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Two-Digit Divisor in Long Division

This is a complete lesson with examples and exercises about two-digit divisor in long division, meant for initial teaching in 5th grade. The first exercises have grids to complete the division, and space for students to write the multiplication table of the divisor in the margin. Then there are conversion problems between inches/feet and ounces/pounds, because those are solved with division.





Often, it is helpful to write the multiplication table of the divisor before you divide.

Example 1. The division is by 16. Here is the multiplication table of 16:

3 × 16 = 48
4 × 16 = 64
5 × 16 = 80
6 × 16 = 96
7 × 16 = 112
8 × 16 = 128
9 × 16 = 144

    0  3
16 

5  5  6  8

16 goes into 5 zero times, so we look at 55.

How many times does 16 go into 55?

Check in the table on the left. We see it goes into 55 three times.

    0  3  4
16 

5  5  6  8
 

-

4  8
        7  6

 

Now, how many times does 16 go into 76?

From the table we can see that it is four times.

    0  3  4  8
16 

5  5  6  8
  - 4  8
        7  6
     -  6  4
   

1  2  8

   

  - 1  2  8

   

0

Lastly, 16 goes into 128 exactly 8 times, and the division is over.

Example 2. We are dividing by 32. Here is the multiplication table of 32:

3 × 32 = 96
4 × 32 = 128
5 × 32 = 160
6 × 32 = 192
7 × 32 = 224
8 × 32 = 256
9 × 32 = 288

1
32 

)

4  7  0  7 
 

-

3  2
    1  5

 


 
32 goes into 47 once.

4
32 

)

4  7  0  7 
 

-

3  2
    1  5  0
 

-

1  2  8
        2  2

 

32 goes into 150 four times.

1  4  7
32 

)

4  7  0  7
 

-

3  2
    1  5  0
  - 1  2  8
    2  2  7
     - 2  2  4
   

3

32 goes into 224 seven times. Notice there is a remainder.

1. Divide. First write a multiplication table for the divisor. Check each answer by multiplying.

Table of 21:
2 × 21 =
3 × 21 =
4 × 21 =
5 × 21 =
6 × 21 =
7 × 21 =
8 × 21 =
9 × 21 =
 


2. Divide. First write a multiplication table for the divisor. Check each answer by multiplying.

a.
Table of 15:
2 × 15 =
3 × 15 =
4 × 15 =
5 × 15 =
6 × 15 =
7 × 15 =
8 × 15 =
9 × 15 =
 

 

b.
Table of 12:
2 × 12 =
3 × 12 =
4 × 12 =
5 × 12 =
6 × 12 =
7 × 12 =
8 × 12 =
9 × 12 =
 
c.
Table of 25:
2 × 25 =
3 × 25 =
4 × 25 =
5 × 25 =
6 × 25 =
7 × 25 =
8 × 25 =
9 × 25 =
 
d.
Table of 16:
2 × 16 =
3 × 16 =
4 × 16 =
5 × 16 =
6 × 16 =
7 × 16 =
8 × 16 =
9 × 16 =
 

3. Divide. Check each answer by multiplying.

a.
Table of 12:
2 × 12 =
3 × 12 =
4 × 12 =
5 × 12 =
6 × 12 =
7 × 12 =
8 × 12 =
9 × 12 =
 
b.
Table of 22:
2 × 22 =
3 × 22 =
4 × 22 =
5 × 22 =
6 × 22 =
7 × 22 =
8 × 22 =
9 × 22 =
 
c.
Table of 14:
2 × 14 =
3 × 14 =
4 × 14 =
5 × 14 =
6 × 14 =
7 × 14 =
8 × 14 =
9 × 14 =
d.
Table of 51:
2 × 51 =
3 × 51 =
4 × 51 =
5 × 51 =
6 × 51 =
7 × 51 =
8 × 51 =
9 × 51 =


4. Mental math! If 20 goes into 800 forty times, then 20 goes into 820 one time more,
    or 41 times. In each box, use the top problem to help you solve the bottom problem.

a. 800 ÷ 20 = 

    820 ÷ 20 =

b. 700 ÷ 50 = 

    750 ÷ 50 = 

c. 150 ÷ 15 = 

   300 ÷ 15 =

d. 480 ÷ 40 = 

    520 ÷ 40 =

e. 600 ÷ 30 = 

    690 ÷ 30 = 

f. 1,200 ÷ 60 = 

   1,320 ÷ 60 =


5. a. How many inches are in one foot?


    b. Convert 245 inches into feet and inches.


    c. Convert 387 inches into feet and inches.



 

6. a. How many ounces are in one pound?


    b. Convert 163 ounces into pounds
    and ounces.


    c. Convert 473 ounces into pounds
    and ounces.


 

7. A newborn baby gains weight at
    approximately one ounce per day.
    Suppose that the baby gained weight
    at that rate for a FULL YEAR.
    (In reality, babies don’t; their
    growth rate slows down.) How many
    pounds and ounces would the baby
    gain in a year?


See also

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.
www.homeschoolmath.net/worksheets/long_division.php



This lesson is taken from Maria Miller's book Math Mammoth Multiplication & Division 3, and posted at www.HomeschoolMath.net with permission from the author. Copyright © Maria Miller.




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