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Long division with remainder - lesson with word problems

This is a complete lesson with instruction and exercises for fourth grade, concerning long division with remainder. Students work on division problems and check their answers. They also get to solve many word problems that involve remainders.




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

At this point there are no
more digits to drop down
from the dividend. The
last subtraction yields 6,
which is the remainder.
So 125 ÷ 7 = 17, R6.

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

1 7

)

7
5 5
9
6
To check:

Multiply the answer (17)
by the divisor (7), and
then add  the remainder (6).

You get the original
dividend (125).

4      
1  7
×    7

1  1  9
+        6

1  2  5

1. Divide. Check each result in the empty space by multiplication and addition.

a. 514 ÷ 3            Check:

b.  673 ÷ 8            Check:

c.  1,905 ÷ 6           Check:

d.  8,205 ÷ 4            Check:



2. Find the divisions that are incorrect. Redo the ones that are wrong below.

a.  
       7 7

4 6 3 

 

-

4 2 

   

  4 9

   

  - 4 2

           7
b.  
       3 5 3

2 4 7 3 

 

-

2 1 

   

   3 7

   

 - 3 5

          2 3
   

- 2 1 

   

c.  
       3 5 1

4 0 5 9 

 

-

3 6 

   

   4 5

     - 4 5
          0 9
d. How can you spot the error in (a) just by looking at the remainder
    463 ÷ 6 = 77 R 7 ?

 

3. Write a division sentence for each problem, and solve it. Lastly, explain what the answer means.

a.  Arrange 112 chairs into rows of 9.

    ______________________________

We get _____ rows, _____ chairs in

each row, and _______________

_______________________________

b.  Arrange 800 erasers into piles of 3.

    ______________________________

We get _____ piles, _____ erasers

in each pile, and _______________

_______________________________



Imagine you are trying to pack some things evenly into some “containers”,
and they do not go evenly. The last container will not be full!

Often students make mistakes with such problems. Read the question carefully.
Sometimes you DO need to count the container that is not full, sometimes not

146 people were transported in vans that each carry 9 passengers. How many vans were needed?

The division is 146 ÷ 9 = 16 R2, so 16 vans will be full and one van will have 2 passengers.

But the answer is, they needed 17 vans.

You pack 1,250 blank CDs into boxes of 200 each. How many full boxes will you get?

6 × 200 = 1,200; so 1,250 ÷ 200 = 6 R50.

6 boxes will be full (and 50 CDs are left over, not packed).

Solve the problems. Sometimes you can use multiplication instead of division.

4. A company bags 2,000 lb of potatoes
    into 12-lb bags. The division is:
    2,000 ÷ 12 = 166 R8.
    How many full bags will they get?
 

5.If you can fit 50 people into one bus,
    how many buses would you need to
    transport 940 people?

 

6. Mr. Eriksson can have 75 days of vacation
    each year. He wants to divide those days into
    4 vacations. How long should he make his
    vacations? Make them as close to the same
    length as possible.

 

7. A farm packs 400 kg of strawberries so that
    they make ninety 2 kg boxes, forty 4 kg boxes,
    and the rest is packed into 6 kg boxes. How
    many full 6 kg boxes will they get?

 

8. Can you pack 412 tennis balls into containers
    evenly so that each container has

    a. 4 balls?

    b. 5 balls?

    c. 6 balls?



9. Mr. Sandback wants to paint 740 blocks with
    6 different colors—red, orange, yellow, green,
    blue, and purple -- in nearly equal amounts.
    How many should be colored with each color?

 

 

 

10. Do one problem from each box by long
      division. Can you then figure out the answers
      to the other two in each box, without actually
      dividing?

a.  211 ÷ 3 =

    212 ÷ 3 =

    213 ÷ 3 =

b.  1,206 ÷ 7 = 

    1,207 ÷ 7 =

    1,208 ÷ 7 =

c.  411 ÷ 5 = 

    412 ÷ 5 =

    413 ÷ 5 =

d.  7,185 ÷ 9 = 

    7,186 ÷ 9 =

    7,187 ÷ 9 =

11. A challenge: if  231 ÷ 6 = 38 R3, then figure
      out what 232 ÷ 6 is.

12. Divide these numbers by 10 and indicate the remainder. There is a shortcut!

a.  787 ÷ 10 =

    66 ÷ 10 =

   340 ÷ 10 =

b.  452 ÷ 10 =

    509 ÷ 10 =

    52 ÷ 10 =

c.  463 ÷ 10 =

    982 ÷ 10 =

    925 ÷ 10 =

 

  What is wrong with the division result 31 ÷ 6 = 4 R7?
   After all, 4 × 6 + 7 = 31, so it seems to check fine.
   Explain.



 




This lesson is taken from Maria Miller's book Math Mammoth Division 2, and posted at www.HomeschoolMath.net with permission from the author. Copyright © Maria Miller.


Math Mammoth Division 2

A self-teaching worktext for 4th grade that covers long division, finding fractional parts with division, word problems, remainder, average, and divisibility.

Download ($5.10). Also available as a printed copy.

Learn more and see the free samples!

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