it shows that you are going to be multiplying those two.0219

What is 30 percent of 100?0224

You know that you are going to be multiplying 0.30 with 100 to find the missing value X.0225

100 times 0.30 is going to be 0; then 0; 0; I'm sorry.0235

If you want to just multiply this 0 out, you can do that.0250

Then multiply this through under; put a 0 here; 3 times 0; 0; 3.0254

3; 0; 0; 0; be careful when you have so many 0s.0264

Within the problem, because we multiplied, how many numbers are behind the decimal point?0269

There is two numbers; one, two; we have two numbers behind the decimal point.0274

You are going to go to the answer starting at the end.0279

You are going to go one, two.0284

That is where the decimal point is going to go; 30.0286

X equals... all this was 30; there is a shortcut.0291

Whenever you multiply a decimal number, to a multiple of 10... that is 10, 100, 1000, 10000.0296

Whenever you have a number multiplied to a number with 10306

and then 0s like 100, there is a shortcut way of doing this.0311

You can count how many 0s there are in that number; 100 has two zeros.0316

Then you are going to move this decimal point two spaces.0324

You know, since you are going to be multiplying, when you multiply, the number tends to get bigger.0331

You are going to go two spaces to the right0337

because moving the decimal point over to the right makes the number bigger.0340

You are going to one, two; that is going to give you 30.0344

Remember if you don't see a decimal point, it is always at the end right there.0348

If you were multiplying this number by 10, let's say you are multiplying it by 10.0356

10 has only one 0.0363

You would only move the decimal point over once to the right.0366

That would be 3.0 which is the same thing as 3.0371

Remember if there is a 0 at the end of a number behind the decimal point, it is as if it is not there.0374

3.0 is the same thing as 3.0379

If you are multiplying by 1000, 1000 has three 0s.0388

You would have to move the decimal point over three spaces.0394

Remember if you have an empty space, you have to fill it in with an extra 0.0398

That is the shortcut when multiplying by a number that is a multiple of 10; 10, 100, 1000, and so on.0404

You just have to count the number of 0s and then move the decimal point over that many spaces.0413

What is 30 percent of 100?--that is 30; 30 is 30 percent of 100.0420

We are just going to do a few more examples.0433

Here 50 percent of 18 is... here 50 percent.0435

Again remember whenever we have to solve using percents,0443

we have to change it to a decimal because you can't solve with a percent.0448

If you have a percent, then you need to change it to a decimal.0453

Remember percent to decimal.0458

If we have a percent, 50 percent, you want to move the decimal point0466

over two spaces between percent to decimal or decimal to percent.0471

From percent to decimal, you start at the end right here.0479

You have to move two spaces to the left because remember decimals are small numbers.0484

You want to turn this number into a smaller number.0488

To do that, you have to move the decimal point over to the left.0492

If you move it to the right, then the number gets bigger.0496

So move it to the side that is going to make it smaller.0499

Two spaces, it is going to be right here.0504

One, two; drop the percent sign; becomes 0.50.0506

Or because this 0 is at the end of a number behind the decimal point, it is as if it is not there.0512

You don't even have to write it.0519

0.50 is the same thing as 0.5; it is the same thing.0520

This is 0.50 or 0.5; of means times.0528

Remember if I am going to multiply two numbers together, I want to write it in parentheses.0535

Times 18 is; is is equals; then the number X which is what we are solving for.0538

As long as you know that you have to multiply the percent with the number,0554

because of is between the two numbers, again 50 percent you change to a decimal.0560

As long as you know that you have to multiply these two, you don't have to write it into this equation0565

because all we are doing is finding percents of a number; of meaning times.0573

You just have to be able to multiply these two numbers together.0579

The reason why I am saying write an equation is because for the next lesson,0582

we are going to have to solve for maybe this number or solve for the percent.0589

This number will be given to you.0598

In that case, when you are solving for another number,0600

this is the easiest way for you to be able to write an equation0603

and know what your variable is, what it is you are solving for,0608

because a variable is always what you are solving for.0611

If you don't want to do it this way, then just make sure you remember to multiply.0616

Of means times; you are going to be multiplying the number with the other number.0622

0.5 times 18; I am going to write that here; 18 times 0.5.0631

8 times 5 is 40; 5 times 1 is 5; plus 4 is 9.0640

Within here, how many numbers are behind the decimal point?0648

I only have one; starting right here, you are going to go inwards one.0650

My answer is going to be 9.0 or 9.0657

9.0 and 9 is the same thing.0663

Again 0 is at the end of a number behind the decimal point so you can just drop it; 9.0666

