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# Dividing a whole number by a decimal

CCSS Math: 6.NS.B.3

## Video transcript

Let's divide 518 by-- so we're
going to divide it by 0.7. So we're dividing this
whole number by a decimal. So we could also
write this as 518 divided-- let me write a
little bit bigger than that, since we have to do
some work with it. 518 divided by-- I'll
do the division sign in white-- divided by 0.7. So the first thing we do, since
we have this decimal here, we're dividing by a decimal. So try to turn this into
a whole number somehow. Well, the best way to turn
this into a whole number is to multiply this by 10, which
is essentially multiplying, shifting the decimal
point over to the right. So this would become a 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 a value does not change. So we need to multiply
both of these times 10. So if we move the decimal
over to the right with the 0.7 to turn into a 7, we also
need to move the decimal over to the right for 518. Now, you're probably
saying, well, I don't see a decimal in 518. Well, there is one. You just didn't have to write
it, because it's 518.00-- and we can add as many
zeroes as we want. So if we move the decimal to
the right, 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 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 actual value 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. You multiply both the numerator
and denominator by 10, you will get 5,180 over 7. So let's clean this
up a little bit, just so we remember what we did. So we moved the decimal
over to the right, one. So now this is just a 7. The decimal is there. In fact, we really don't have
to write the decimal anymore. It's just a 7.0-- you
could imagine 7.0, so we can just
write this as a 7. And then the 518, the
decimal is now out here. So this is 5,180. And let's increase the
sign right over here. Now, this is just a straight-up
long division problem. How many times does 7 go into 5? Well, it goes 0 times. 0 times 7-- 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. And now we can
bring down this 8. 7 goes into 28 four times. 4 times 7 is 28. Subtract, you get a 0. Now we can bring down another 0. We want at least get
to the decimal place. So we bring down another
0 right over here. When I say get to
the decimal place, we could put the
decimal place up here too, just to
make sure we're keeping track of the
right place values or that we can have the
decimal in the right place. So notice, I'm very particular. When I'm doing 7 goes into 51,
I put the 7 right above the 1 in the 51's place. When I'm saying 7
goes into 28, I'm putting the 4 right above
the 8 in this one's place when we're doing the division. So now we say how many
times does 7 go into 0? Well, it goes 0 times. 0 times 7 is 0. Subtract, you have no remainder. So we could keep going, and
we'll just keep getting zeroes like this. But we see that this
is equal to 740.