Uploaded by videosbyjulieharland on 18.05.2011

Transcript:

>>Hi this is Julie Harland

and I'm your math gal.

Please visit my website

at yourmathgal.com

where you could search for any

of my videos organized

by topic.

We'll be translating verbal

expressions

into algebraic expressions

so there's some terms we need

to know.

The first one is sum.

When you see the sum

that refers to addition

so when you see this word sum

it means we're going

to be adding.

Okay, sum is the same thing

as adding.

So we read this,

the sum of a number

and 6 makes sense,

if you have a sum you've got

two things.

So the two things we have,

so you've got a number and 6.

Usually it's separated

by that word and, okay?

So what do we call the number?

Well let's just use

a variable.

I'm gonna use n for a number.

So we could write n,

that's one part of the sum

and 6 is the other part

of the sum.

So that's how we would write

the sum of a number and 6.

What about the difference

of a number and 2?

Difference refers

to subtraction

so when you see the word

difference it means we

are subtracting.

And again notice this is

of a number and 2.

The two parts are separated

by that word

and so whatever comes first

you'll put before the minus

sign and what comes

after the word

and is what you

would subtract.

That's how you would

differentiate what comes first

and what comes second.

So again, let's just use n

again to represent the number,

it has to be a variable,

and 2.

So n minus 2 is how we would

write the difference

of a number in 2.

Alright next one, the product

of a number and 5,

product means multiplication

so when you see the word

product you have to associate

that with multiplying.

We've got a number and 5

so how would we write a number

and 5 multiplied together?

Well you could say n times 5,

right?

Often you would write this

as 5 times n.

And the most simplified way

of writing it is you know

when you have a dot between it

and you have a variable

and a number you can just put

it together

and write it as 5n.

Now you could also put a

parenthesis around the n

or a parenthesis around the 5

or a parenthesis

around both of them.

There's more

than these three ways

to show a product

but 5 n is probably the

simplest way

of writing this answer

so that would be the product

of a number and 5.

The last one will be the

quotient or ratio.

Both of those words

represent subtraction.

Both quotient

and ratio mean division

but we usually don't write the

division sign

when we are doing algebra

so a more common way

of writing this answer,

again we're separating a

number and 4

so those are the two things,

you could of course say the

number is n, n divided by 4

and it doesn't matter whether

it says quotient or ratio,

both of them mean the

same thing.

That represents division

so whatever comes first goes

before the division sign

so we have a number and 4,

those are the two things.

I forgot to circle it up here,

here we go.

So the more common way

of writing this is

as a fraction

so we say the quotient

of a number divided by,

we use the fraction bar,

and 4.

So this is the way we usually

want to write our answers

when we are doing algebra

so when we're working

with variables.

So we've got the sum

of a number and 6 and plus 6.

The difference of a number

and 2, n minus 2.

The product of a number

and 5 is 5n.

It looks funny to put n5.

We always put the coefficient,

the number part,

in front of the variable.

And the last is the quotient

or the ratio

of a number and 4.

The way we write that is n

over 4 so whatever comes first

you put in the numerator

and what comes second, and 4,

that's what goes

in the denominator.

Alright there are a lot

of ways of expressing

subtraction and there's a lot

of little nuances here.

Let's look at these,

6 more than a number,

that refers

to addition cause we're doing

more than something

so we're going to add it

so if it says 6 more

than a number, think of 6 more

than your age.

Well you have to know your age

and then you would add 6

to it.

So in this case 6 more

than a number means you start

with the number

so we have a number

and then we're gonna do 6 more

than that so we're going

to add 6 to it.

Now the question is could you

write 6 plus n?

Certainly because n plus 6

does happen

to be the same thing

as 6 plus n.

But these next three are

subtraction

and it's gonna make a

difference what comes first

before the minus sign

and what comes

after the minus sign.

So look at this first one,

7 less than a number.

So one technique is thinking

about how you would answer

this question,

7 less than my age,

how would you get that answer?

You would take your age

and then you would subtract 7

from it.

So instead of starting

with an age we're gonna start

with a number, okay,

and then we're gonna subtract

7 from it.

So this is tricky.

It's not 7 minus n. What it's

saying is 7 less

than a number means you have

to start with a number

and then subtract 7 from it.

Now look at this third one,

it's not the same.

It says 7,

oops it is the same.

I didn't mean

to put less than.

I meant to put 7 less

a number.

A little bit different.

Seven less a number,

well first

of all most people don't talk

that way but you might see

this once in a while.

Seven less a number means we

start with 7 less a number

means we take away

that number.

So this is 7 minus n,

that's pretty tricky.

What's the difference?

It doesn't have

that word less than.

So again for this one 7 less

than a number,

if you're not sure how

to do it, put

in something you would know

like your age

and then do the same thing

using a number as opposed

to your age.

Seven less a number,

that's like saying 7 less 2.

You mean you start with 7,

subtract 2.

And how about this last one,

9 decreased by a number.

