1. Long Division
by One-Digit Numbers

2. What is this problem asking us?) 5
36,987
If we divided 36,987 into 5 groups of equal size, how many would be in each group?

3. Real Life Example ) 5
36,987
If Janice has 5 years to repay a small business loan for $36,987, how much will she need to pay each year?

4. ) How do we solve it? 5 36,987 5 is our divisor
Look at the first number and ask how many 5’s are in 3
There are none, so we ask how many 5’s are in 36

5. ) 5
36,987
How many 5’s are in 36?
Recall your multiplication facts to find the one that will give an answer near 36.
5 x 7 = 35

6. ) 7 5 36,987 35 9 1 5 x 7 = 35 Now ask how many 5’s are in 19
Place the 7 above the division bar
Subtract 35 from 36
Bring down the next digit in the dividend 9 1
Now ask how many 5’s are in 19

7. 5 x 3 = 15 7 3 ) 5
36,987
Place the 3 above the division bar
Subtract 15 from 19
Bring down the next digit in the dividend 35 9 1 15 4 8
Now we ask how many 5’s are in 48

8. 5 x 9 = 45 7 3 9 ) 5
36,987
Place the 9 above the division bar
Subtract 45 from 48
Bring down the next digit in the dividend 35 1 9 15 48 45
Now we ask how many 5’s are in 37 3 7

9. 7 3 9 7
Place the 7 above the division bar
Subtract 35 from 37
There are no more numbers to bring down
The remainder is 2, which means 2 are left over
The quotient or answer to our problem is 7,397 with a remainder of 2 ) 5
36,987 35 1 9 15 48 45
5 x 7 = 35 3 7 35
remainder 2

10. Our Real Life Example
7,397
about ) 5
36,987
If Janice has 5 years to repay a small business loan for $36,987, how much will she need to pay each year?

11. 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?

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

13. ) 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.

14. ) 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

15. ) 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

16. ) 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

17. 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 2 6 24 24 3 7 3 36
remainder 1

18. 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

19. 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

20. 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

21. 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

22. 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

23. 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

24. 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

25. 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

26. 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

27. 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

28. 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

29. 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

30. 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.