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The ideas in this lesson are taken from Multiplication Division 2 ebook. Only a few examples of each problem type are shown; you should make more problems of each kind for the student.


Remainder in long division
Free lesson plan from HomeschoolMath.net

Do you remember?
14 bananas divided between 3 people gives 4 bananas to each and 2 bananas that cannot  be divided. 14 carrots divided between 5 people gives 2 carrots to each and 4 carrots that cannot be divided.

14 ÷ 3 = 4,
remainder 2.

3 × 4 + 2 = 14.

  





14 ÷ 5 = 2,
remainder 4.

5 × 2 + 4 = 14.

The remainder is always LESS than the divisor.  Otherwise we could divide some more. For example, if in the banana situation the remainder was more than 3, we could continue dividing the remaining bananas between 3 people.

How do we check the division if it is not exact?  Look at the pictures above.  If we end up with 3 people each having 4 bananas and 2 bananas left over, then the total amount of bananas is 3 × 4 + 2 = 14.  Or if 5 people have 2 carrots each and there are 4 carrots left over, then all together we have 5 × 2 + 4 = 14 carrots.

So to check the division that was not exact, multiply your result by the divisor as normal, and then ADD THE REMAINDER.  You should get the original dividend.

 

When using long division, the division is not always exact either.

At this point we don't have
any more digits to drop down
from the dividend.  In the last
subtraction we end up with 6,
which is the remainder.  
So 125 ÷ 7 = 17, R 6.

Note that the remainder 6 is
LESS THAN 7, the divisor

       
1 7

-

    7
5 5

9
6
      

4   
17
×  7

119

119 + 6 = 125 

To check we multiply the answer (17) by the divisor (7), and then add the
remainder (6). We get the original dividend (125).

Example problems

1.  Do these problems in your notebook.  Write down here the result and the remainder.  Check each division by multiplying and then adding the remainder.

321 ÷ 2 =

532 ÷ 9 = 

221 ÷ 3 =

922 ÷ 6 = 

490 ÷ 4 =

 324 ÷ 6 = 



2.  Do the word problems in your notebook.

a.  While playing with matches, Annie had 204 matches.  She divided them into piles of 8 matches. How many piles dud she make?  How many matches were left over?
b.  If she divides them into piles of 20, how many piles does she get now?  Don't use long division but just think (or use real matches to help).

3.  Remember?  Multiply by 10, and make a division sentence.

10 × 21 = 

___ ÷ 10 = 21

10 × 90 = 

___ ÷ 10 = ___

10 × 87 = 

___ ÷ 10 = ___



4.  Based on the previous exercise, divide the following numbers by 10.

780 ÷ 10 = ___

150 ÷ 10 = ___

450 ÷ 10 = ___

120 ÷ 10 = ___

460 ÷ 10 = ___

440 ÷ 10 = ___



5.  Based on the previous exercise, divide the following numbers by 10 and indicate the remainder.

787 ÷ 10 =          

151 ÷ 10 = 

 

452 ÷ 10 =          

126 ÷ 10 = 

 

463 ÷ 10 =          

982 ÷ 10 = 

Is this number divisible by another?

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