Operations and Algebraic Thinking 189-200
Sal represents division as equal groups of objects.
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- Since multiplication is repeated addition, is division also repeated subtraction?(15 votes)
- Good question! In a way, we can think of division as counting how many times we would need to subtract the divisor, starting from the dividend, to get to 0.
For example, for the problem 12 divided by 3 (or 3 into 12), we would need to subtract 3 four times from 12 to get to 0:
12-3=9, 9-3=6, 6-3=3, and 3-3=0.
So the answer is 4.
Also in long division problem, every digit in the answer involves a subtraction step. This, in a way, can be thought of as repeated subtraction.
Have a blessed, wonderful day!(23 votes)
- Why do we need to learn division?(6 votes)
- Example: Suppose you need to read a 63-page book in 7 days. You plan to read the same number of pages each day. You want to know how many pages to read each day. Then you would divide 63 by 7, to get 9 pages each day.
This is just one of many situations where you would need to divide numbers.
In higher levels of math such as algebra and geometry later on, you will need to know division.
Have a blessed, wonderful day!(13 votes)
- Does that mean that 3 x 4 = 12?(4 votes)
- What exactly is division(1 vote)
- [Instructor] So it looks like we have some angry cats on our hands, meow, yeah they seem angry. And what we want to do is think about how can we separate these angry cats 'cause the only thing worse than an angry cat is 12 of them coordinating potentially to take over the world. And so what we're going to think about is can we divide these 12 angry cats into equal groups and just for the sake of this video let's say we want to divide them into three equal groups, how could we do that? Well let me see if I can do it, let's see maybe this is one group right over here, maybe this is another group right over there, and then this is another group. Are those three equal groups? Let's see this top group has four, this group has three, and this one has five, so no these aren't three equal groups so that won't work it has to be not just three groups, three equal groups. So let me see if I can do something different. I could have these four in a group and then I could have these four in a group, I think this is going to work out this time. And then I could have these four in a group. And as I just said out loud all of these groups have exactly four angry cats in them, which is a little bit more manageable and so this works out. I have just divided the 12 into three equal groups and how many cats are in each of those equal groups? Well we can see very clearly that there are four cats in each of those equal groups. So the way to think about division in this example is you started with 12 and you divide it into three equal, three equal groups and we ended up with four cats, four cats per group. Now what if we wanted to interpret it slightly differently? So let's bring in 12 more angry cats which is always a dangerous thing to do but we're doing it for the sake of learning so it's worth it. Meow, yep more angry cats. And now let's imagine 12 divided by three, 12 divided by three, but this time we're not going to think about the three as three equal groups, we're going to think about it as 12 divided into groups of three. So groups of three. So each of the equal groups will have three in them and so then that's going to tell us how many equal groups we're able to have. So let's do that, let's create groups of three. So let's see that's a group of three angry cats right over there. This is another group of three angry cats, this is a group of three angry cats and then this is a group of three angry cats. So how many equal groups of three angry cats do I have? Well I have one, two, three, and four equal groups. So if I want to take 12 angry cats and divide them into groups of three I end up with four equal, four equal groups. So there you have it, there's two different ways that we can imagine division. And the same exact division expression 12 divided by three, you could do it as 12 being divided into three equal groups and then the answer would be how many things per group. Or you could say hey 12 divided into groups of three and then that would end up with four equal groups.