Video: Dividing Integers Representing Capacities

A group of elephants drink 982 liters of water each day. How many days will 4910 liters of water last?

04:05

Video Transcript

A group of elephants drink 982 liters of water each day. How many days will 4910 liters of water last?

In this problem, we’re given an amount of water, 4910 liters. And we’re told that a group of elephants drink 982 liters every day. We need to find out how many days this large amount, 4910 liters, will last. So in other words, we need to divide 4910 by 982. How many lots of 982 are there in 4910?

This is an interesting question cause we might normally say let’s use long division. But we can’t find the number of 982s in four, 49, or even if we look at the first three digits of our number, 491. We have to just consider the whole number. How many 982s are there in 4910? We can’t do it bit by bit. So how could we find the answer if we don’t know our 982 times table?

Well, one method we could use is to start with 4910 and then use repeated subtraction, taking away more and more lots of 982 until we get to zero. That way, we could find out how many 982s there are in 4910.

Another method we could use is reasoning. Let’s use this method here now. Which multiplication fact do we know about 982 straight away without really thinking about it? Well, we can say that 10 lots of 982 are 9820. The digits shift one place to the left. Now compare this answer, 9820, by the number that we need to divide, 4910. What do we notice?

We know that half of 9000 is 4500. So could we say that 4910 might be around about half of 9820? It could be. It might be a good idea to work out what five times 982 is worth. To do this, we can use short multiplication. And even if we’re wrong, we could adjust our answer to find out what four lots of 982 or maybe six lots of 982 are.

But let’s start with five lots to begin with, 982 multiplied by five. Two times five equals 10. This is looking promising. The number that we need to get close to, 4910, ends in a zero. Eight times five equals 40. We’ve got one 10 underneath. So that gives us 41 tens. Looks like we might have found the right answer. We have a one in the tens place, which is what we needed. Now nine times five equals 45. So nine hundreds times five is 45 hundreds. We’ve got four hundreds underneath. So this takes us to 49 hundreds, 4910.

We estimated that there might be five lots of 982 in 4910. And so we worked out the multiplication. And we were right. There was. If a group of elephants drink 982 liters of water each day, then we know that 4910 liters of water will last five days.

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