LEARN MATH STEP BY STEP THROUGH VERY EASY PROCESS

RULES & REGULATION OF RATIO

__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 1 ^{st} 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 = 1 ^{st} term ( Antecedent ), **

** y = 2 ^{nd} 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**

**1 ^{st} part = ------------ X n, 2^{nd}
part = ----------- X n,**

** ****x + y + z x + y + z**

**z**

** 3 ^{rd} part = ------------ X n**

** x + y + z**

** final Quantity **

**J) Multiplying ratio =
-----------------------**

** original quantity**