Basic Math Writing Equations

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For the next lesson, we are going to be writing equations.0002

An equation is a math statement with two expressions equaling each other.0007

The previous lesson, we went over expressions, how to write expressions.0014

Remember an expression is a math statement that also uses numbers and variables.0017

An equation is when two of those expressions are equal to each other.0025

The main difference between expression and equation is that equation has an equal sign.0030

If you look at the first four letters of equation, it is almost the full word equal.0041

Think of equation as equal or having an equal sign whereas expressions do not.0051

If I just said A plus 3, A plus 3 without equaling 5, that would be considered an expression.0059

But if you see A plus 3 equal to 5, then that becomes an equation.0070

Here we are going to use words and operations into words to write this two ways,0079

as an equation using numbers and variables and using just words only.0091

To go over our different operations, this for addition, we can use plus.0101

We can use more than.0108

For the subtraction, we can use minus; we can use less than.0111

For multiplication, we can use times or product.0116

For division, we can say divided by; we can say quotient.0122

This one, when you see the word is, that means equals.0129

You can say A plus 3 equals 5; then you can say A plus 3 is 5.0136

Also to go over this, more than and less than, when you see the word than,0146

just like when we were writing expressions, you have to switch.0150

For example, if I say A more than B, more than means plus.0155

But instead of saying A plus B in that order, we have to switch those two.0167

Instead of A plus B, you are going to write B plus A.0174

It is for this one and this one.0180

Whenever you see the word than, you are going to switch them.0182

Let's do a few examples; write each as an equation.0188

For the first one, 10 minus A is 5.0192

We know that... we can write that...minus means minus; A.0197

Then is you know is equal; and 5.0205

That is it; that would be our equation; 10 minus A equals 5.0211

The second one, the product of 7 and 8 is X.0217

Product means times; 7 times 8 is X.0223

I know that this means times; this means product.0239

But when I start writing equations, I don't want to use this anymore.0244

I don't want to use the X to represent multiplication because, X, we use that as a variable.0248

Since we are using it as a variable, as an unknown number, unknown value,0257

I don't want to write it here because it looks like I have a variable.0261

Instead of using the X to represent times, you can either for now write the little dot.0269

But even this later on, you are not going to be able to do that anymore.0279

The best way to show two numbers being multiplied together is in parentheses.0284

To write each of them in parentheses.0290

That is the best way to represent multiplication, two numbers being multiplied together.0292

If you see two numbers written in parentheses like this, then that means times.0299

It means 7 times 8.0305

The next one, a number plus 4 is 10; here it just says a number.0310

A number plus 4 is 10; we know this is plus 4 equals 10.0317

But we don't know that that is; anything unknown, we write as a variable.0325

You can just pick whatever variable; you can say A.0333

You can say B; you can say D; whatever your favorite letter is.0336

You are going to write that as a number.0340

The next one, 6 is P divided by 3; 6 equals P divided by 3.0346

Or divided by can also be written as a fraction.0359

This can be 6 equals P divided by 3.0365

You can write it like this; or you can write it like that.0373

Let's do a few more; 12 is 2 more than A.0381

12 is 2 more than A; we know more than is plus.0387

But you see that word right there.0393

Instead of writing 2 plus A, I have to write A plus 2.0396

You are going to leave it like that.0405

A number multiplied by 2 is 20; a number; again we see that, a number.0409

I can say M multiplied, times, 2 is 20; M times 2 equals 20.0417

When it comes to multiplying letters and numbers together, you don't have to write it like this.0433

We can just stick them together with the number in front.0442

I can write M times 2 as 2M.0445

When you have a number in front of a variable like that, it means multiply them.0450

This is 2 times M; you can write it in that way.0456

Here they said a number first; a number multiplied by 2.0461

You would think you write it like that.0467

But when you have a number times a variable, you always write the number in front.0469

You don't have to write anything between them.0477

You don't have to write the dot; you don't have to write parentheses.0478

Only when it comes to numbers with variables.0481

Or you can do it with variable to variable also.0485

If it is M times N, then you can just write them together like that.0487

Just be careful, you cannot write it with a number being multiplied to a number.0493

If I want to say 2 times 3, if I put them together like that, then that just becomes 23.0497

