Question Video: Applying the Properties of Operations in a Mathematical Problem | Nagwa Question Video: Applying the Properties of Operations in a Mathematical Problem | Nagwa

# Question Video: Applying the Properties of Operations in a Mathematical Problem

Complete the expression 6324 ÷ 12 = 17 + ＿.

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### Video Transcript

Complete the expression 6324 divided by 12 equals 17 plus what.

In this expression, we have two calculations that are worth the same. We know this because of the equal sign in between them. On the left-hand side, we have a calculation that we could work out the answer to, 6324 divided by 12. And whatever this is worth, we know that it has the same value of 17 plus a mystery number. This is the mystery number we need to find. So how are we going to be able to complete the expression and find this missing number?

Well, first, we could find what the expression on the left-hand side is worth, 6324 divided by 12. And after we’ve done this, we could subtract 17 to see what number we’d need to add to 17 to make this total. To begin with then, let’s find out how many 12s there are in 6324. And we can do this using long division. Rather than look just at the first digit, we need to begin by thinking about the first two digits. How many 12s are there in 63?

To help us here, we can think about some multiplication facts that we already know about the 12 times table. For example, we know that 10 lots of 12 are 120. Now, if we find half of this amount, this will be the same as finding five lots of 12. And half of 120 is 60. So we can say that there are five lots of 12 in 63. Five lots of 12 are 60. And if we subtract this from 63, we can see that the remainder is three. There are no 12s in three. So we need to bring down another digit. This will be the digit two. And it’s going to turn our three into 32.

How many 12s are there in 32? We know two 12s are 24. And this is as close as we can get to 32 without going above it. So there are two lots of 12 in 32. To find the remainder, we need to subtract two lots of 12, which is 24, from 32. We know the difference between 24 and 30 is six. So the difference between 24 and 32 will be two more than six. The difference is eight. There are no 12s in eight. So again, we need to bring down another digit. This time, it’s a four. How many 12s are there in 84?

We can start counting at a multiplication fact we already know. We’ve already said five 12s are 60. This means that six 12s are 12 more than 60 or 72. And so seven 12s are another 12 on top of that, which takes us to 84. There are seven lots of 12 in 84. And of course, if we subtract seven lots of 12, which is 84, from the number we were dividing, which was 84 as well, we get a remainder of zero. There’s nothing left over. And so, here is our answer. 6324 divided by 12 equals 527.

Remember, to find our missing number, we still need to subtract 17. And to understand why we need to do this, let’s replace our division expression, 6324 divided by 12, with the answer that we found, which was 527. We can now see that 527 is equal to 17 plus something. So to find out what that something is, we need to subtract 17 from 527. Well, we know that 27 is made up of 17 and 10. So if we subtract 17 from 527, we’re left with 510. And so our missing number is 510.

Our completed expression is 6324 divided by 12 is equal to 17 plus 510.

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