Anonymous
Anonymous asked in Science & MathematicsMathematics · 1 month ago

# Why does long division work?

Hi. My Grade 2 student asked me why long division worked? Why was long division done this way? I was at a loss to answer her.

Can you help me explain in a simplistic way? Thanks.

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• Anonymous
1 month ago

Second grade is a bit young for long division, isn't it?  Is this a GATE class?

If your student has a grasp of division in general, and is familiar with money, then the following description might help.

Suppose you have \$7.44 to divide evenly between three people, and suppose also that the amount is in dollar bills, dimes and pennies.  You also have access to a change machine that will either exchange ten dimes for one dollar or ten pennies for one dime.

You begin with 7 dollar bills, 4 dimes and 4 pennies.

Start with the dollar bills.  With 7 of them, you can give all three people \$2 each.  That's the most number of whole dollars you can give them and still have everyone have the same amount.

There's one dollar left over, and you can't divide that, so exchange it for ten dimes.

Now you have 10+4 = 14 dimes and 4 pennies.

Divide up the dimes.  You can give each person 4 of them, and there will be 2 dimes left over.  You can't divide those two dimes into three equal parts, so change them for 20 pennies.

Now you have 20 + 4 = 24 pennies.  Divide those into 3 piles of 8, giving 8 pennies ot each of the three people.

Each person received the same amount, 2 dollars, 4 dimes and 8 pennies, or \$2.48, and there's nothing left over at the end, so there is no remainder.

That's basically doing the same operations as long division of 744 by 3, expressed in terms of dollars, dimes and pennies as "manipulatives".

The reason it works is that every step distributes an equal amount to each person, so the process really does divide a large number into equal shares.

• Vaman
Lv 7
1 month ago

I think that the answer is here. suppose some one wants to 300/250. First divide by ten both the numerator and denominator, You get 30/25. Again

divide up and down by 5. You get 6/5. One need not remember higher multiplication tables. Simply divide numerator and denominator by smaller numbers, repeatedly. This is called, I think the long division.

• Dixon
Lv 7
1 month ago

The explanation for why it works is beyond the understanding of a typical Grade 2 student (or teacher) which is why it is taught by rote. And that is not to be patronising, the process actually conceals a lot of subtle arithmetic "tricks".

Added: Most mathematics students probably don't understand why long division works until they do polynomial long division and the remainder theorem, which is quite advanced. And even then, those topics are often taught as being "just like long division", so plenty of mathematics students might never take the time to fully understand how it works.

• 1 month ago

Because it is the reverse (inverse?) of multiplication, and multiplication is jus a short-cut way to add up a whole bunch of identical ("the same") numbers. Tel the student she can trust math.