PROPORTION
If two ratios w : x and y : z are equal, that is w : x = y : z then the four quantities w, x, y & z are said to be in proportion. This is also written as w : x : : y : z, the quantities w, x, y, z which are called the terms of the proportion, need not all be of the same kind. However the terms of the first ratio must be of the same kind, and the terms of the second ratio must also be of the same kind.
For your better understanding, we will provide you some example –
Example.1) Show the numbers such as 12, 36, 72, 216 are in proportion
Ans.) As per the given condition 12, 36, 72, 216 are in proportion because –
12 1
----------- = ---------- = 1 : 2
24 2
72 1
And ---------- = --------- = 1 : 2
216 2
So, numbers such as 12, 36, 72, 216 are in proportion.
Example.2) Show the quantities 4 h, 12 h, 16 L, 48 L are in proportion.
Ans.) As per the given condition 4 h, 12 h, 16 L, 48 L are in proportion because –
4 h 1
----------- = --------- = 1 : 3
12 h 3
16 L 1
------------- = ---------- = 1 : 3
48 L 3
So, the quantity such as 4 h, 12 h, 16 L, 48 L are in proportion.
The first and the fourth terms of a proportion are called the “EXTREMES”, while the second and the third terms are called the “MEANS”. The fourth term is also called the “FOURTH PROPORTION” to the other three terms.
w y
If, w : x = y : z, then -------- = -------- or wz = xy
x z
hence we can conclude that, the product of the "Extremes" = the product of the "Means"
above rule is known as the “CROSS PRODUCT RULE”.