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Division By Chunking

Published on Nov 22, 2015

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DIVISION BY CHUNKING

195/7

195/7

HOW MANY CHUNKS OF 7 CAN YOU SUBTRACT FROM 195?
Division can be thought of as repeated subtraction of the divisor from the dividend.

For the problem: 195/7, one might ask how many groups of 7 can you subtract from 195?
Photo by JD Hancock

EACH CHUNK IS 7

  • 5 Chunks is 35
  • 2 Chunks is 14
  • 1 Chunk is 7
Instead of subtracting one group of seven at a time, it is often more efficient to subtract multiples of chunks of seven. It is easier to deal with friendly chunks which are multiples of 10, 5, 2, and 1
Photo by Leo Reynolds

SUBTRACT 10 CHUNKS

195-70 =125
I like to subtract the largest chunk I can. In this case I'll subtract 10 chunks at one time.
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SUBTRACT ANOTHER 10 CHUNKS

125-70 =55
Since 125 still remains, I think I'll subtract another 10 chunks. Don't forget to keep a record of the number of chunks being subtracted. That will lead you to your answer.
Photo by Leo Reynolds

SUBTRACT 5 CHUNKS

55 - 35 = 20
With only 55 remaining, I can subtract 5 chunks and leave 20.
Photo by Leo Reynolds

SUBTRACT 2 CHUNKS

20 - 14 =6
And because 2 times 7 is 14, I can subtract 2 chunks and leave only 6.
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STOP.

NO MORE SUBTRACTION!
With only 6 remaining, no more chunks of 7 can be removed. So I am left with a remainder of 6.
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ADD CHUNKS TO GET QUOTIENT.

10 + 10 + 5 + 2 + R6
Photo by Leo Reynolds

195/7 =27 R6

(MEASUREMENT DIVISION)
How many 7s can you subtract from 195? You can subtract 27 groups (chunks) of 7. And you are left with a remainder of 6.
Our quotient is 27 r6.

This may seem a lengthy process. But for many students it is easier to understand than the traditional division algorithm.

And just like the traditional algorithm, it moves quickly once you understand how it works.
Photo by Leo Reynolds