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Question Video: Adding and Subtracting Multidigit Numbers to Solve Word Problems Mathematics

In a library, there are a total of 3,152 science books, English novels, and mathematics books. The number of science books is 1,023, and the number of English novels is 1,210. How many mathematics books are there in the library?

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Video Transcript

In a library, there are a total of 3,152 science books, English novels, and mathematics books. The number of science books is 1,023, and the number of English novels is 1,210. How many mathematics books are there in the library?

In this problem, we need to find the number of maths books that there are in a library. And we’re given some information to help us. Firstly, we’re told the overall total of science, English, and the maths books altogether. And this is 3,152. You know, if we were to represent this problem using a bar model, we’d start off by drawing a bar and labeling it with this number. This is the whole amount.

Now, we know there are three parts to this whole amount. There’s a number of science books, English novels, and mathematics books. Now, we don’t know the number of maths books. This is the part we need to find. So we can label this with a question mark. But we can split the rest of the bar into two parts because there are two pieces of information that we do know. We’re told that the number of science books is 1,023 and the number of English novels is 1,210. So how are we going to find the value of this missing part?

Well, it’s a good job we sketched a bar model ’cause it gives us a good idea of what to do. Our problem is going to involve subtraction because we need to find the difference between the total amount, which is 3,152, and the total of science and English books. But we don’t know an amount for that yet. We just know these amounts separately. So to solve this problem, there are actually two ways we could do it. The first method we could use is to add together 1,023 and 1,210. This will give us the total amount of science and English books. And then whatever this amount is, we could take it away from the whole amount to find the number of maths books.

Another way of finding the same answer would be to start with the whole amount and then just take away the two amounts of books that we already know, so 1,210, and then from whatever’s left take away 1,023. Let’s quickly show how these two methods will give us the same answer.

1,023 plus 1,210 gives us a total of 2,233. Remember, this is the total number of science and English books. Now, we can take this number and subtract it from the total amount. We’ll have to do a bit of regrouping to get there, but the answer’s 919. Now, if we check this just by showing the second method, we could start with the whole amount and subtract just the number of English novels. This gives us the answer 1,942. Now we’d need to do our second subtraction and take away the number of science books, 919.

We used a bar model to help us work out what we needed to do to solve this problem. And there were two ways. Both of them would’ve found us the correct answer, didn’t matter which one we chose. The number of mathematics books that there are in this library is 919.

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