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Mastering Long Division

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by

Danielle Biddle

on 11 August 2013

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Transcript of Mastering Long Division

Let's start with the basics
Step 1:
Look at the question. Can the divisor go into the first number of the dividend?
Step 2:
We have figured out that 4 goes into 24 six times.
Step 3:
What are we trying to figure out in the problem below?
That's right! The question is - how many times can 4 go into 24?
This is a question you should all be able to answer without using long division, but it is a good start to help us understand and start thinking about the process o f long division .
Now the question is, how does long division work?
If the answer is yes, write how many times it can go in above the first number of the dividend.
If the answer is no, you need to look at the next number and see if the divisor can go into the double digit number.
Let's try step 1
Can 4 go into 2?
No. What do we do next?
If you said to look at the next number in the dividend, you are correct!
Can 4 go into 24?
How many times?
Well done! 4 goes into 24 six times.
Copy this problem into your book. Place the 6 where you think it should go, then show the person sitting next to you. Do you both have the 6 in the same place? Tell your partner what you think you do next.
If you placed the 6 above the 4, you are correct!
Now for the next step of long division!
We need to multiply 6 and 4. Then we write the product under the 24 from the dividend. This helps us see if there is anything left over or if the divisor went in evenly.
The product of 6x4 is 24. To find out if we have anything left over we subtract the product from the numbers of the dividend we were looking at. (24 -24)
In this case, when we multiply 6 and 4 we get the same number as the two numbers of the dividend (24), so we have nothing left over.
What do we do next? Tell your partner what you think the next step is.
Mastering Long Division
Look at the next number in the dividen. What is it?
If you said 6, you are correct! Now we need to drag the 6 down to make sure we are considering any leftover numbers from the last step.
6
24
-
_____
0
6
Were there any leftover numbers in the last step?
If you said no, you are correct!
After dragging the 6 down, we can see that there was nothing left over in the last step so we just have 6. This means we have to look at how many times 4 goes into 6.
6
24
-
_____
0
6
1
4 can go into 6 one time. What do we do next?
6
24
-
_____
0
Repeat:
6
24
-
_____
0
6
1
Keep in mind that the question is asking you how many times 4 goes into 24,652. With such a big number, long division helps us figure out the answer by doing a few smaller steps. If we look at how many times 4 goes into the individual numbers (or pairs of numbers), it makes the problem much more manageable.
Continue using the same method of multiplying 4 by the number of times it goes into the dividend in each new step. Write that number under the last step, and then subtract to find the difference.
If 4 goes into 6 one time we need to multiply 4x1 and write the product under the 06 from the last step. Then we subtract 4 from 6 and are left with 2. Can 4 go into 2? What do we do next?
4
_____
-
2
Finish the problem and compare with your partner.
What happens if the divisor doesn't go into the dividend evenly?
If you were thinking about remainders, you are spot on!
Remainders can be shown in a variety of ways. Tell your partner one way to show a remainder. Can you think of any others?
Remainders can be shown by using an 'r'. This tells us what is left over because there wasn't enough to make another whole and fit into the dividend evenly. Using the 'r' to express what is left is the simplest way to show that the divisor didn't go into the dividend evenly.
A more complex way to show a remainder is by using decimals. This tells us exactly how many times the divisor goes into the dividend.
Another complex way to express a remainder is by using fractions. Did you get all three ways?
If a divisor doesn't go into the dividend evenly, I would like you to be able to express the remainder by using decimals.
It is a little tricky at first, but once you get it you'll be set for life!
Let's give it a go!
We'll start with something not too tricky and work our way up to more complex long division problems.
Now that you are experts with long division the first bit shouldn't be too tricky.
We know that 4 can't go into 2, so we have to see how many times it can go into 26.
From the earlier problem we know that 4 can go into 24 six times evenly.
6
24
-
2
___
____
4 goes into 26 six times with a remainder of 2. In the earlier problem we learned that the next step is to bring down the next number of the dividend and put it next to the 2. However, there aren't any more numbers to bring down.
What do we do now? Talk to your partner and think about what we need to do next.
6
24
-
2
___
____
Since there aren't any more numbers for us to bring down, we have to make some.
How could we add numbers without changing the value of the number we have?
By making the number a decimal!
Every whole number could be written with a decimal behind it and as many zeroes as you would like to write out.

For example: 2 is the same as 2.000000
Let's turn 26 into a decimal and try to solve the problem as normal. Don't forget that when add a decimal to a number you also need to bring the decimal point up to the line where the quotient is, or you won't get the correct answer.
6
24
-
2
___
____
.
.
Don't forget this decimal point!
000
0
Now we can find out how many times 4 goes into 20.
Finish solving this problem with your partner. Check with another pair to see if you got the correct answer.
You are on your way to being a long division expert!
The answer is....
6163
If you are correct you have just earned 500 house points!
Full transcript