Video: Solving Word Problems Using Long Division of Multidigit Numbers by 3-Digit Numbers

A truck can carry 605 watermelons in one trip. How many trips will it take to transport 50,820 watermelons?

06:48

Video Transcript

A truck can carry 605 watermelons in one trip. How many trips will it take to transport 50820 watermelons?

This problem describes a truck delivering watermelons. And we’re told that it can carry 605 watermelons in one trip. Then the question asks us, how many trips will it take to transport 50820 watermelons? How many lots of 605 are there in 50820? To find the answer, we’re going to need to divide 50820 by 605. In other words, we need to divide the large amount of watermelons into batches of 605, one for each trip. And we’ll be able to tell the number of trips we need to make. To calculate the answer, we’re going to need to use long division because these numbers are so large. How many lots of 605 are there in 50820?

We’re dividing by a three-digit number. So starting with a single digit or even a two-digit number simply aren’t large enough. In fact, if we look at the first three digits of our number, we still can’t divide by 605 because 508 is still too small. We’re going to need to look at the first four digits. How many lots of 605 are there in 5082? There’s one number that we can multiply 605 by that would be a good starting place here. We know that when we multiply by 10, the digits in a number shift one place to the left. And so we know that 10 lots of 605 will be 6050. Although this is too large, at least it gives us a good starting point. Perhaps we should work backwards and see what nine lots of 605 are.

To find nine lots of 605, we simply need to subtract one lot of 605 from 6050. And there’s a quick way we could do this involving partitioning. We could split 6050 into a pair of two-digit numbers. On the left, we can see six and zero. This tells us the number of hundreds in the number. 60 hundreds are the same as 6000. So if we start off with 60 hundreds and we subtract 600, we’re left with 54 hundreds, which is the same as 5400. And our right-hand pair of digits shows the tens and the ones in our number, which is equal to 50. We’ve already subtracted 600, so now let’s just subtract the five. 50 take away five leaves us with 45. So we can say that nine lots of 605 equals 5445.

Remember the number we’re looking to get close to is 5082. So this is still too large. Let’s subtract another lot of 605 and see what eight lots of 605 are worth. Again, we can partition our number into the number of hundreds and then a two-digit number on the end to help us. 5400 is the same as 54 hundreds. And if we subtract 600 from 54 hundreds, we’re left with 48 hundreds or 4800. So we’ve subtracted the 600, part of 605. Now we just need to subtract the five. Our tens and our ones are 45. So if we take away five from this, we’re left with 40. Eight Lots of 605 are equal to 4840. So we can complete the first part of our division. There are eight lots of 605 in 5082. Now, we need to calculate the remainder.

We said that eight lots of 605 was 4840. And if we subtract this number from 5082 we can see what we have left. Two ones take away zero ones equals two ones. Eight tens take away four tens leaves us with four tens. We can’t subtract eight hundreds from zero hundreds. So we need to exchange with the thousands column. We’ll take one thousand and we’ll exchange it for 10 hundreds. And now we have 10 hundreds to take away our eight hundreds from which is going to leave us with two hundreds. Our remainder is 242. Now, we can’t divide this number by 605. So we’re going to need to include another digit. And we’ve got one more digit at the top that we can bring down. 242 is going to become 2420.

How many lots of 605 do we expect to be in this number? Well, we could think of 605 as being very close to 600. So we can count in six hundreds to see how close we can get to 2420. One lot of 600 is 600; two lots of 600 equals 1200. Then we have 1800 — notice how this is just our six times table with two zeros on the end. And then four lots of 600 equals 2400 which is very close to 2420. Let’s try multiplying 605 by four then. Five fours are 20; zero tens multiplied by four is zero. We’ve already got two tens that we’ve exchanged. So the answer is two. And then, as we’ve said already, six hundreds multiplied by four is 24 hundreds or 2400. It makes 2420 exactly.

So we can complete our answer by writing that there are four lots of 605 in 2420. And then, just as a neat way to show there’s no remainder, we can subtract four lots of 605 which we’ve said was 2420 from the number that we had, which was 2420 itself. And of course, this leaves us with nothing at all. And so we used long division to help find the answer. If a truck can carry 605 watermelons in one trip, the number of trips that it will take to transport 50820 watermelons will be 84. The correct answer is 84 trips.

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