Lesson 4: Division with Decimal Results #3

[One speaker]

[Video begins with a white screen displaying the problem to be solved: “21 ÷ 8 = ?”]

Speaker: Twenty-one divided by eight. Let’s get started by setting this up. We have twenty--one divided by eight [writes “ 8 ⟌21”]. Now we can look at this and say, “does eight go into two?” Well, eight cannot go into two because it’s larger than two, so we’re going to look at twenty-one, and we’re going to say, “how many times can eight go into twenty-one?”

Well, we know eight times two is sixteen, which is kind of close, and then we can think about it and look at eight times three. Well eight times three is twenty-four, and that’s over twenty-one, so we can’t use three. So we know, okay, let’s use two [puts a ‘2’ directly above the ‘1’]. Two times eight is sixteen [writes “16” below ‘21’]. Okay, now we can subtract that off [puts a minus sign in front of the ‘16,’ and puts a line underneath it], and we have one minus six—well, we can’t take six ones away from one one, so we need to come over to the tens place [crosses out the two in ‘21’] and regroup, and so that leaves us with one group of ten here [writes a small ‘1’ in front of the two in ‘21’] and we bring the other group of ten over to the ones place [puts a small ‘1’ in front of the one in ‘21’], and that will give us eleven ones.

And now we have eleven minus six is five [puts a ‘5’ underneath the ‘6’], and one minus one is zero. But because we still have something here, we want to keep going. So we can put our decimal point and a zero [writes “.0” to the right of ‘21’], and then we add our decimal point up top as well [puts a decimal point after the ‘2’ at the top]—see if we can get that to show up. Okay, and now we can bring down that zero [draws an arrow from the zero down to the end of the line at the bottom, and then adds a ‘0’ next to the five], and so now we’re looking at fifty. Well, how many times can eight go into fifty?

We know that eight times six is forty-eight, so let’s try that [puts a ‘6’ next to the decimal point at the top], and let’s extend that out a little ways [extends the line at the top a little further]. So we have six times eight is forty-eight [writes “48” underneath ‘50’], okay, and when we subtract that off [puts a minus sign in front of the ‘48’ and draws a line underneath it], we can’t take eight away from zero, so we’ve got to regroup [crosses out the ‘5’], which leaves us with four groups of ten [puts a ‘4’ in front of the five], and one group of ten comes over here to the ones place [puts a ‘1’ in front of the zero in ‘50’].

So ten minus eight is two [puts a ‘2’ underneath the eight in ‘48’], four minus four is zero, which we don’t need to write, but we still have something there, so we can add another zero and keep going [adds a zero next to the zero that already exists under the bracket], and let’s bring that zero down [draws an arrow from the zero just written to the end of the line that’s under ‘48,’ then writes a ‘0’ below the arrow]. And now we can look at, how many times does eight go into twenty? Well, we tried that at the beginning and we knew it was two, so two [puts a ‘2’ next to the six above the bracket]—two times eight is sixteen [writes “16” underneath the ‘20’ at the bottom], so we can subtract that off [puts a minus sign in front of the ‘16,’ then places a line underneath it], and we have, have to regroup [crosses out the two in ‘20’ and puts a ‘1’ to the left of it] and bring a group of ten over to the ones place [puts a ‘1’ in front of the zero in ‘20’]—so ten minus six is four [puts a ‘4’ underneath the six], and one minus one is zero.

Now if we look up here, we know from our video that sometimes we can stop at the hundredths place. But if we want to stop hundredths place, we actually need to go one place further in order to determine if we round up or down in the hundredths place. So we’re going to keep going one more time, and we’re going to add another zero [puts another zero next to the two zeros already under the bracket], and bring that down [draws an arrow from the zero just written down to the right of the six in ‘16,’ and puts a ‘0’ below it]. And so now, we’re going to say, “how many times can eight go into forty?”

Well, eight times five is forty [puts a ‘5’ next to the two above the bracket]—so eight times five is forty [writes “40” below the forty at the very bottom, puts a minus sign in front of it and a line below it]—and now we actually got to where we have no remainders [puts a ‘0’ underneath the line], and so, we could write our answer as two and six hundred twenty-five thousandths [writes “2.625” on the right], or if we were rounding [writes “2.” underneath the ‘2.625’ just written], we would look to the right of our hundredths place and we would see it’s a five, so we round up. So our rounded answer to the nearest hundredths [writes “63” to the right of ‘2.’] would be two and sixty-three hundredths (2.63).

[End of video.]