Simple division technique

This division technique can only be used if the divisor could be factorized.

Example 1:

272 ÷ 16 = 17

1. Find the factors of the divisor. Choose one of the factors. 16 = 4 × 4 or 16 = 8 × 2 For example, I will use 8 × 2


2. Divide the dividend by one of the factor. 272 ÷ 8 = 34


3. Divide the quotient from 2. by the second factor. 34 ÷ 2 = 17


4. Therefore, the quotient is 17

Note: Try with 4 × 4. What will happened if the remainder is not zero? Please look at the next example.

Example 2:

275 ÷ 16 = 17 with remainder 3

1. 16 = 4 × 4


2. 275 ÷ 4 = 68, r. 3


3. 68 ÷ 4 = 17


4. The quotient is 17, with remainder 3

Note: Try with 2 × 8

Remainder when a number is divided by a nine

Do you know that there is an easy way to find the remainder when a number is divided by 9?

Example 1:

43 ÷ 9 = 4, remainder = 7

quick remainder: 4 + 3 = 7

Example 2:

28 ÷ 9 = 3, remainder = 1

quick remainder: 2 + 8 = 10 ?

If the addition is ? 9, cast out the 9s, until it is lest than 9.

10 – 9 = 1

Example 3:

2345 ÷ 9 = 260, remainder = 5

quick remainder: 2 + 3 + 4 + 5 = 14

14 – 9 = 5

Example 4:

4489 ÷ 9 = 498, remainder = 7

quick remainder: 4 + 4 + 8 + 9 = 25

25 – 9 = 16

16 – 9 = 7

Python: Make division always produce real numbers

A division of 7/3 in Python will gives a result of 2. However, this is not correct. Since Python always assume that the numbers are whole numbers, the result will be truncated from 2.5 to 2.

A work around is to write one or both of the numbers as a decimal:

>>> print 7/3.0
2.5

>>> print 7.0/3
2.5

>>> print 7.0/3.0
2.5

In order to change this behaviour of Python, throughout the program execution, so that Python will always produce real numbers, a module division has to be imported.

>>> from __future__ import division

>>> print 7/3
2.5