Find the missing number.
The diagram shows a part-whole model. We can see that the whole amount is 773. And this whole amount has been split into two parts. There’s a part that at the moment is missing. And our second part is 73. Now, we can see that both parts are labelled. For example, the number 73 is labelled number of ones. Now, in the number 773, there’s only the digit three in the ones place. But we also know that each 10 is worth 10 ones. So we could say that the seven tens in our tens column are worth 70 ones. That’s why we can write the number of ones in 773 as 73.
Now, it would be very easy to look quickly at our part-whole model and think, “What do we add to 73 to make 773? Well, surely, the answer must be 700. 700 plus 73 equals 773. This is often the way that a part-whole model does work. But as we’ve mentioned already, both parts have been labelled. And we can see that the part on the left is labelled number of hundreds. So we can see now why we can’t just write 700 in there. There aren’t 700 hundreds in 773.
Let’s complete our place-value grid to see how many hundreds there are. There are seven hundreds in 773. And so, the missing number in our part-whole diagram is the number seven. Instead of showing us two numbers that we add together to make 773, our part-whole model shows us the place value of different digits that we can then add together to make 773. Our first part — and that’s the missing number — shows the number of hundreds, which we said was worth 700. And our second part shows us the number of ones. 73 ones are worth 73. And now, we can combine the two values together and we get the total. Our missing number is the number of hundreds that there are in 773. The answer is seven.