Topic G: Partial quotients and multi-digit decimal division
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- [Instructor] What we're going to do in this video is get a little bit of practice estimating dividing with decimals. So for example, we wanna figure out approximately, that's what these kind of squiggly equal sign means. This means approximately equal. So what does 80 divided by 1.94 approximately equal? So we wanna estimate what this is. So pause this video and see if you can figure it out. So before we even look at these choices, how would we try to do this in our head? Well, we could say 1.94, it's hard to do that in our head to divide it into 80 but it's awfully close to two. So we could say this is close to, this is approximately equal to 80 divided by two 'cause once again, 1.94 is awfully close to two and then this is easy to figure out. That is going to be equal to 40. So our first expression, you could say is approximately equal to 40. Is it exactly equal to 40? No but it's pretty close. So I would select that choice. Let's do another one. So pause this video and see if you can figure out the approximation. What is 209 divided by three roughly equal to? So once again, here we don't have any clear decimals. If we were to divide it out, we would get a decimal answer for our quotient but what we could do is well, is either one of these, is for example 209, is it close to a multiple of three that we might recognize? Well, you might immediately recognize, well, if you think about multiples of three, you think in terms of, well, three times six is 18, three times seven is 21. Well, this is close to 210. So this is approximately equal to 210 divided by three. Now, why is this interesting? Well, 210 is just 21 times 10. So if 21 divided by three is seven, 210 divided by three is going to be equal to 70. So once again, 209 is pretty close to 210. Remember, we're just estimating and so 209 divided by three would approximately be equal to 70 which is that choice right over there. Let's do one more example. So once again, pause the video and figure out what 6.86 divided by 1.12 is approximately equal to. Alright, so here I would just try to round to the nearest whole number and see if that helps my division in my head. So 6.86 is approximately seven if we round up to the nearest whole number and if I say seven divided by, and if we round down, 1.12, seven divided by one, this is much easier for us to do in our head. So that is going to be seven. Now, once again, it's very important to realize these are estimations. It's not going to be exactly equal to seven but it's definitely gonna be much closer to seven than 70, 700 or 7000.