# Proportions

*
*

*Proportion. Crosswise lied terms. Ratios.*

Overturned ratios. Derived proportions.

Overturned ratios. Derived proportions.

*
Proportion
*
is an equality of two ratios. From a proportion
follows:

*ad*=

*bc*(cross products are equal). Inversely, from

*ad*=

*bc*the next proportions follow:

All these proportions and some others can be received from the original proportion

*
a
*
/
*
b
*
=
*
c
*
/
*
d
*
by the next rules:

*
Crosswise lied terms of any proportion can be changed by places.
*

*
Ratios in any proportion can be changed to overturned ones.
*

*
Derived proportions
*
. If

*then the next so called derived proportions, received from the original, also take place:*

All these and a lot of other proportions can be united by the two base formulas:

where

*m, n, k, l –*any numbers.

E x a m p l e : If
*
m
*
=
*
n
*
=
*
k
*
=
*
*
1,
*
l
*
=
*
*
0, then
we receive: