# Dividing 3-Digit Numbers by 2-Digit Numbers

## Before we begin:

Before proceeding with this lesson, it would be helpful for you ;

Let's divide 672 by 42.

We start from the largest place values. How many times does 42 fit into 67? You have to approach this with a bit of estimation. If there were two, it would be 40 + 40 = 80 (in fact, the actual total would be even more), which is more than 67, so we can say there's one.

I'm writing 1 over the 7.

I'm multiplying 1 by 42 and subtracting the result from 67.

I'm bringing down 2 next to 25.The number becomes 252.

Now I need to divide 252 by 42, similar to before, I should think about how many times 42 fits into 252.

If you're having trouble figuring out how many there are, try to estimate by rounding the numbers.

When rounding, you don't necessarily have to take rounding rules into account. For example, 252 is rounded to 250, but thinking of it as 260 is not that important, because your aim is to find an approximate result, you don't necessarily have to make the best estimate. You can try, and depending on your result, you can give one more or one less and recalculate.

We estimated that there are six. We need to multiply 6 by 42 and look at our result. The result can be larger than 252 (in this case, we need to try a smaller number), it can be smaller (in this case, we need to try a larger number), or if we are lucky, we can find exactly 252.

6 times is a perfect fit ! so write this to the quotient, above the number 2.

I need to multiply 6 by 42 and subtract it from 252 to find out how much more I need to divide, or to see if I have a remainder left.

I have no remainder, the result is 16.

our teachers have taught you all these steps, or you have learned them through YouTube channels or websites, now let's examine it in a bit more detail.

# Actually, what is happening

What does 'how many 42s are in 67' mean? Is 67 just the number we know, or does it represent something else?

67 does not represent the 67 we know, the number 672 is a number composed of 6 hundreds, 7 tens, and 2 ones. If we break down the hundreds, one hundred means ten tens, so 6 hundreds would be 60 tens, and I already have 7 tens, so I can think of it as having a total of 67 tens,

I'm distributing 67 tens into 42 buckets.. one ten falls into each bucket, so when I write 1 in the quotient, I'm not writing it to another digit, I'm writing it to the tens place.

25 tens cannot be distributed equally into 42 buckets.That's why I need to convert these 25 tens to ones. 25 tens make 250 ones, in fact, this number you see doesn't represent 25, it represents 250.

I had two more ones on hand, and when I bring down those two ones, bingo! My count becomes 252, so I hit two birds with one stone. I'm both taking into account the two ones and converting the 25 tens into ones.

Now I need to distribute these 252 ones into 42 buckets again..

You need to use estimation to find out how many can go into each bucket. This depends on your skill and how much practice you have done. If you practice a lot, your estimation ability will improve.

You can make the best and fastest estimates by rounding the numbers. As I said before, you don't have to stick to the rounding rules, it's an estimate after all! You can estimate a little more or less. Estimation should not be an extra problem for you to overcome.

We estimated six, and when we tried it, we saw that it fit exactly. I'm writing 6 in the ones place in the quotient because I have six ones in each of my buckets.

Since I've distributed the ones, to find out how many ones I have left, I'm multiplying 6 by 42 to calculate the distributed ones. Distributing 6 ones into each of 42 buckets means 6 * 42 = 252 ones have been distributed.

Since I've distributed the ones, to find out how many ones I have left, I'm multiplying 6 by 42 to calculate the distributed ones. Distributing 6 ones into each of 42 buckets means 6 * 42 = 252 ones have been distributed.

# Alternative Ways

In fact, when dividing 672 by 42, we are looking for the answer to the question of how many 42s there are in 672. You can think of this division as taking large or small bites from a big meal, piece by piece.

Let's try to estimate by multiplying 42 by 10, 100, or 1000. For example, multiplying by 10 makes sense, as multiplying by 100 would give 4200, which is too much. Why am I trying to estimate by taking 10, 100, or 1000? Because multiplying by these numbers is simple, so we can estimate easily.

Twenty times will also be too much, it would result in a number in the 800s (400+400), whereas the number I want to divide starts with 600, so ten times seems to be the ideal figure.

Let's take another bite, 10 will be too much, let's give it 5.