Place value when multiplying and dividing by 10 | Math | 4th grade | Khan Academy

What is 700s * 10?

Well, let's focus first on this times 10 part of our expression. Because multiplying by 10 has some patterns in math that we can use to help us solve.

One pattern we can think of when we multiply by 10 is if we take a whole number and multiply it by 10, we'll simply add a zero to the end of our whole number. So, for example, if we have a whole number like 9 and we multiply by 10, our solution will be a 9 with one zero at the end, or 90. Because 9 * 10 is the same as 9 10, and 9 t is 90.

So, let's use that pattern first to try to solve here. We have 700s, so seven times we have 100, or 700, and we're multiplying again times 10. Using this pattern over here, our solution will add a zero at the end.

So, if we had 700 10 times, we would have 700 with a zero on the end or 7,000. So, 700s * 10 is equal to 7,000.

But there's another pattern we could use here. Another pattern to think about when we multiply by 10 is that when we multiply by 10, we move every digit one place value—one place value left or one place value greater.

So, let's look at that one on a place value chart. Here, we have a place value chart. To use that earlier example, when we had 9 ones and we multiplied it by 10, our 9 moved one place value to the left. It moved up to the T, and now we had 9 tens. We filled in a zero here because there were no ones left—there were zero ones left—and so we saw that 9 * 10 was equal to 90.

So again, it's the same as adding a zero at the end, but we're looking at it another way. We're looking at it in terms of place value and multiplying by 10 moved every digit one place value to the left. So, if we do that with the same question—7 hundreds—if we move hundreds one place value to the left, we'll end up with thousands.

So, 700 * 10 is 7, or as we saw earlier, 7,000. So either one of these is a correct answer: 700 * 10 is 7,000.

And here's an example with division. Now we have dividing by 10, and as you might predict, dividing by 10 is the opposite of multiplying by 10. So our patterns are also the opposite. Instead of adding a zero to the end of a whole number, we would drop a zero at the end.

So for an example, if we had 40 / 10, we would drop that zero and end up with four. If you divide 40 into groups of 10, you have four groups.

Let's use that over here: 212 or 21. So, we have 212 tens. So 21 10 times is how we got the zero there.

And we divide that by 10. We can use this first pattern we thought of and just drop the zero on the end. Let's drop that zero, and our answer will be 21. But we could also use the place value pattern. We could think in terms of place value.

Instead of moving one place value to the left, one place value larger, we're going to move one place value smaller or to the right—one place value to the right.

So, what's one place value smaller than 21 T? If we have 212 T divided by 10, we want to move this 10 one place value to the right, or smaller, which is ones. So, our solution would be 212 1s, which is equal to what we already saw—simply 21.

So, 21210 / 10, we could write the number out and drop a zero, or we could think about place value and move one place value to the right. Either way, our answer is 21 1s.