Video: Solving Word Problems Using Long Division of Multidigit Numbers by 2-Digit Numbers

Matthew receives a weekly allowance which totals $1820 in a year. Using that there are 52 weeks in a year, determine how much he receives each week.


Video Transcript

Matthew receives a weekly allowance which totals 1820 dollars in a year. Using that there are 52 weeks in a year, determine how much he receives each week.

We’re told that Matthew receives a certain amount of money each week. This is his weekly allowance. We’re also told the total that he gets over the course of a year and that’s 1820 dollars. We know that a year is made up of 52 weeks. And so, Matthew gets 52 of these weekly allowances. So the question asks us to use this information to try to work out how much he gets every week. 52 weeks multiplied by something equals 1820.

What do we need to do to solve the problem? Well, we can juggle the multiplication around a little and look at the inverse. The inverse of multiplication is division. And if we divide 1820 by 52, we’ll find out the amount that Matthew gets each week. If you imagine Matthew having his yearly amount in front of him and also 52 envelopes one for each week. If he split up the yearly amount into 52, inside each envelope would be the amount that we’re looking for. So, how are we going to divide 1820 by 52? We can use long division.

There are no 52s in one and 18 is too small too. So we need to start by looking at the first three digits. How many 52s are there in 182? We can use estimation to give us a good idea where to start. We can round 52 to 50. We know that two lots of 50 is 100 and three lots of 50 equals 150. So perhaps, three lots of 52 might take us close. Three lots of 50, as we’ve just said, equals 150. And three lots of two equals six. So three lots of 52 equals 156. This is fairly close to 182. We don’t need to think about four times 52.

So we know there are three lots of 52 in 182. So we can write the digit three at the top. And now, we need to calculate how much the remainder is. We said that three lots of 52 was 156. So let’s subtract this from 182. We can’t subtract six ones from two ones. So we’re gonna have to exchange to help us. We’ll exchange one ten. So we now have seven tens instead of eight tens. And we’ll exchange it for ten ones. And now we can complete the subtraction. 12 ones take away six ones leaves us with six ones. And seven tens take away five tens leaves us with two tens. And in our hundreds column, we’re taking away 100 from 100. So that’s a zero. Our remainder is 26.

How many 52s are in 26? Well, 26 is too small. 26 is actually half of 52. And if you want to challenge, pause the video and think about how you could use this to help. But in the meantime, we need to make this a three-digit number. And so, we need to bring down our final zero. How many 52s are in 260? Again, we can use estimation to help. We’ll think of 52 as being worth 50. And let’s round 260 down to 250. So we’re dealing with multiples of 50. How many 50s are in 250? Well, we know five times five equals 25. And so, five times 10 lots of five equals 10 lots of 25 or 250. It looks like five might be a good estimate. Let’s partition 52 again to help us multiply it by five. As we’ve just said, five multiplied by 50 equals 250 and five multiplied by two equals 10. 250 plus 10 equals the 260 that we’re looking for. There are five lots of 52 in 260. And we can check there’s no remainder by subtracting 260 from 260. Of course, the answer is zero. There’s no remainder.

And so, we found the number of dollars that Matthew receives every week. We used long division to help us find the answer. Matthew’s weekly allowance comes to 1820 every year. We know that there are 52 weeks in a year. And so, every week, we know that Matthew gets 35 dollars.

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