Lesson 4: Multiplication with Decimal Numbers #3

[One speaker]

[Video begins with a white screen as it displays “4.9 x 1.2 = ?” in the top-left corner.]

Speaker: Four and nine-tenths times one and two-tenths. We’re going to start by stacking our numbers, and we usually put the one with the most digits on top, but in this case they both have the same number of digits, so I’m going to place our larger number on top, just because it makes it a little bit easier.

So we have four and nine-tenths [writes “4.9”] times one and two-tenths [writes “x 1.2” underneath ‘4.9,’ and then draws a line underneath all of it]. Okay, and then we’re going to start multiplying by columns beginning with the number in the bottom right. So I’m going to multiply by both columns, and then we’ll move to the one, and multiply by both columns.

Before we do that though, let me make it so we can see decimal points a little bit better. Okay, so now if we begin in the bottom right, we have two times nine is eighteen, so we’ll place our eight there and carry our one [puts an ‘8’ underneath the ‘2’ and puts a ‘1’ above the ‘4’]. Then we have two times four is eight, plus one is nine [puts a ‘9’ underneath the ‘1’]. And now we move to the column to the left, and we want to remember to put our zero before we begin [puts a ‘0’ underneath the ‘8’].

And now we have one times nine is nine [puts a ‘9’ underneath the nine that was just written a minute ago], and one times four is four [puts a ‘4’ to the left of the last nine that was written]. And now we will add those two together [puts a plus sign in front of the ‘4’ at the bottom and draws a line underneath the “98 + 490”].

And so we have eight plus zero is eight [puts an ‘8’ directly below the zero]. Nine plus nine is eighteen, so I’ll write my eight and carry my one [puts an ‘8’ underneath the two nines and puts a ‘1’ above the lower of the two fours]. And four plus one is five [puts a ‘5’ below the four].

And now, it looks like we’re done, but we have to remember our last step of moving the decimal place over—decimal point over, excuse me—because if we were to estimate this, four point nine can round to five [writes a ‘5’ below the ‘9’ of the original problem], approximately five [puts a multiplication sign after the ‘5’] and one point two is approximately one [writes a ‘1’ after the multiplication sign], and so five times one is five [writes “= 5” after the ‘1’], but our answer of five hundred eighty-eight (588) is nowhere near five, so that should be a big red flag to us. But if we remember our last step, we count the number of decimal places that we have—one, two—and then we move our decimal place over that many spaces, so one, two [puts the decimal between the five and the eight in ‘588’ to now make it “5.88”]

And so then we can see, yes, our answer is indeed close to five, our answer is five—let’s rewrite it—five and eighty-eight hundredths [writes “5.88” over to the right and draws a box around it].

[End of video.]