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 both sides of (1) by the product 950 x 500 and simplify the left side by 500 and the right side by 950, we obtain the cross product law:

500 * x* = 950 x 15 (2)

where the numerator of a side is multiplied by the denominator of the other side.

(2) is a linear equation of the type * a x *=

*, wich solution is*

**b***=*

**x***/*

**a***(*

**b***divided by*

**a***).*

**b**Thus the solution of our problem is the 'rule of 3' formula:

950 x 15** x **= --------------- = 28.5 min = 28 min 30 s

500

The rule of 3 can be obtain directly from the proportionality equation (1), multiplying both sides of (1) by 950 and simplifying the left side by 950.

Thus, the rule of 3 solves a proportionality equation, that is in fact a linear equation as well, with coefficients inverses of integers…