# 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: _____________ Long division worksheets
Create an unlimited supply of worksheets for long division (grades 4-6), including with 2-digit and 3-digit divisors. The worksheets can be made in html or PDF format - both are easy to print. You can also customize them using the generator.
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