RATIO
It has been discussed earlier in earlier class study or modules about the Ratio, but here we will learn some more important facts about the Ratio.
By explaining through Ratio, we can compare the size of two quantities of the same kind in many different ways. One of them is ratio. The ratio of two quantities x & y of the same kind and in the same unit of measurement is the fraction x / y. It is also denoted as x : y ( we should read as “x to y” or “x is to y” ). In the ratio x : y, x is the 1st term or the ‘Antecedent’ and y is the second term of the ‘Consequent’.
There are some important rules and information has been described below –
A) Any ratio is a number, so there are no units.
B) A ratio exists only between quantities of the same kind measured in the same units
C) In a ratio x : y, x = 1st term ( Antecedent ),
y = 2nd term ( Consequent )
D) There can be no ratio between quantities of different kinds, for your better understanding as per the example – if there are two numbers with unit like 16 kg and 10 meters, then these cannot be described as ratio, even in case of three numbers where the units are different such as 25 Seconds, 15 kilometers and 65 liters, the ratio cannot be defined as because units of the given numbers are different.
E) On the other way, we can say if the given number is unit is convertible in the same form of unit, then we can express those units in ratio form. For your better understanding, there are some example are given below –
If there are two different units that is 2.5 Kilometers and 650 meters and to be described as ratio, then we have to find the possibility of getting same units and if there is any possibility to conversion in same unit then we have to do it. There are two numbers with unit are given such as 2.5 kilometers and 650 meters. Kilometers can be convertible into meters, as 1 km = 1000 meters, so, 2.5 kilometers = 2500 meters and another given number is 650 meters, now we can observe that unit of both the numbers are same, so now we can define the ratio of given numbers = 2.5 kilometers : 650 meters
= 2500 meters : 650 meters
= 250 : 65 = 50 : 13
F) A ratio does not change if its Antecedent and Consequent are multiplied or divided by the same number.
a : b = ( a X k ) : ( b X k ), where a & b are numbers and k is common multiplying number.
1.5 1.5 X 100 150
1.5 meters : 32 meters = ------- = ----------- = --------
32 32 X 100 3200
a : b = ( a ÷ k ) : ( b ÷ k ), where k ≠ 0 is any number.
120 120 ÷ 10 12
120 liters : 180 liters = ------- = ---------- = -------
180 180 ÷ 10 18
2
= -------- = 2 : 3
3
G) To express a ratio in the simplest form, take these steps, take these steps –
1) If the Antecedent and the Consequent are integers then divide both by their HCF.
2) If the Antecedent or the Consequent or both are fraction then multiply both by the LCM of their denominators.
H) If the ratio of 1) two quantities be a : b, then the quantity may be expressed as ak & bk.
2) Three quantities be x : y : z, then the quantities are xk, yk, zk
I) If a number ‘n’ is divided into three parts in the ratio x : y : z then,
x y
1st part = ------------ X n, 2nd part = ----------- X n,
x + y + z x + y + z
z
3rd part = ------------ X n
x + y + z
final Quantity
J) Multiplying ratio = -----------------------
original quantity