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Long division when there is a zero in the dividend

This is a complete lesson with instruction and exercises for fourth grade, where students divide four-digit numbers using long division, and the quotient may have a zero. The lesson also shows an example and exercises of short, even divisions, and some word problems


Study the example carefully. We need to place a zero in the quotient.
2  4
4 

)

9  6  2  0

-

8
1  6
 
2  4  0
4 

)

9  6  2  0

-

8
1  6

-

1  6

0  2    

 
2  4  0  5
4 

)

9  6  2  0

-

8
1  6

-

1  6

0  2  0

   

- 2  0

   

 0

At this point, the
division is even.
Continue normally,
multiplying
4 × 4 = 16.
 
Now, 4 does not go into 02,
so place a zero in the quotient.
You can either continue as
usual, OR drop ANOTHER
digit from the dividend.
   
   
Dropping another digit
from the dividend, we
get 020. 4 goes into
20 five times.

1. Let's practice! There will be a zero in the quotient. Multiply to check.

a.      Check: b.      Check:
c.      Check: d.      Check:

2. For more practice, do these in a notebook or blank paper. Use grid paper if possible.

    a.  8,115 ÷ 3 b.  6,540 ÷ 5 c.   9,163 ÷ 7 d.  6,378 ÷ 6


Short, even division

2,156 ÷ 7 is easy to do mentally:

2,100 ÷ 7 is 300, and 56 ÷ 7 is 8. So the answer is 308.

If we use the division corner, we get a really “short” division. That is because the division is even from the start. So, simply move on to the next digit in the dividend. You do not have to multiply & subtract.

th   h     t    o
0  3
7 

2  1  5  6 
 
th   h     t    o
0  3  0
7 

2  1  5  6 
 
th   h    t     o
0  3  0  8
7 

2  1  5  6 
         
7 goes into 21
three times.
 
7 goes into 5
zero times...
 
...so look at the
two digits (56).
7 goes into 56
eight times.

3. Divide.

a. b. c.
d. e. f.

 

4. Mary divided her 285 buttons
    evenly into the five
    compartments. Find out how
    many buttons are

     a. in one compartment

     b. in three compartments

     c. in four compartments.


5. A gallon of ice cream costs $12.96. You and
    your brother each pay for 1/8 of the cost, and
    mom will pay the rest.

    a. Find each person's share of the cost.

        You: _____________

        Your brother: _____________

        Mom: _____________

    b. Find each person's share of the
        ice cream in cups.
        (Hint: 1 gallon is four quarts, and a quart is four cups.)

        You: _____________

        Your brother: _____________

        Mom: _____________




This lesson is taken from my book Math Mammoth Division 2.

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!

See more topical Math Mammoth books



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