It means I've got to start

with 9 and then I'm gonna

decrease it so I have

to take something away from it

and I'm gonna take away the

number, again I'll call it n.

These are pretty tricky,

the ones for subtraction.

So you can see we have the

word difference,

which means subtraction

but here's some other ways

that subtraction might

come up.

You also might see minus

or you might see subtracted

from, decreased by, is here,

etcetera, there's a few more

that might pop up.

By the way,

these are all

just expressions.

They're not equations.

We're not solving

for anything.

We're just writing

an expression.

Notice there's no verb.

Six more than a number,

7 less than a number,

etcetera.

No verb. It's not going

to be an equation.

There's going

to be no equal sign.

We're simply writing an

expression from English

into mathematical symbols.

Let's try doing some

that are used

for multiplication.

Alright first one here,

twice a number,

what does that mean?

Twice a number just means 2

times the number

so we're gonna use n

for the number,

2 times the number you would

just write as 2n.

Now this next one I'm putting

two things together.

It says 3 times a number,

well what would that be?

That would be 3n.

Okay 3 times a number

subtracted from 10.

Okay, so what are you gonna

start with?

Three times the number

or the number 10?

Well you're subtracting

from 10 so that means you've

got to start off with 10

and then you're gonna subtract

something from it

and what are you

gonna subtract?

Three times a number,

that would be 3n.

So there are a couple examples

where we've got multiplication

in the mix

and the second one also has

the subtraction.

Okay try these two

on your own.

Put the video on pause and see

if you could write this

as an expression.

Go ahead and let the number be

n. Okay so what do we have?

Five added to the product of 9

and a number.

So we're adding 5 to something

so I have to do this

part first.

The product, remember,

means multiplication

and what are the two parts?

I've got 9 and a number.

So how do I write the product

of 9 and a number?

I do 9 times n which is 9n.

And then it says I'm gonna add

5 to that so then I add 5.

That's what you should get.

Alright, excellent.

Six less than the quotient

of a number and 4 so 6 less

than something means I'm gonna

take away 6 from something.

So I know I'm gonna subtract 6

from something,

now I've gotta figure

out what I'm subtracting

it from.

What am I subtracting 6 from?

The quotient,

okay remember what the

quotient means,

we write that as a fraction,

fraction bar

and we have the number and 4

so we'll put n

in the numerator,

cause that comes before the

word and, so in the 4

in the denominator

so we've got n over 4 minus 6.

So now we've written 6 less

of the quotient

of the number and 4.

[ Silence ]

>>Please visit my website

at yourmathgal.com

where you can view all

of my videos

which are organized by topic.

and I'm your math gal.

Please visit my website

at yourmathgal.com

where you could search for any

of my videos organized

by topic.

We'll be translating verbal

expressions

into algebraic expressions

so there's some terms we need

to know.

The first one is sum.

When you see the sum

that refers to addition

so when you see this word sum

it means we're going

to be adding.

Okay, sum is the same thing

as adding.

So we read this,

the sum of a number

and 6 makes sense,

if you have a sum you've got

two things.

So the two things we have,

so you've got a number and 6.

Usually it's separated

by that word and, okay?

So what do we call the number?

Well let's just use

a variable.

I'm gonna use n for a number.

So we could write n,

that's one part of the sum

and 6 is the other part

of the sum.

So that's how we would write

the sum of a number and 6.

What about the difference

of a number and 2?

Difference refers

to subtraction

so when you see the word

difference it means we

are subtracting.

And again notice this is

of a number and 2.

The two parts are separated

by that word

and so whatever comes first

you'll put before the minus

sign and what comes

after the word

and is what you

would subtract.

That's how you would

differentiate what comes first

and what comes second.

So again, let's just use n

again to represent the number,

it has to be a variable,

and 2.

So n minus 2 is how we would

write the difference

of a number in 2.

Alright next one, the product

of a number and 5,

product means multiplication

so when you see the word

product you have to associate

that with multiplying.

We've got a number and 5

so how would we write a number

and 5 multiplied together?

Well you could say n times 5,

right?

Often you would write this

as 5 times n.

And the most simplified way

of writing it is you know

when you have a dot between it

and you have a variable

and a number you can just put

it together

and write it as 5n.

Now you could also put a

parenthesis around the n

or a parenthesis around the 5

or a parenthesis

around both of them.

There's more

than these three ways

to show a product

but 5 n is probably the

simplest way

of writing this answer

so that would be the product

of a number and 5.

The last one will be the

quotient or ratio.

Both of those words

represent subtraction.

Both quotient

and ratio mean division

but we usually don't write the

division sign

when we are doing algebra

so a more common way

of writing this answer,

again we're separating a

number and 4

so those are the two things,

you could of course say the

number is n, n divided by 4

and it doesn't matter whether

it says quotient or ratio,

both of them mean the

same thing.

That represents division

so whatever comes first goes

before the division sign

so we have a number and 4,

those are the two things.

I forgot to circle it up here,

here we go.

