1. The “traditional” algorithm
Long Division
The “traditional” algorithm

2. Steps: Divide Multiply Subtract Bring Down Repeat
Long Division
Steps:
Divide
Multiply
Subtract
Bring Down
Repeat

3. 2184 DIVIDED BY 24 is what number 24 goes into 2184 how many times?
Long Division
Example:
2184 ÷ 24 = n
Read this properly!
2184 DIVIDED BY 24 is what number or
24 goes into 2184 how many times?

4. Long Division 2184 ÷ 24 = n Use this symbol for division:
Example:
2184 ÷ 24 = n
Use this symbol for division:
____ )
Call this symbol a “gazinta”
Read this properly!
2184 DIVIDED BY 24 is what number or
24 goes into 2184 how many times?
I do not know what it is really called, but “gazinta” works. Try saying it out loud a few times.

5. 24 goes into 2184 how many times?
Long Division
Example:
2184 ÷ 24 = n
Read this properly!
24 goes into 2184 how many times?
Use this symbol for division:
____ )
Call this symbol a “gazinta”
_______
24) 2184
24 goes into 2184 n times. n

6. Long Division: Step 1: DIVIDE
_______
24) 2184
Work the DIVIDEND (2184) from LEFT to right.
24 does not go into 2.
24 does not go into 21.
24 DOES go into 218.
How many times does 24 go into 218?
10 x 24 = 240…too much.
9 x 24 = This works.

7. Long Division Step 2: Multiply
_______
24) 2184 9
216 2
9 x 24 = 216.
1. Place a 9 over the 8 (because 24 will go into 218.)
2. Place a 216 under the 218 (because 9 x 24 = 216)
Step 3: Subtract
3. Write a 2 under the 6 (because 218 – 216 = 2)
Mathematical note:
This is actually PARTIAL DIVISION. We are actually dividing 2184 by 24 and getting x 24 = We write it in this manner so that we may continue with the next step.

8. Long Division: Step 4: Bring Down24 1 9
_______
24) 2184
9 x 24 = 216. 4
216 2
4. Bring down the next digit (4). Write it next to the 2 on the bottom line.
5. Repeat the entire process, only now, do 24 divided by 24 (which = 1). Write the 1 over the 4 in the answer. Multiply 24 x 1 to get 24. Then subtract: 24 – 24 = 0.

9. 24) 2184 Long Division 9 1 _______ 24 x 91 2160 2184 + 216 2
2184 ÷ 24=91
Check your answer by multiplying. 24
x 91
2160
2184
_______
24) 2184 9
216 2 24 1 +

10. Long Division NOTES: If there is a remainder, you can:
Write it as a fraction with
Continue the dividend with .000… etc. for as long as necessary.
Use the remainder, when appropriate.
remainder
divisor

11. Long Division Try this: 36) 3132 36 goes into 3 zero times
36 x 9 = 324…too big.
36 x 8 = So 36 goes into times.
= 25.
Bring down the 2.
36 goes into 252 seven times.
Since 7 x 36 = 252, there is no remainder.
Try this:
36) 3132 2 9
288 8
252 25 7

12. Long Division Check: 87 x 36 = 8 7 x 3 6 6 x 7 = 4 2 6 x 80 = 4 8 0
This proves that 3132 divided by 36 = 87.

13. Long Division a b ) b a Tricks:
All division problems can be written as fraction problems:
a ÷ b = = a b ) b a
This means that all fraction rules apply to division problems. This means that you can REDUCE division problems as if they were fractions!

14. Long Division
This means that all fraction rules apply to division problems. This means that you can REDUCE division problems as if they were fractions!
So: ÷ 36= (divide both by 2)
becomes ÷ 18= (divide both by 2)
which becomes 783 ÷ 9 = (divide both by 3)
which becomes 261 ÷ 3 = 87

15. Long Division ÷ ÷ ÷ So: 3132 ÷ 36= (divide both by 2)
becomes ÷ 18= (divide both by 2)
which becomes 783 ÷ 9 = (divide both by 3)
which becomes 261 ÷ 3 = 87
3132 36 2 ÷ 2
1566 18 =
783 9 ÷ =
783 9 = ÷ 3
261 3 = 87

16. Long Division
Extra Practice:
76 ÷ 3 =
11562 ÷ 47 =
342 ÷ 24 =

17. Long Division Extra Practice: 76 ÷ 3 = 25.333… or 25 11562 ÷ 47 = 246
342 ÷ 24 = 14.25 1 3

18. Additional Resources http://www.mathsisfun.com/long_division.html
lesson-1.html
Math comedy sketch: