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“Mutual caring relationships require kindness and patience, tolerance, optimism, joy in the other's achievements, confidence in oneself, and the ability to give without undue thought of gain.”
So first, let's talk about what division is. Well, division is basically the opposite of multiplication - instead of seeing what you get when you add a number so many times, in division you are instead looking for a number which, using multiplication, will give you the other number in the problem.
But that sounds confusion so let me show you a quick example.
If I have 10/2 (the slash means 'divided by' you probably know that but, I'll make sure)
What am I asking? I'm asking how many times 2 goes into 10.
So we think about 2 and we think about 10 and we think 2 goes into 10 exactly 5 times.
But let's check. 2*5=10 right? Well, that's the same thing as 2+2+2+2+2 and that also equals 10. So 10/2=5
And that's how division works in a nutshell.
Now let's move on to harder problems. Long division helps us solve them.
Suppose I have 93/3 this is much more difficult and time consuming to do the way we did 10/2. So we'll need an easier way. Luckily long division is here.
So, you'll notice the 93 is inside the little half box thing (that's the long division sign) and the 3 is on the outside to its left. This tells us that 93 is being divided by 3.
Now let me explain what is happening there. So we a ####### the 93 with the 3 and we get to 9 and we ask: How many times does 3 go into 9? The answer is 3 so, we put a 3 on top of the 'half box' and multiply the 3 by 3 and we put the answer (9) underneath the 9 in the 93.
Now we subtract them. 9-9=0 So now we have 0 but we're not yet finished, there's still that 3 up there. So we bring it down next to the 0 into the ones place (the 0 is in the tens place).
And we ask again: How many times does 3 go into 3? Once of course! So we put a 1 next to the 3 up on top of the box and multiply 3 by 1 and we put the answer (3) underneath this 03 abomination and subtract once more. 3-3=0 And we're done! There are no more digits up there to worry about and that and the 0 tell us that we got exactly the answer.
93 / 3=31
I hope that you're able to follow that, if not, look at the whiteboard picture and read the text until it makes sense. Feel free to ask questions too and I'll answer them. But, I'm going to move on in this post.
So you noticed the other long division problem on the whiteboard. 78/4
Well, we just learned how this works so let's do it again. We bring the 4 to the 7 and ask: How many times does 4 go into 7? 4 goes into 7 only once (if it were more we'd have numbers bigger than 7!) so we place a 1 on top of the box and bring 4 under the 7 and we subtract.
7-4=3 and now we bring the 8 down to the 3 and we have 38. How many times does 4 go into 38? 4 goes into 38 almost 9 times (9*4=36) so we put a 9 on top of the box and multiply 9 by 4 and we put the answer (36) underneath the 38 and subtract.
...this is bad. We have a leftover 2. What are we going to do with it? There are no more numbers in 78 for us to bring down and 2 is too small for 4. 2 in this case is called the 'Remainder' it is what's left over after the division with whole numbers. If you notice the squiggly lines in place of the = the squiggly lines means that it 78/4 is approximately 19 but not exactly.
BUT WE'RE SMARTER THAN THAT! I'll show you how to get rid of that 2 and get the exact answer.
There we go. The answer is to bring decimals into the mix. I'm not sure how familiar you are with these little dudes but, decimals are used when you have something which is less than 1 but not quite 0.
Anyway, what is going on here? Well, it's the same problem but I went a step further instead of stopping at the 2.
So let's skip all the explanation because you remember when I explained it up there. Let's get to the 2. What did I do? Well, I evoked the power of the infinite decimal. Remember, there are an infinite amount of zeros after a decimal point because they do not add any value to the number.
So when we got to that 2 and I didn't see any more numbers up there, I added a decimal point to 78 and I put one after 19 on top of the box. And now we have 78.0 so I brought down the 0 next to the 2 and now we have 20. So, how many times does 4 go into 20?
4 goes into 20, 5 times. So we put that 5 on the right side of the decimal and multiply 4 by 5 and we put that 20 under the other one. 20-20=0
And boom goes the dynamite. We did it. We showed that Remainder who is boss and we found the exact answer to ## # # ## # # # ##.#
##### is another example of that process - on the right - with a much larger number (remember with long division large numbers become easy) I showed it with the exact answer and decimal place and also with the remainder. I don't know if you need commentary on that one though.
I hope this has helped. If you have any questions or need more examples ask and I'll do my best.
Unfortunately, kidzworld is censoring much of my post for some reason. The ##### are mostly equations like Seventy-Eight divided by Four and a few others. Hopefully I can get someone to fix that for me but, in the meantime, I hope you can understand this regardless. Sorry about that.
For example, an easy problem: 50/5
First, before you divide, you need to know your multipication.
What is 50 / 5?
Let's say you didn't know that
1. We're going to start by the first digit number. The first digit if 5. So, does 5 fit into 5?
1 x 5 = 5. So, we put 1.
5-5 = 0. Bring down the 0, that's 0.
50 / 5 = 10
"ice cream girl" wrote:Thanks for the help guys!
Definitely. For some reason my whiteboard pictures got taken out but I replaced them. Not sure whether you saw them.
What EvanescentWonderland said is also very concise and helpful.
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