Long Division Algorithm Explained

Long Division : 

Long Division

What does a duck have to do with long division? : 

What does a duck have to do with long division?

Slide 3: 

D ucks M ay S wim B ackwards R egularly

Slide 4: 

D ivide M ultiply S ubtract B ring Down R epeat

Slide 5: 

The mnemonic device Ducks Swim Backwards Regularly can help you remember the steps of this long division algorithm. This method is effective for solving problems with large dividends.

Let’s take a look at an example… : 

Let’s take a look at an example… 2901 – 3 or 3 2901

Slide 7: 

Which number is which? ? 3 2901 Divisor Dividend Quotient Divisor = The number of groups you break the dividend into. Dividend = The number that is to be divided. Quotient = Your solution.

Slide 8: 

D ivide 3 2901 Step 1: Divide Can 2 divide into 3 groups? No

Slide 9: 

D ivide x 3 2901 Step 1: Divide Can 2 divide into 3 groups? No Write an x above the 2 digit in 2,901 to hold the place value.

Slide 10: 

D ivide x 3 2901 Step 1: Divide Can 29 divide into 3 groups? Yes

Slide 11: 

D ivide x9 3 2901 Step 1: Divide Can 29 divide into 3 groups? Yes 29 divides into 3 9 times Write 9 above the 9 digit in the dividend.

Slide 12: 

M ultiply x9 3 2901 Step 2: Multiply 3 x 9 = ?

Slide 13: 

M ultiply x9 2901 27 Step 2: Multiply 3 x 9 = ? 3 x 9 = 27 Write 27 under the 29.

Slide 14: 

S ubtract x9 2901 - 27 Step 3: Subtract Subtract 27 from 29.

Slide 15: 

S ubtract x9 2901 - 27 2 Step 3: Subtract Subtract 27 from 29. Write the 2 in the correct place value.

Slide 16: 

Is your difference larger than your divisor? 2 (the difference) < 3 (the divisor) so we can continue. Phew! If your difference is larger than your divisor, then stop and go back! Check your original division. You can make another group with your dividend.

Slide 17: 

B ring Down x9 2901 - 27 2 Step 4: Bring Down Bring down the next digit of the dividend.

Slide 18: 

B ring Down x9 2901 - 27 20 Step 4: Bring Down Bring down the next digit of the dividend.

Slide 19: 

R epeat x9 2901 - 27 20 Step 5: Repeat Start the process again.

Slide 20: 

D ivision x9 2901 - 27 20 Step 5: Repeat 1.) Divide: Can 20 divide into 3 groups? Yes

Slide 21: 

D ivision x96 2901 - 27 20 Step 5: Repeat 1.) Divide: Can 20 divide into 3 groups? Yes 20 divides into 3 6 times Write 6 above the 0 digit in the dividend.

Slide 22: 

M ultiply x96 2901 - 27 20 Step 5: Repeat 2.) Multiply: 3 x 6 = ?

Slide 23: 

M ultiply x96 2901 - 27 20 18 Step 5: Repeat 2.) Multiply: 3 x 6 = ? 3 x 6 = 18 Write 18 below the 20.

Slide 24: 

S ubtract x96 2901 - 27 20 - 18 Step 5: Repeat 3.) Subtract: Subtract 18 from 20.

Slide 25: 

S ubtract x96 2901 - 27 20 - 18 2 Step 5: Repeat 3.) Subtract: Subtract 18 from 20. Write the 2 in the correct place value.

Slide 26: 

B ring Down x96 2901 - 27 20 - 18 21 Step 5: Repeat 4.) Bring Down: Bring down the next digit of the dividend.

Slide 27: 

R epeat x96 2901 - 27 20 - 18 21 Step 5: Repeat Repeat the process again.

Slide 28: 

D ivide x96 2901 - 27 20 - 18 21 Step 5: Repeat 1. Divide: Can 21 divide into 3? Yes

Slide 29: 

D ivide x967 2901 - 27 20 - 18 21 Step 5: Repeat 1. Divide: Can 21 divide into 3? Yes 21 divides into 3 7 times. Write 7 above the 1 in the dividend.

Slide 30: 

M ultiply x967 2901 - 27 20 - 18 21 Step 5: Repeat 2: Multiply 3 x 7 = ? 3 x 7 = 21

Slide 31: 

S ubtract x967 2901 - 27 20 - 18 21 Step 5: Repeat 2: Subtract Subtract 21 from 21. The difference is 0.

A difference of 0 means that we have divided the divisor evenly into the dividend. : 

A difference of 0 means that we have divided the divisor evenly into the dividend. In short…we’re finished!

Slide 33: 

Solution x967 2901 - 27 20 - 18 21 2901 – 3 = 967

Slide 34: 

Now that you have learned an algorithm for long division, there are a few things you must remember… Division is sharing a number of items to find out how many equal groups can be made, or how many items would be in each group. It is just as important to understand what division is as it is to be able to use this algorithm. And… This is only one of the methods for long division. There are other methods that you can use.

Slide 35: 

D ivide M ultiply S ubtract B ring Down R epeat

Slide 36: 

D ucks M ay S wim B ackwards R egularly

Good Luck! : 

Good Luck!