MILESTONE 5: Division

To practice division mentally, go to


Division is the opposite of multiplication. If you already know the various techniques of multiplication, you can learn to divide easily.

Suppose there are 30 pennies on the table. How many times can you take 6 pennies out? Picture yourself taking out 6-pennies at a time. You can do so 5 times only before no pennies are left on the table. You may also observe that 6 pennies multiplied 5 times results in 30 pennies

Now tell me rapidly: Out of 30 pennies, how many times can you take out

  • 5 pennies ?
  • 30 pennies ?
  • 1 penny ?
  • 0 pennies ?

If you thought of 30 divided by 0 to be “30” or “0” then you need to review the definition of Division. Once again imagine that there are 30 pennies on the table. Now take out 0 pennies. How many are left? 30 pennies are left, correct? Now take out 0 again, and again, and again. You may do so hundreds of times, and still there will be 30 pennies left on the table. Can you see that you may take 0 out of 30 an unlimited number of times? In other words, 30 divided by 0 is infinity.

The operation of division computes how many times a quantity (divisor) can be taken out of another quantity (dividend). That result is called the quotient.

When the division is exact, that is to say, the divisor can be taken out of the dividend an exact number of times, the divisor is called a factor of the dividend.

When the division is not exact, a remainder is left after division. When the remainder is further divided by the divisor into portions less than a unit, then we get fractions.

Both factors and fractions are taken up in subsequent milestones.

A proper understanding of division helps one round up all the earlier concepts in math. By the time one completes the Elementary School, one should have developed the ability of divide mentally with single digit numbers. This understanding then forms the basis of middle school math.

Here are some videos from the Khan Academy that explain division:

Division 1

Division 2

Division 3: More long division and remainder examples

Level 4 division

Partial Quotient Division

Partial Quotient Method of Division 2


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