1. Long Division
by One-Digit Numbers

2. What is this problem asking us?
682 ) 4
If we divided 682 into 4 groups of equal size, how many would be in each group?

3. Real Life Example
682 ) 4
If Grandma has 682 dollars that she wants to share it equally with four of her grandchildren, how much will each grandchild receive?

4. How do we solve it? 682 ) 4 4 is our divisor
Look at the first number and ask how many 4’s are in 6
Recall your multiplication facts to find the one that will give an answer near 6.
There is one four in six.

5. 1 682 ) 4 4 2 8 4 x 1 = 4 Now ask how many 4s are in 28
Place the 1 above the division bar
Subtract 4 from 6
Bring down the next digit in the dividend 2 8
Now ask how many 4s are in 28

6. 1 7 682 ) 4 4 28 28 2 2 There are no 4’s in 2. 4 x 0 = 0 remainder
There are no 4’s in 2.
4 x 0 = 0
682 ) 4 4
Place the 0 above the division bar
Subtract 0 from 2
There are no more numbers in the dividend to bring down.
There are two left over. 28 28 2
remainder 2

7. 1 7
The answer to the problem is called the QUOTIENT.
682 ) 4 4
The QUOTIENT is
170 remainder 2 28 28 2
remainder 2

8. What is this problem asking us?) 6
8,437
If we divided 8,437 into 6 groups of equal size, how many would be in each group?

9. Real Life Example ) 6
8,437
Can you think of a word problem that can be expressed as the division problem written above?

10. ) How do we solve it? 6 8,437 6 is our divisor
Look at the first number and ask how many 6’s are in 8
There is one, so we multiply and begin to work through the steps to solve the problem.

11. ) 1 6 8,437 6 4 2 6 x 1 = 6 Now ask how many 6’s are in 24
Place the 1 above the division bar
Subtract 6 from 8
Bring down the next digit in the dividend 6 4 2
Now ask how many 6’s are in 24

12. ) 1 4 6 8,437 6 24 24 3 6 x 4 = 24 Now ask how many 6’s are in 3
Place the 4 above the division bar
Subtract 24 from 24
Bring down the next digit in the dividend 6 24 24 3
Now ask how many 6’s are in 3

13. ) 1 4 6 8,437 6 24 24 3 3 7 6 x 0 = 0 Now ask how many 6’s are in 37
6 x 0 = 0 ) 6
8,437
Place the 0 above the division bar
Subtract 0 from 3
Bring down the next digit in the dividend 6 24 24 3
Now ask how many 6’s are in 37 3 7

14. 1 4 6
6 x 6 = 36 ) 6
8,437
Place the 6 above the division bar
Subtract 36 from 37
There are no more numbers to bring down
The remainder is 1, which means there is one left over
The quotient or answer to our problem is 1,406 with a remainder of 1 6 24 24 3 7 3 36
remainder 1

15. 3 6 2,538 7 -21 4 3 -42 ) 25 ÷ 7 or how many groups of 7 are in 25
Think of a your seven facts
7x3=21
Place the 3 above the bar
Subtract 21 from 25
Bring down the next digit in the dividend ~ THREE
43 ÷ 7 or how many 7’s are in 43 3 6 )
2,538 7
-21 4 3
-42
7 x 6 = 42

16. 3
7 x 6 = 42 ~ Place the 6 above the division bar
Subtract 42 from 43
Bring down the next number in the dividend ~ EIGHT
How many 7’s are in 18
7 x 2 = 14
Place the 2 above the bar
Subtract 14 from 18
Our quotient is 362 with a remainder of 4 6 2 )
2,538 7
-21 4 3
-42 1 8
-14 4
remainder

17. 4 7 8 3,792 -32 5 9 -56 ) 37 ÷ 8 or how many groups of 8 are in 37
Think of a your eight facts
8 x 4 = 32
Place the 4 above the bar
Subtract 32 from 37
Bring down the next digit in the dividend ~ NINE
59÷ 8 or how many 8’s are in 59 4 7 ) 8
3,792
-32 5 9
-56
8 x 7 = 56