So the more common way

of writing this is

as a fraction

so we say the quotient

of a number divided by,

we use the fraction bar,

and 4.

So this is the way we usually

want to write our answers

when we are doing algebra

so when we're working

with variables.

So we've got the sum

of a number and 6 and plus 6.

The difference of a number

and 2, n minus 2.

The product of a number

and 5 is 5n.

It looks funny to put n5.

We always put the coefficient,

the number part,

in front of the variable.

And the last is the quotient

or the ratio

of a number and 4.

The way we write that is n

over 4 so whatever comes first

you put in the numerator

and what comes second, and 4,

that's what goes

in the denominator.

Alright there are a lot

of ways of expressing

subtraction and there's a lot

of little nuances here.

Let's look at these,

6 more than a number,

that refers

to addition cause we're doing

more than something

so we're going to add it

so if it says 6 more

than a number, think of 6 more

than your age.

Well you have to know your age

and then you would add 6

to it.

So in this case 6 more

than a number means you start

with the number

so we have a number

and then we're gonna do 6 more

than that so we're going

to add 6 to it.

Now the question is could you

write 6 plus n?

Certainly because n plus 6

does happen

to be the same thing

as 6 plus n.

But these next three are

subtraction

and it's gonna make a

difference what comes first

before the minus sign

and what comes

after the minus sign.

So look at this first one,

7 less than a number.

So one technique is thinking

about how you would answer

this question,

7 less than my age,

how would you get that answer?

You would take your age

and then you would subtract 7

from it.

So instead of starting

with an age we're gonna start

with a number, okay,

and then we're gonna subtract

7 from it.

So this is tricky.

It's not 7 minus n. What it's

saying is 7 less

than a number means you have

to start with a number

and then subtract 7 from it.

Now look at this third one,

it's not the same.

It says 7,

oops it is the same.

I didn't mean

to put less than.

I meant to put 7 less

a number.

A little bit different.

Seven less a number,

well first

of all most people don't talk

that way but you might see

this once in a while.

Seven less a number means we

start with 7 less a number

means we take away

that number.

So this is 7 minus n,

that's pretty tricky.

What's the difference?

It doesn't have

that word less than.

So again for this one 7 less

than a number,

if you're not sure how

to do it, put

in something you would know

like your age

and then do the same thing

using a number as opposed

to your age.

Seven less a number,

that's like saying 7 less 2.

You mean you start with 7,

subtract 2.

And how about this last one,

9 decreased by a number.

It means I've got to start

with 9 and then I'm gonna

decrease it so I have

to take something away from it

and I'm gonna take away the

number, again I'll call it n.

These are pretty tricky,

the ones for subtraction.

So you can see we have the

word difference,

which means subtraction

but here's some other ways

that subtraction might

come up.

You also might see minus

or you might see subtracted

from, decreased by, is here,

etcetera, there's a few more

that might pop up.

By the way,

these are all

just expressions.

They're not equations.

We're not solving

for anything.

We're just writing

an expression.

Notice there's no verb.

Six more than a number,

7 less than a number,

etcetera.

No verb. It's not going

to be an equation.

There's going

to be no equal sign.

We're simply writing an

expression from English

into mathematical symbols.

Let's try doing some

that are used

for multiplication.

Alright first one here,

twice a number,

what does that mean?

Twice a number just means 2

times the number

so we're gonna use n

for the number,

2 times the number you would

just write as 2n.

Now this next one I'm putting

two things together.

It says 3 times a number,

well what would that be?

That would be 3n.

Okay 3 times a number

subtracted from 10.

Okay, so what are you gonna

start with?

Three times the number

or the number 10?

Well you're subtracting

from 10 so that means you've

got to start off with 10

and then you're gonna subtract

something from it

and what are you

gonna subtract?

Three times a number,

that would be 3n.

So there are a couple examples

where we've got multiplication

in the mix

and the second one also has

the subtraction.

Okay try these two

on your own.

Put the video on pause and see

if you could write this

as an expression.

Go ahead and let the number be

n. Okay so what do we have?

Five added to the product of 9

and a number.

So we're adding 5 to something

so I have to do this

part first.

The product, remember,

means multiplication

and what are the two parts?

I've got 9 and a number.

So how do I write the product

of 9 and a number?

I do 9 times n which is 9n.

And then it says I'm gonna add

5 to that so then I add 5.

That's what you should get.

Alright, excellent.

Six less than the quotient

of a number and 4 so 6 less

than something means I'm gonna

take away 6 from something.

So I know I'm gonna subtract 6

from something,

now I've gotta figure

out what I'm subtracting

it from.

What am I subtracting 6 from?

The quotient,

okay remember what the

quotient means,

we write that as a fraction,

fraction bar

and we have the number and 4

so we'll put n

in the numerator,

cause that comes before the

word and, so in the 4

in the denominator

so we've got n over 4 minus 6.

So now we've written 6 less

of the quotient

of the number and 4.

[ Silence ]

>>Please visit my website

at yourmathgal.com

where you can view all

of my videos

which are organized by topic.