Dividing a whole number by a decimal

Let's divide 500 and 18 by 0.7.

So we're dividing this whole number by a decimal.

So we can also write this as 518 divided by.

Let's write it a little bigger.

We're going to have to some work with it. 518 divided by 0.7.

So the first thing we do since we have this decimal here we're dividing by decimal is try to turn this into a whole number somehow.

Well the best way to turn this into a whole number is to multiply it by ten.

Which is essentially multiplying by shifting the decimal point over to the right.

So this would become 7.

But we can't just do that only for what we're dividing by we also have to do that to the 518.

So that the value does not change.

So we need to multiply booth of these times ten.

So if we moved the decimal over to the right with the 0.7 to turn into a 7 we also need to move the decimal over the right to 518.

Now you're probably saying "I don't see a decimal in 518".

Well there is one you just didn't have to write it cause it's 518 point 00 and we can add as many zeroes as we want.

So if we move the decimal to the write it becomes 5,180.

So really what we're saying is 518 divided by 0.7 is the same thing as 5,180 divided by divided by 7.

Notice all we did by moving the decimal one place to the right is we multiplied both of these numbers by 10 which is not going to change the accuracy of the decimal.

One other way of thinking about this, if you wanted to write this as a fraction this is the same thing as 518 over 0.7 0.7.

You multiply both the numerator and the denominator by 10 you'll get 5,180.

You'll get 5,180 over 7.

Over 7.

So let's clean this up a little bit so we remember what we did.

So we move the decimal over to the right.

So now this is just a seven.

The decimal is there.

In fact we don't have to write the decimal anymore.

It is just 7.

Solet's just write this as a 7.

Then the 518 the decimal is now out here so this now 5,180.

So let's increase, increase this sign over here.

Now this is just a strait up long division problem.

How many times does 7 go into 5?

We'll it goes in 0 times

Actually let's just cut to the chase 7 doesn't go into 5.

It does go into 51.

7 times 7 is 49.

So it goes 7 times .

7 times 7 is 49.

Subtract 51 minus 49 is 2.

Now we can bring down this 8.

7 goes into 28 4 times.

4 times 7 is 28.

subtract and you get a 0.

Now we bring out another 0.

Now we can at least bring out the decimals place.

So bring down another 0 right over here.

What I say by when you get to the decimal place you can put the decimal place up here to make sure keeping track of the right place values.

Or that we have the decimal int he right place.

So you know some very particular what I'm doing .

7 goes into 51.

I put the 7 right above the 1 in the 51's place.

So 7 goes into 28.

I'm putting the 4 right above the 8 int he ones place when we're doing division.

So now we can say how many times 7 goes into 0.

We'll it goes into zero times 0 times 7 in the end is 0.

So yo subtract and you have no remeinder .

So we could keep going and will just keep getting zeroes like this.

But you see that this is equal to 740.

700 and 40.