# Mathedu

Learn math by practice

# Re-engineering Math

## Mental Calculation and Distributivity

The distributivity law tells that, whatever the numbers a, b and c, we may distribute the factor a on the terms b and c:

a x ( b + c ) = a x b + a x c

For instance:

2 x ( 4 + 6 ) = 2 x 4 + 2 x 6

Indeed:

2 x 10 = 8 + 12 = 20

But what is this useful to?

You may use it for mental calculationâ€¦ with a little help of writing!

For instance, you may find any result in the table of 12, such as:

8 x 12 = 8 x ( 10 + 2 ) = 8 x 10 + 8 x 2 = 80 + 16 = 96

You may even multiply 2 numbers with 2...

## Why is the number 0 such a big discovery?

When children learn how to count, they begin with 1, as when matematicians construct the "natural" integers set, they begin with 0.

It seems to be a small difference, but it changes many things, even from a practical point of view.

Indeed, the digit 0 is fundamental for the decimal numeration system. And the decimal numeration system is very useful to make additions, subtractions and multiplications.

As a matter of fact, any basis may be used instead of the 10 basis...

## Distance Units Conversion and orders of magnitude

The International System distance measurement unit is the meter. But in everyday life, we use many other distance measurement units. How is it possible to express any distance, whatever its order of magnitude or usage measurement unit, in meters?

For the so called "metric system", we use the multiplication or division by a power of 10, that is 10 multiplied by itself a given number of times.

For instance, as 1 cm = 1/100 m, we have to divide a distance in centimeters by 100...

## Why is there leap years?

Well, the day length is exactly the time by which the earth makes a turnaround on itself. And the year is exactly the time by which the earth makes a complete revolution around the sun.

Thus, the number of days of the year must be the ratio of the year length on the day length say, in seconds.

The problem is that there is no reason for that ratio to be an integer. And in fact, it is not.

The closest integer to that ratio is 365. That is why we say that a year is 365...