That doesn't say 2 times 3 so you can't write it like that.0505

Only when you are multiplying a number with a letter, a variable, or variable with variable.0509

Only when a variable is involved, you can write them together.0517

M times 2 equals 20; this can be written as 2M equals 20.0522

The quotient of a number and 4 is 40; quotient is divide.0532

Quotient of... what are the two things that we are dividing?--a number and 4.0541

A number again is just a variable; you can say Z.0548

Z divided by 4 equals 40; again we can write this as a fraction.0556

This can be Z over 4 equals 40; Z divided by 4 equals 40.0569

The last one, 2 added to a number is 21.0581

2 added to a number P equals 21.0588

Again you can use whatever variable you want; 2 plus P equals 21.0598

Write the equations using words.0610

You can write this several ways because we know that addition, we can use plus.0614

We can use added; we can use the sum.0619

Here we can say 5 plus Z is 9; I am going to use sum.0628

I am going to say the sum of 5 and Z.0636

If you use sum, then you have to write the two things that you are going to be adding together.0648

5 and Z, those are the two things; equals translates to is; 9.0654

The sum of 5 and Z is 9.0666

Here 3; this is is; 18; 18 minus A.0671

You can also say 3 is A less than 18.0691

Remember that here, I had to switch these because of this.0706

The next one, the product of 2 and B; or you can say 2 times B.0714

The product of 2... be careful, you are not going to say 2 times B because you already said product.0726

You already used that word to show operation; here you are going to write and.0739

You are saying between this and B; this is... and then 10.0748

The product of 2 and B is 10.0762

The fourth one, 36 divided by 3 is 12.0768

Or I can say the quotient of 36 and 3 is 12.0772

It is okay if yours is a little bit different than what I wrote as long as you use the words correctly.0797

Make sure if you are going to use less than or more than here, then you are going to switch.0804

You can say Z more than 5 is 9.0810

We are going to determine if the equation is true or false.0820

The first one, 12 is the sum of 10 and 2.0824

I am going to write it as an equation first.0831

12 equals... we know is is equals... the sum... we are going to add.0832

We are going to be adding what and what?--10 and 2.0840

10 plus 2; is this true?--12 equals 10 plus 2?--yes it is true.0844

Number two, the product of 6 and 3 is 15.0857

Product means we are going to be multiplying.0861

6 and 3, remember if you are going to multiply two numbers,0866

the best way for you to write that is to write them each in parentheses.0869

6 and 3, is, equals, 15; 6 times 3 we know is not 15.0875

This one is false.0888

The next one, 8 minus 10 is 2; equals 2.0895

This may look right; this may look true.0906

But it is actually not because here this is 8 minus 10.0909

If I had 10 minus 8, this equals 2.0916

But that is not the equation; it is 8 minus 10.0923

Remember this number is smaller than this number.0926

If I have a number line, this is 0; say this is 8.0935

If I am going to start at 8 and then go backwards 10 because that is what minus says,0947

then I am going to be... all the way to here is... that is 8.0953

I moved 8 spaces; but then I have to move 2 more.0959

Where am I going to land?--if I move 10 spaces, then I am going to land at -2.0964

Then this is not true; this is false because 8 minus 10 is -2.0972

Again you are starting at +8 and then you are going to move backwards 10 spaces on the number line.0979

You are going to land at -2; so this is false.0986

You can also think of this as +8 and -10.0997

Remember minus and negative is the same thing.1002

If you want, you can circle this sign with that number.1006

This is +8 and -10; we know that this is the bigger number.1010

We have to give this the sign of that number if you remember from going over integers; +8 minus 10.1018

Another way you can think of this for integers, if you have 8 apples.1028

It is a +8; you have something; you have 8 apples.1035

But let's say you need 10 apples.1039

Say you are going to bake an apple pie or something.1042

You need 10 apples; negative means that you need it or you borrowed it.1044

You have 8; you need 10; are you short?--do you have 2 left?1052

No, you don't have 2 apples left.1059

You used up all of your apples and you need 2 more.1060

That would be a -2 because you are short 2; that is a -2.1065

It would be 8 minus 10 would be -2.1072

That is it for this lesson; thank you for watching Educator.com.1080