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

Question Video: Applying the Properties of Operations in Mathematical Problems

Complete the expression 9840 ÷ 16 = (_ − 15).


Video Transcript

Complete the expression 9840 divided by 16 equals what take away 15.

Here, we have an expression with two calculations either side of an equal sign. And the equal sign tells us that the expression is balanced. Both sides of the equal sign are worth the same. So, the answer to 9840 divided by 16 is exactly the same as the missing number that we’re looking for take away 15. So, the first thing we can do to help us to find our missing number is to work out the answer to the division.

What is 9840 divided by 16? We can use long division to help find the answer. Before we start, let’s make a note of all the multiples of 16 that we know already. Perhaps we could use these to help us as we go through the calculation. Well, we know what one lot of 16 is. And two 16s are 16 doubled. So, that’s 32. If we double 32, we get the answer to four lots of 16, which is 64. 10 16s, we know, are 160. And half of this will give us five lots of 16. Half of 160 is 80.

So, there, we have some quick number facts about multiples of 16. Perhaps we might find them useful. Now, we can’t divide nine by 16; it’s too small. So, we must look at the first two digits. How many 16s are there in 98? Well, we can see straightaway one of our number facts can help us. We know that five 16s are 80. This means we can work out what six 16s are if we add 16 to 80. 80 plus 16 equals 96. And so, we can say straightaway that there are six lots of 16 in 98. Let’s write the six at the top.

Now, we said that six 16s were worth 96. And if we subtract 96 from the 98 that we began with, we have a remainder of two. Now, again, two is too small to be dividing by 16. So, we need to include another digit. And this time we need to bring down a digit from the top. How many 16s are there in 24? We know that two 16s are 32. And this is too large, so there’s only one lot of 16 in 24. Let’s calculate the remainder.

We know one lot of 16 is worth 16. And if we subtract this from 24, we get the answer eight. A quick of working this out is by counting up from 16 to 24. We can’t calculate the number of 16s in eight, so let’s bring down our final digit. How many 16s are there in 80? Once again, those facts we worked out at the start are proving useful. We know that five 16s are worth 80. So, there are five lots of 16 in 80. And this time, there’s no remainder. Five 16s are 80. And if we subtract 80 from 80, we get the answer zero. There’s no remainder.

So, now, we know that the division on the left-hand side of our expression is worth 615. Now, we can write our expression as a subtraction. What take away 15 equals 615? We can find the answer by adding 15 to 615. We know that two lots of 15 equal 30, and so 615 plus 15 equals 630. We can complete the expression using the number 630. 9840 divided by 16 is equal to 630 take away 15. Both sides of the expression are worth 615. And our missing number is 630.

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