Long Division The “ traditional ” algorithm. Long Division Steps: 1. Divide 2. Multiply 3....

Long DivisionLong DivisionThe The ““traditionaltraditional”” algorithm algorithm

Long DivisionLong DivisionSteps:Steps:

1.1. DivideDivide

2.2. MultiplyMultiply

3.3. SubtractSubtract

4.4. Bring DownBring Down

5.5. RepeatRepeat

Example:Example:

2184 2184 ÷ ÷ 24 = 24 = nn

Long DivisionLong Division

Read this properly!

2184 DIVIDED BY 24 is what number

or

24 goes into 2184 how many times?

Example:Example:

2184 2184 ÷ ÷ 24 = 24 = nn


Read this properly!

2184 DIVIDED BY 24 is what number

or


Use this symbol for division: ____

)

Call this symbol a “gazinta”

I do not know what it is really called, but “gazinta” works. Try saying it out loud a few times.

Example:Example:

2184 2184 ÷ ÷ 24 = 24 = nn


Read this properly!


Use this symbol for division: ____

)

Call this symbol a “gazinta”

_______

24) 2184

24 goes into

2184 n times.

n

Long Division: Long Division: Step 1: Step 1: DIVIDEDIVIDE

_______

24) 2184

Work the DIVIDEND (2184) from LEFT to right.

1. 24 does not go into 2.

2. 24 does not go into 21.

3. 24 DOES go into 218.

4. How many times does 24 go into 218?

a)10 x 24 = 240…too much.

b)9 x 24 = 216. This works.

Long Division Long Division Step 2: Step 2: MultiplyMultiply

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)

3. Write a 2 under the 6 (because 218 – 216 = 2)

_______

24) 2184

9

2162

Mathematical note:

This is actually PARTIAL DIVISION. We are actually dividing 2184 by 24 and getting 90. 90 x 24 = 2160. We write it in this manner so that we may continue with the next step.

Step 3: SubtractStep 3: Subtract

Long Division: Long Division: Step 4: Bring Step 4: Bring DownDown

_______

24) 21849 x 24 =

216.

9

2162

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.

4

24 0

1


2184 ÷ 24=91

Check your answer by multiplying.

_______

24) 2184

9

216224 0

1

24

x 91

24

2160

2184

+


NOTES:

If there is a remainder, you can:

a)Write it as a fraction with

b)Continue the dividend with .000… etc. for as long as necessary.

c)Use the remainder, when appropriate.

remainder

divisor


2

Try this:

36) 3132

a. 36 goes into 3 zero times

b. 36 goes into 31 zero times

c. 36 goes into 313….

36 x 9 = 324…too big.

36 x 8 = 288. So 36 goes into 313 8 times.

d. 313 - 288= 25.

e. Bring down the 2.

f. 36 goes into 252 seven times.

g. Since 7 x 36 = 252, there is no remainder.

0

0

9

8

25

288

2

7

252

0


Check: 87 x 36 =

8 7

x 3 6

6 x 7 = 4 2

6 x 80 = 4 8 0

30 x 7 = 2 1 0

30 x 80 = 2 4 0 0

3 1 3 2

This proves that 3132 divided by 36 = 87.


Tricks:

All division problems can be written as fraction problems:

a ÷ b = = abab

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!


This means that all fraction rules apply to division problems. This means that you can REDUCE division problems as if they were fractions!

So: 3132 ÷ 36= (divide both by 2)

becomes 1566 ÷ 18= (divide both by 2)

which becomes 783 ÷ 9 = (divide both by 3)

which becomes 261 ÷ 3 = 87


So: 3132 ÷ 36= (divide both by 2)

becomes 1566 ÷ 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

261

3

=783

9÷

2

2

=÷3

3= 87


Extra Practice:Extra Practice:

a)a) 76 ÷ 3 =76 ÷ 3 =

b)b) 11562 ÷ 47 =11562 ÷ 47 =

c)c) 342 ÷ 24 =342 ÷ 24 =


Extra Practice:Extra Practice:

a)a) 76 ÷ 3 = 25.333… or 25 76 ÷ 3 = 25.333… or 25

b)b) 11562 ÷ 47 = 24611562 ÷ 47 = 246

c)c) 342 ÷ 24 = 14.25342 ÷ 24 = 14.25

13

Additional ResourcesAdditional Resources

a)a) http://www.mathsisfun.com/long_division.htmlhttp://www.mathsisfun.com/long_division.html

b)b) http://www.coolmath4kids.com/long-division/long-http://www.coolmath4kids.com/long-division/long-division-lesson-1.htmldivision-lesson-1.html

c)c) http://www.mathplayground.com/howto_longdivision.htmlhttp://www.mathplayground.com/howto_longdivision.html

d)d) http://www.ehow.com/video_4991171_long-division.htmlhttp://www.ehow.com/video_4991171_long-division.html

e)e) http://www.youtube.com/watch?v=3ULXhiJqlPshttp://www.youtube.com/watch?v=3ULXhiJqlPs

f)f) http://www.youtube.com/watch?v=8OpsFZqH2ewhttp://www.youtube.com/watch?v=8OpsFZqH2ew

Math comedy sketch:Math comedy sketch:

http://www.youtube.com/watch?v=oti7DJ9P24Mhttp://www.youtube.com/watch?v=oti7DJ9P24M

Long Division The “ traditional ” algorithm. Long Division Steps: 1. Divide 2. Multiply 3....

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