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The Cross Product Law as a Linear Equation

Proportionality calculations lead to the use of the so-called 'rule of 3', also nammed the 'cross product law'.

Let's study it with an example.

If it lasts 15 minutes to bake 500 g of rastbeef, how much time shalll I bake my 950 g rastbeef?

Let's call x the time in minutes that we are looking for.

Then the time per gram is either 15 min over 500 g, or x min over 950 g:

  x               15
------    =    ------    (1)
950            500

If we multiply...

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Adding and Subtracting a Percentage

As we saw in a previous post, adding a percentage is a multiplication.

For instance, adding 20% to a tax free price, to obtain the VAT included price, is multiplying by (1+20/100)=1.20=1.2.

But what I would like you to know today, is that subtracting a percentage is NOT a division, but a multiplication as well!

For instance, a coupon of 30% on a price of $100 is subtracting 30% of $100, that is (30/10)*$100=$30. The reduced price is $100-$30=$70, that is 0.70 times $100.

Another way to...

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About the Euclidian Division

The Euclidian Division is the way integers divide together without introducing the fractions.

It deals with problems of sharing quantities of objects that can not be individually shared.

For instance, if we want to share 13 marbles between 3 children equally, then each child will receive 4 marbles, and it will remain 1 marble unshared.

This is written 13 ÷ 3 = 4, remains 1, that is equivalent to 13 = 4 x 3 + 1.

The definition of the Euclidian division is so: a ÷ b, with a and b...

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Compare Integers and Decimal Numbers.

The decimal notation is very useful to compare numbers, as soon as we are able to order the 10 digits from 0 to 9: 0<1<2<3<4<5<6<7<8<9.

To know which number is the greatest between 2 natural integers a≥0 and b≥0, we first compare the number of digits of a and b. If a has more digits than b, then a>b, and reversely. For instance 96<456 and 16>0.

If a and b have the same number of digits, then we compare the digits that are the most to the left. If they are different, then the greatest...

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Greatest Common Divisor and the Fractions

In arithmetics, the numbers by which we may divide an integer, their 'divisors', are quite important.

For instance, if you find a number that divides both the numerator and the denominator of a fraction, for instnace 2 for the fraction 6/4, then you may simplify the fraction: 6/4=3/2, because
6=2x3 and 4=2x2.

The integers that divide both the integer p and the integer q are called the 'common divisors' of p and q.

The positive common divisors of 2 integers p and q are all lower than both...

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Helix in architecture: Spiral Stairs

"Spiral" Stairs are stairs that go up together with tunling around a central axis.

They follow a mathematical curve called "helix".

But what is the equation of an helix?

Let's suppose that the vertical axis "z" is the central axis around wich the helix turns, oriented to the top, and that the first horizontal axis "x" is along the basis of the stairs.

Let the parameter a be the horizontal angle of a dot on the curve with the "x" axis.  Then the horizontal projection of the dot has...

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