Get The Best Grades With the Least Amount of Effort

Here is a collection of proven tips, tools and techniques to turn you into a super-achiever - even if you've never thought of yourself as a "gifted" student.

The secrets will help you absorb, digest and remember large chunks of information quickly and easily so you get the best grades with the least amount of effort.

If you apply what you read from the above collection, you can achieve best grades without giving up your fun, such as TV, surfing the net, playing video games or going out with friends!

What is seen to be true for in these examples, is true for any element of W. So, we can say :

For every whole number a, a ÷ 1 = a

Division is inverse operation to Multiplication :

Look at the following Examples.

144 ÷ 18 = 8 and 8 x 18 = 144; 81 ÷ 3 = 27 and 27 x 3 = 81.

What is seen to be true for in these examples, is true for any element of W. So, we can say :

For any three whole numbers a, b(≠0) and c, a ÷ b = c means a = b x c

Division by zero is not defined :

9 ÷ 0 = ? Is it possible to assign any whole number to this quotient ? Suppose, if possible, 9 ÷ 0 = a where a is a whole number. Since division is the inverse process of multiplication, we have a x 0 = 9. But, any whole number x 0 = 0 [see zero property of multiplication above.] So a x 0 = 0 and not 9. Thus there is no whole number which when multiplied by zero gives a non zero whole number.

Therefore 9 ÷ 0 can not be equal to any whole number.

Thus division by zero is not defined.

Division by zero is not defined.

What about 0 ÷ 0 ?

Let 0 ÷ 0 = b Then 0 = b x 0. This is satisfied for all values of b. So 0 ÷ 0 has innumerable Answers. It can not be any one umber.

So, we can say

0 ÷ 0 is indeterminate.

Division of zero with any number gives zero :

Look at the following Examples.

0 ÷ 34 = 34 ; 0 ÷ 5617 = 0

What is seen to be true for in these examples, is true for any element of W. So, we can say :

For every whole number a, 0 ÷ a = 0

Progressive Learning of Math : Whole Numbers

Recently, I have found a series of math curricula (Both Hard Copy and Digital Copy) developed by a Lady Teacher who taught everyone from Pre-K students to doctoral students and who is a Ph.D. in Mathematics Education.

This series is very different and advantageous over many of the traditional books available. These give students tools that other books do not. Other books just give practice. These teach students “tricks” and new ways to think.

These build a student’s new knowledge of concepts from their existing knowledge. These provide many pages of practice that gradually increases in difficulty and provide constant review.

These also provide teachers and parents with lessons on how to work with the child on the concepts.

The series is low to reasonably priced and include