Dividing by a Decimal
[One speaker]
[Video starts with title: Dividing by a Decimal. Changes to a blank page.]
Instructor: Welcome to the video on dividing by a decimal.
Here we have an example, twelve divided by one point five [or 12÷1.5]. Previously we’ve shown the dividend as a decimal. The dividend is this number [points to the number on the left of the division sign], it’s the original amount that we started with. In this case, our divisor, which is this number [points to the number on the right of the division sign] is actually a decimal as well. So how would we go about doing this?
You may have been taught that when doing the division algorithm with a decimal and the divisor, that just move the decimal over however many spaces you need. So in this case we move the decimal over one space.
For example, you may have been taught to do twelve divided by one point five, and then move the decimal over. So, since we had to move the decimal over one place here on the one point five, we move the decimal place over one space in the dividend as well [writes: 1.5 ⟌12. An arrow points the movements of the decimal point one space to the right in both numbers leaving it like: 15⟌120]. Now our problem is the same as one hundred twenty divided by fifteen [writes: 120÷15, on the right side of the page]. So why does this work? Let’s look at it for a second.
Let’s say we have six divided by two [or 6÷2]. We can represent six divided by two with the following squares. [six squares in two columns of three show up right next to the problem]. Here we have six boxes, if we divide them into two groups, or two sets, how many would we have in each set? We have one, and two sets [circles each set], and each set has three inside of it. So six divided by two equals three [writes next to the squares: =3].
Now, what if we multiply both of these by ten? Instead of being six divided by two, we had sixty divided by twenty [or 60÷20]. In this case we’ve just multiplied six times ten is sixty, and two times ten is twenty. What would we get? Here we have sixty, and if we want to divide it into twenty different sets, we want to find out how many would be in each set [sixty squares appear next to the problem making twenty rows of three boxes each]. So sixty divided by twenty. So, we have twenty rows going across each of these. Ten here [points to a group of ten rows], and another ten [points to the second group of ten rows]. So if we wanted to divide this by twenty we can very easily select each row and that would make twenty sets [circles one row of three boxes]. We could easily just divide by rows. So this would be our first group [circles the first row], here’s our second group [circles the second row], and so on all the way down to our twentieth group [circles the last row]. So we’ve taken sixty boxes and divided by twenty, and look, once again there are three in each box. So our answer to sixty divided by twenty is also three [writes next to the squares: =3].
This demonstrates that as long as you multiply both numbers by the same number, in this case, ten, that your division problem will still come out the same, you’ll still get the same answer.
Now, if we go back up, all we did up here [goes back to the first problem 12÷1.5] is instead of dividing twelve by one point five, we divided a hundred and twenty by fifteen. In this case that meant that we multiplied both by ten. Twelve times ten is a hundred and twenty, one point five times ten is fifteen.
[New page, blank]
So just to go over the steps one more time. When you’re doing the division algorithm and there’s a decimal in the divisor, multiply both numbers by the power of ten that will make the divisor an integer [shows the last phrase on the screen, goes back to the blank page].
For example, eight point seven two divided by two point one three [or 8.72÷2.13]. In this case we have two digits after the decimal points. So we need to move this decimal two place values to the right [pointing to the number on the right side of the dividing sign]. We do that by multiplying by one hundred [writes: x100 at the right side of the problem].
So if we multiply both numbers by one hundred, we will get eight hundred seventy-two divided by two hundred thirteen [or 872÷213]. Eight hundred seventy-two divided by two hundred and thirteen will give us the same answer as eight point seven two divided by two point one three.
Let’s do one more quick example, forty-three point eight seven five divided by two point one [43.875÷2.1]. In this case, our decimal only needs to move over one place value [pointing to the number on the right side of the dividing sign]. So we only need to multiply both numbers by ten. I’ll write ten out here, multiply by ten [writes: x10 at the right side of the problem]. So once we do that we will get four hundred thirty-eight point seven five divided by twenty-one [or 438.74÷21].
And this will give us the same answer as our original problem.
[End of video.]