50 percent of 18 is 9; 50 percent means half.0673

50 percent means half; what is half of 18?0679

Half of 18 is 9 meaning if you had let's say 18 pieces of candy.0684

You had to split it in half; you can only take half of them.0690

You take half; your brother or sister has to take the other half.0695

Then you would take 9; your brother or sister would take the other 9.0699

50 percent means half.0704

All you have to do is 50 percent of 18, you just figure out what half of 18 is.0705

The next one, here 8 percent; from percent to a decimal.0712

Again you are going to start right here.0723

You are going to move two spaces to the left.0724

You are going to go one and two.0727

Point... there is an empty space right here.0731

You have to fill it with a 0; 0; 8.0735

Then again you are going to drop the percent because it is no longer a percent.0740

0.08; 8 percent is 0.08; of means times; 6.0743

Again write it in parentheses when you are multiplying two numbers.0752

Is equals the number X or blank.0759

0.08 times 6; 0.08 times 6; 8 times 6 is 48; this is just 0.0764

How many numbers do I have behind the decimal point?0785

I only have two; there is none right here.0789

Decimal point is at the end right here; I only have two.0791

From the end, I am going to go in two spaces; one, two; right there.0795

8 percent of 6 is 0.48.0803

The next one, 99 percent of 100 is.0815

99 percent changes to a decimal because you are solving with it; 99 percent.0819

You are going to go one, two; it is going to be 0.99.0826

Of means times; 100 in parentheses; equals something; 0.99 times 100.0836

Let's do our shortcut; remember if you want, you can multiply it out like this.0846

Remember whenever you multiply a number that is a multiple of 10, meaning 10, 100.0852

Or I'm sorry; not a multiple of 100; but if you have a power of 100; 10, 100, 1000, and so on.0859

What that means is any number with a 1 with a bunch of 0s; 10, 100, 1000, 10000, and so on.0866

Since I have 100 and 100 has two 0s, I am going to take the decimal point.0878

I am going to move it two spaces.0887

But remember I have to move it to the right two spaces0889

because when you multiply by 100, that means your number has to get bigger.0892

To make this number bigger, I am going to move it to the right.0897

One, two; that is where my decimal place is going to go.0900

That is going to be 99.0.0904

Or remember if it is at the end of a number, you can just drop it.0909

You can make it invisible; 99; 99 percent of 100 is 99.0914

Whenever you find a percent of 100, it is always just that number.0921

If I have 1 percent of 100, that is going to be 1.0925

If I have 2 percent of 100, that is going to be 2.0931

If I have 100 percent of 100, that is going to be 100.0935

Whenever you take a percent of 100, it is just going to be this number without the percent sign.0938

68 percent of 100 is 68; that is only if this number is 100.0945

Let's just do a few more; what is 25 percent of 60?0958

This is what we are solving for; I can make that into my variable.0966

Use a question mark; you can do a little blank; is equals.0971

25 percent; percent to decimal; I am going to change 25 percent.0980

Start right here at the end; you are going to go in one, two.0993

It is going to be 0.25; of means times.0997

Again since you are multiplying two numbers together,1007

you are going to write it in parentheses like that.1009

To solve this, I have to... to find the what, to find this, I have to multiply 0.25 with 60.1011

60 times 0.25; this is 0; 6 times 5 is 30; put a 0 here.1023

2 times 0 is 0; 2 times 6 is 12.1035

Add them together; 0; 0; 5; 1.1043

How many numbers are behind decimal points?--I only have one, two.1049

You are going to start here; you are going to go one, two.1056

Remember 0s are at the end of a number behind the decimal point.1060

This is just going to be 15; X, this unknown, is 15.1063

That means 15 is 25 percent of 60.1069

What number is 10 percent of 10?1078

Again what number is the same thing as just what or blank or question mark.1081

You are looking for the number.1087

Is 10 percent; one, two; 0.10; of 10.1089

I know that 10 times 10 is 100.1107

You can just move the decimal point over that many times.1111

Or we can just use our shortcut.1113

Since I am multiplying a decimal by 10, how many 0s do I have in 10?1116

I only have one 0.1121

I am going to move this decimal point over one time.1124

It is going to be 1.0; but that is the same thing as 1.1128

You can just drop this 0.1136

If the decimal place is at the end of a number, then you can just make that invisible.1139

You can just write that as 1; that means 1 is 10 percent of 10.1145

Find 5 percent of 40; we want to find 5 percent of 40.1156

5 percent; this right here is the same thing as this.1162

We still have to change this; be careful.1168

Just because you don't see the percent sign doesn't mean that you can just drop this number down.1171