18. 4
8 x 7 = 56 ~ Place the 7 above the division bar
Subtract 56 from 59
Bring down the next number in the dividend ~ TWO
How many 8’s are in 32
8 X 4 = 32
Place the 4 above the bar
Subtract 32 from 32
Our quotient is 474 7 4 )
3,792 8
-32 5 9
-56 3 2
-32
no remainder

19. 5 8 1,763 3 -15 2 6 -24 ) 17 ÷ 3 or how many groups of 3 are in 17
Think of a your three facts
3 x 5 = 15
Place the 5 above the bar
Subtract 15 from 17
Bring down the next digit in the dividend ~ SIX
26 ÷ 3 or how many 3’s are in 26 5 8 )
1,763 3
-15 2 6
-24
8 X 3 = 24

20. 5
3 x 8 = 24 ~ Place the 8 above the division bar
Subtract 24 from 26
Bring down the next number in the dividend ~ THREE
How many 3’s are in 23
3 x 7 = 21
Place the 7 above the bar
Subtract 21 from 23
Our quotient is 587 with a remainder of 2 8 7 )
1,763 3
-15 2 6
-24 2 3
-21 2
remainder

21. 2 7 9 2,473 -18 6 7 -63 ) 24 ÷ 9 or how many groups of 9 are in 24
Think of a your nine facts
9 x 2 = 18
Place the 2 above the bar
Subtract 18 from 24
Bring down the next digit in the dividend ~ SEVEN
67 ÷ 9 or how many 9’s are in 67 2 7 ) 9
2,473
-18 6 7
-63
9 x 7 = 63

22. 2
9 X 7 = 63 ~ Place the 7 above the division bar
Subtract 63 from 67
Bring down the next number in the dividend ~ THREE
How many 9’s are in 43
9 x 4 = 36
Place the 4 above the bar
Subtract 36 from 43
Our quotient is 274 with a remainder of 7 7 4 )
2,473 9
-18 6 7
-63 4 3
-36 7
remainder

23. 7 4 1,499 2 -14 9 - 8 ) 14 ÷ 2 or how many groups of 2 are in 14
Think of your doubles
2 x 7 = 14
Place the 7 above the bar
Subtract 14 from 14
Bring down the next digit in the dividend ~ NINE
9 ÷ 2 or how many 2’s are in 9 7 4 )
1,499 2
-14 9
- 8
2 x 4 = 8

24. 7
2 x 4 = 8 ~ Place the 4 above the division bar
Subtract 8 from 9
Bring down the next number in the dividend ~ NINE
How many 2s are in 19
2 x 9 = 18
Place the 9 above the bar
Subtract 18 from 19
Our quotient is 749 with a remainder of 1 4 9 )
1,499 2
-14 9
- 8 1 9
-18 1
remainder

25. 2 2 3 6,843 -6 8 - 6 ) 6 ÷ 3 or how many groups of 3 are in 6
Recall your multiplication facts x 2 = 6
Place the 2 above the bar
Subtract 6 from 6
Bring down the next digit in the dividend ~ EIGHT
8 ÷ 3 or how many 3’s are in 8 3 )
6,843 -6 8
- 6
3 x 2 = 6

26. 3 x 2 = 6 or how many groups of 3 are in 6
Place the 2 above the bar
Subtract 6 from 8
Bring down the next digit in the dividend ~ FOUR
How many 3’s are in 24
Place the 8 above the bar
Subtract 24 from 24
Bring down the THREE
3 x 1 = 3 ~ Now subtract
Our quotient is 2,281 2 2 8 1 3 )
6,843 -6 8
- 6 2 4
-24 3
- 3
no remainder

27. Try These On Your Own ) ) ) ) ) 6 4 3,927 8,146 9 8 3,506 4,468 7
We will check them using webmath.com b. 6 ) 4 ) a.
3,927
8,146 d. ) 9 ) c. 8
3,506
4,468 7 )
8,338 e.