How many threes are there in 6690?
To solve this problem, I want us to think about a different question: how many threes are there in nine? Here are nine yellow marbles. How could we find out how many threes there are? How about grouping them into groups of three? We have our first group: one, two, three. We can count out our second group: one, two, three and our last group: one, two, three.
How many groups of three were there in nine? Three. Nine has three groups of three. The thing is if we needed to draw them out — 6690 marbles — to figure out how many threes there are in 6690, that would take a very long time. There has to be a better way.
Another word for grouping is dividing. We’ve divided our nine into groups of three because nine divided by three equals three. We can take our 6690 and divide it by three to find out how many threes there are in that number. And when we do that, we start by saying how many times will three go into six? I know that three goes into six two times because two times three is six. Six minus six equals zero.
Then, we bring down our six. We bring down our next value. We need to ask the same question again “how many times does three go into six?” Two times. So we multiply two times three. Two times three equals six. We’ll do subtraction again. Six minus six equals zero. Bring down the next value which is a nine and then ask the question “how many times does three go into nine?” Nine divided by three is three. Three times three equals nine. We need to do subtraction. Nine minus nine equals zero.
We look at the next digit which is a zero and we bring it down. And then we ask the question “how many times does three go into zero?” Well, three can go into zero zero times. Zero times three equals zero. And at the very bottom here, we have zero minus zero, which equals zero. So we have no remainder.
This top value is called the quotient. And in our case, it tells us the number of threes that there are in 6690. There are 2230 different groups of three in that value.
How many threes are there in 6690? 2230 of them.