75 tens divided by 10 equals what? 65 tens, 75 thousands, 75 tens, 75 ones, or 75 hundreds?
What do we notice about all the possible answers that we’ve just read? Well, none of them are written as a number. They’re all an amount of ones, tens, hundreds, or thousands. So this gives us a clue as to how to find the answer. We don’t need to find the exact value of what 75 tens divided by 10 is as a number. We need to think about place value and give the answer as a number of ones, tens, hundreds, or a thousands. So what this question is really asking us is what happens to a number of tens when we divide it by 10.
Let’s sketch a place value grid to help us think about this. Place value grids help us to understand the value of each digit in a number. And we know that each column to the left of another column is worth 10 times as much. The column with the lowest value in a whole number is the ones column. And to the left of the ones column is the tens column. Tens are 10 times greater than ones. And to the left of the tens column is the hundreds column. If a digit moves from the tens to the hundreds columns, it’s become 10 times greater. And the opposite is true if we move in the other direction, 10 times smaller than a number of hundreds is the same number of tens. This is the same as dividing a number of hundreds by 10.
Listen carefully cause the next fact is important. The same is true when we look at the column to the right of the tens column. 10 times less than a number of tens is the same number of ones. So if we have 75 tens and we make them worth 10 times less, they’ll now be worth 75 ones. And that’s our answer. We haven’t had to do any calculation. We simply need to understand how place value works.
But let’s prove our statements true by actually working out with the numbers involved. We’ll start off with 75 tens. Now we can’t write 75 in the tens column because we can only fit one digit in each column. 75 tens is actually worth 750. And we put a zero in the ones place as a place holder. Now, when we divide this number by 10, each of the digits is going to move one place to the right. So the five is going to shift to the ones place. And the seven is going to shift from the hundreds place to the tens. 750 divided by 10 equals 75. We can think of 75 as 75 ones. When we divide a number of tens by 10, we get the same number of ones.
So 75 tens divided by 10 equals 75 ones.