Adding Real Numbers Application

Knowledge encountered:

Addition and Subtraction
Number line
Positive and Negative numbers

At the beginning of the week,

Stewart's checking account had a balance

of negative fifteen dollars and eight cents.

On Monday morning he deposited a check

for four hundred twenty-six dollars and ninety cents.

On Tuesday morning he deposited another check

for [one] hundred dollars.

How much was in Stewart's checking account

after the second deposit, so after both of these deposits right over here?

So, he starts off with a negative balance,

so a negative balance means

that he's overdrawn his checking account.

He actually owes the bank money now.

Luckily, he's now going to put some money in his bank account,

so he'll actually have a positive balance in his checking account.

So, he starts off with negative fifteen dollars and eight cents,

and then to that, he adds

four hundred twenty-six dollars and ninety cents.

And then he adds another hundred dollars.

So, he started off with negative fifteen dollars and eight cents,

and then to that, he adds four hundred twenty-six dollars

and ninety cents and a hundred dollars.

So, that's five hundred and twenty-six dollars and ninety cents.

And so, how much is he going to have in his bank account?

He started, owing fifteen dollars and eight cents,

and then he's going to add

five hundred twenty-six dollars and ninety cents.

So, one way to visualize it,

is if you think about it on the number line,

and this is zero right over here.

He starts off at negative fifteen-point-zero-eight,

but then he's going to add

five hundred and twenty-six dollars [and ninety cents].

This is fifteen-point-zero-eight to the left,

that's how much he owes,

and to that, he's going to add

five hundred and twenty-six [dollars and ninety cents].

So, I'm not drawing this to scale,

but to that he's going to add

five hundred and twenty-six dollars and ninety cents.

So, the amount that he's going to be in the positive

is going to be

five hundred twenty-six dollars and ninety cents,

minus the fifteen-point-zero-eight.

And, so, essentially it's going to be this length right over here,

that's how much he's going to be in the positive,

That's going to be five hundred twenty-six dollars and ninety cents,

minus fifteen dollars and eight cents.

So, that's going to be--

and we can even just rewrite this

so that it actually looks exactly like that.

That's the exactly the same thing as

five hundred twenty-six dollars and ninety cents,

minus--

minus--

adding a negative is the same thing

as subtracting a positive--

minus fifteen-point-oh-eight.

--I will do this in another color--

Five hundred and twenty-six dollars and ninety cents,

minus fifteen dollars and eight cents.

Let's see, zero is less than eight,

let's make that a ten and borrow from this nine,

so that becomes an eight--

or I guess you could say, we are regrouping--

Everything up here is larger than everything there,

so ten minus eight is two,

eight minus zero is eight,

we have our decimal.

Six minus five is one.

Two minus one is one,

and then you have five minus nothing.

So, he is left

with five hundred eleven dollars and eighty-two cents,

after his second deposit.