It is still a percent; you have to change this to a decimal.1176

5 percent; again start at the end; you are going to go one, two.1189

Going to be point, space right here, 0, 5; of is times; 40.1196

You are going to multiply these two numbers together; 0.05 times 40.1212

0 times 5 is 0; 0 times 0 is 0; put a 0 down there.1220

4 times 5 is 20; 4 times 0 is 0; add the 2.1229

Be 0, 0; remember we are adding them down; 200.1239

How many numbers total are behind decimal points?--I only have two; these two.1245

I am going to go from here; I am going to go one, two; in two spaces.1251

My answer is 2.00 which is remember the same thing as just 2.1258

My answer is going to be 2; 5 percent of 40 is 2.1265

100 percent of 18; 100 percent of 18.1276

When I say 100 percent, I am trying to say all of it.1282

This is like saying all of 18; 100 percent of 18 is all of 18.1289

What is all of 18?1295

All of 18, if you have 18 pieces of candy, what is all of it?1297

How many would be considered all of it?--18.1301

100 percent of 18 is just 18.1304

If you want to just solve it out, 100 percent into a decimal is going to be one, two, 1.0.1308

Or remember this is the same thing as 1.1318

Even though you don't see a decimal here, numbers always have a decimal point.1323

It is just if you don't see it, if it is invisible, it is always at the end.1329

100 percent is the same thing as 1 in decimal.1334

It is like saying 1, or 1.0 if you want, times 18.1338

What is 1 times 18?--isn't that 18?1346

Again shortcut, if you have 100 percent, you are saying what is all of it?1352

All of 18 is 18.1357

1 percent of 2000; into a decimal.1361

Right here, you are going to go one, two; the decimal point.1372

Empty space; you are going to fill it in with a 0; and 1.1378

1 percent in decimal is 0.01; be careful that you don't just make it 0.1.1383

Of, times; 2000; multiply it out; times 0.01; this is 0; 0; 0; 2.1392

Then this is just all 0s so I don't have to write that in.1414

It is like adding 0s.1418

If I add 0s to this number, it is just going to be that same number.1419

From here, how many numbers are behind decimal points?--two.1426

Start from here; you are going to go one, two, decimal point.1430

My answer here is going to be 20.00.1435

Again if the 0s are behind the decimal point at the end of a number, you can just drop them.1446

I can drop this, drop this; it will be 20 point.1450

But then I can just drop that, make that decimal point invisible if it is at the end.1454

It will just be 20.1458

The final example, a bag of candy contains 40 pieces.1467

If Susanna ate 20 percent of the candy or everything in the bag of candy, how many pieces did she eat?1475

A whole bag contains 40 pieces; she ate 20 percent of it.1487

How many pieces did she eat?--look at this; 20 percent of the candy.1491

What is the candy?--how many pieces does the bag of candy contain?--40 pieces.1504

It is like saying she ate 20 percent of the 40 pieces.1510

20 percent, again if I want to solve with this number, I have to change it to a decimal.1516

20 percent to decimal; I am going to start here; go one, two; is 0.20.1523

Of is times; you are going to multiply what?1537

The 40 because she ate 20 percent of all the pieces; times 40.1541

Here thing is going to be...1554

Remember if the 0 is at the end of a number and it is behind the decimal point, I can just drop it.1557

This is the same thing as 0.2 times 40.1562

I can't drop this 0; be careful here.1566

Don't drop the 0 because this 0 is not behind the decimal point.1569

Decimal point is right here; right there.1574

Since it is not behind the decimal point, I can't drop the 0.1579

But this one, I can; that will just make it easier to multiply.1583

40 times 0.2 is going to be 80.1587

I only have one number behind the decimal point.1595

Start here; you are going to go in one space.1598

0.2 times 40 is going to be 8.1601

Good thing with word problems is that you can estimate if your answer sounds correct.1607

Let's say I forget to count how many numbers I have behind decimal points and I just leave it as 80.1613

80 can't be my answer because if the bag of candy contains only 40 pieces, Susanna ate 20 percent of it.1620

Would it make sense if my answer was 80, that she ate 80 pieces?1631

There is only 40 pieces; I know this answer sounds correct.1637

It seems correct; it seems reasonable; remember 50 percent is half.1646

If Susanna ate 100 percent of the candy, that means she would have eaten all of the candy.1653

Then my answer would just be 40.1658

If Susanna ate 50 percent of the candy, remember 50 percent is half of the number.1661

If this said 50 percent, then you would have to just find half of 40.1671

She would have eaten 20 pieces of candy.1676

She only ate 20 percent; that means she has to have eaten less than half.1680

If 20 is half, we know 8 is reasonable then because it has to be less than half.1685

That is it for this lesson; thank you for watching Educator.com.1695