Question Video: Decomposing Two-Digit Numbers in Multiple Ways in Place Value Tables Mathematics • 1st Grade

Which place value table also shows 74? Hint: Regroup tens into ones.


Video Transcript

Which place-value table also shows 74? Hint, regroup 10s into ones. We’re given three possible answers to choose from, 40 10s and 34 ones, four 10s and three ones, or four 10s and 34 ones.

Underneath the question, we can see a large place-value table. And in it, a two-digit number has been modeled using 10s and ones blocks. Underneath each of the pictures of blocks, we can see how many blocks there are. The number contains seven 10s and four ones. We know that the seven 10s have a value of 10, 20, 30, 40, 50, 60, 70. And of course, four ones are worth four. So our place-value table shows 74, and it’s being broken up into seven 10s, which we said will worth 70, and also four ones. 70 plus four equals 74.

Now, as we’ve said at the start, there are some smaller place-value tables at the bottom. These are our possible answers. These place-value tables don’t show the blocks. They just tell us how many 10s and ones there should be. And our question asks us which one of these place value tables shows 74 just like the one in the middle. To help us solve the problem, we’re given a hint. We’re told to regroup 10s into ones. You know, there’s something important that we know about 10s blocks. Each lot of one 10 is worth exactly the same as 10 ones. So, we could take one of our 10s blocks and regroup it into 10 ones, just like this. Instead of seven 10s, we now have six 10s. And instead of four ones, we now have 10 more ones. So we have 14 ones.

Six 10s are worth 60, and we know that 14 ones have a value of 14. And because 60 plus 14 equals 74, we know that six 10s and 14 ones make 74. If we look at our possible answers, though, none of them have six 10s in them. Maybe we ought to try exchanging another 10. Let’s swap this 10 here for 10 ones. Remember, each time we do this, we’re not making the number get bigger or smaller. It still shows 74. Instead of six 10s, we now have five 10s. And we have another 10 ones. So instead of 14 ones, we have 24 ones. We know that 50 plus 24 equals 74, so we can split up 74 into five 10s and 24 ones. Now, none of our possible answers say five 10s. But two of them have four 10s in the tens place.

Let’s regroup one more 10 into ones. Instead of five 10s, we now have four 10s. And we have another 10 ones. So instead of 24 ones, we have 34 ones. Four 10s are worth 40, and we’ve split 74 into 40 plus 34. Can you see the answer now? By regrouping 10s into ones, we’ve found another place-value table that also shows 74. Four 10s are worth 40, and 34 ones are worth 34. And we know that 40 and 34 go together to make 74. The place-value table that shows 74 is the one that shows four 10s and 34 ones.

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