Ratios and proportions are used in equation. A ratio is an equation of two numbers, and a proportion is an equation of two ratios .
Ratio
A ratio is an equation of two numbers of the similar elements. The ratio of two numbers is given by using the colon icon (:) . The ratio of two numbers x and y is given as: x:y, where x is the antecedent and y is the consequent. The ratio x:y signifies xq:yq where q is the similar component q is multiplied to provide equivalent fractions whose easiest formula will be x/y. It can be studied as x:y, as x ratio to y or x to y.
Characteristics of ratio
Some important characteristics of radio are as follows:
a) If a ratio is multiplied by the same formula, both in both the antecedent and consequent, then there is no substitute in the real ratio. Eg M:N=2M:2N.
b) If the antecedent and consequent of a ratio are divided by the actual unit, then there is no substitute in the real ratio. Eg M: N = M/2: N/2.
c) If two ratios are similar, then their reciprocals are also similar. Eg if M:N= O: P then N: M= P: O.
d) If two ratios are similar, then their cross -multiplications are also similar. Eg M: N= O: P then M*P=N*O.
e) The ratios for a set of equations may be similar but the real answer may be different. Eg 10:20=1:2 and 120:240=1:2; therefore the ratio 1:2 is equal, but the real answer is distinct.
Proportion
Proportion refers to the equation of the ratios. If two ratios are similar, then they are said to be symmetrical to each other. Two proportional ratios are indicated by a double colon (::). If two ratios 1:2 and 3:4 are similar, they are shown as 1:2::3:4, where 1 and 4 are the extreme terms and 2 and 3 are the mean terms.
Characteristics of proportion
Important characteristics of proportion are as follows:
a) For two numbers in a proportion, i.e 1/2=3/4, 1/3=2/4 , grasps correctly .
b) For two numbers in a proportion, i.e 1/2=3/4, 2/1=4/3, grasps correctly.
c) For two numbers in a proportion, i.e. 1:2::3:4, the outcome of the mean terms is similar to the outcome of the extreme terms, i.e 1*4=2*3.
d) For two numbers in proportion, i.e.= 1/2=3/4, (1+2)/2=(3+4)/4 is absolutely correct.
e) For two numbers in proportion, i.e. = (1-2)/2=(3-4)/4 is absolutely correct.
Types of Proportion
Direct Proportion
When two units ascend and descend in the equal ratio, then two units are said to be in direct proportion. It indicates if one units ascends or decreases, then the other unit will ascend or descend. It is shown as x is proportional to y. Eg If the speed of the vehicle increases, then the distance travelled will also increase.
Inverse Proportion
When two units are conversely related to each other, i.e. adding to one results in a descend in other and results in the other and a descend in the other results result in an increase in the first unit. Eg if the speed of the vehicle increases , then the time taken to travel the same distance decreases .
Continued Proportion
If the ratio 1:2=3:4 , then it is observed that the result of the first ratio is similar to the antecedent of the same ratio, and so on; then 1:2:3:4 is said to be the continued proportion. If the consequent and antecedent are not equal for same ratios, then they can be transformed into ongoing proportion by multiplying.
