Partial Quotients Method
The Partial Quotients Method, the Everyday Mathematics focus algorithm for division, might be described as successive approximation. It is suggested that a pupil will find it helpful to prepare first a table of some easy multiples of the divisor; say twice and five times the divisor. Then we work up towards the answer from below. In the example at right, 1220 divided by 16, we may have made a note first that 2*16=32 and 5*16=80. Then we work up towards 1220. 50*16=800 subtract from 1220, leaves 420; 20*16=320; etc..


________
16 ) 1220 
 800  50
 
420 
 320  20
 
100 
 80  5
 
20 
 16  1
  
4  76
ans: 76 R4

When we know how many groups there are and how many things are to be shared, but we don't know how many are in each group, we divide to share equally.
Division is the inverse of multiplication. Inverse operations undo each other. For example: 5 x 20 = 100 and 100 divided by 20 = 5.
Division is a simpler way to do repeated subtraction.
Divisibility Rules:
Number

Divisibility Rule

2

All even numbers or all numbers with 0, 2, 4, 6, or 8 in the ones place.

5

All whole numbers with 5 or 0 in the ones place.

10

All whole numbers with 0 in the ones place.

3

Any whole number whose digits add up to a multiple of 3.
For example: 204 is divisible by 3 because 2 + 0 + 4 = 6 and 6 is a multiple of 3 because 2 x 3 = 6.

Any number, except 0, is divisible by 1 and itself. For example: 30 divided by 1 = 30 and 30 divided by 30 = 1.
Division of 0 is a special case of divisibility because any number, except 0, will divide into 0. Zero divided by any number, except 0, is zero. For example: 0 divided by 3 = 0.
Division by 0 cannot be done.
When we divide we can use the expanded division algorithm. Go to the Click Me button below for expanded algorithm power point to see how to use the division algorithm.