Ratio and Proportion

The ratio refers to the comparison of terms by division whereas proportion refers to the equality between two ratios. The ratio between two quantities such as ‘a’ and ‘b’ can be expressed as

 a:b or a/b.

 Proportion is usually indicated by using ‘::’ or ‘=’ such as x:y=a:b. When four different terms are in proportion the product of the two middle values(the second and third values) is equal to the product of the two extreme values(the first and fourth values).

There are many uses and tricks for ratio and proportion. Here is more information on the definition as well as the formulas of ratio and proportion.

 Ratios

Ratios refer to the relationship between two or more different quantities of different objects where the amount of one object is contained in the other. Ratios are usually used for comparison in two quantities and also follow the method of division that is considered to be the most efficient.  

The ratio is denoted by using the colon “: ”  

Proportions

Proportion usually depicts a comparative relation between a part share or a number to the whole amount. Equivalent ratios are said to be in proportion. When two sets of quantities(or numbers)are increasing or decreasing in the same ratio, they are said to be directly proportional to each other. 

 Proportion is denoted by – (::) and (=).

 The two types of proportions are direct proportion and inverse proportion. 

• Direct proportion

 The direct relationship between two numbers or quantities is known as direct proportion. When one number increases the other number also increases and vice versa. Direct proportion is usually written as y∝x. 

 For example: When the speed of a car is increased it is said to cover more distance in a fixed amount of time. This describes that the proportion is in direct relation with one quantity to another.

• Inverse proportion

This refers to the indirect relationship between two quantities, i.e. an increase in one quantity would mean a decrease in the other quantity. 

Inverse proportion is mostly written as

y ∝ 1/x. 

 For example: when the speed of the vehicle increases it covers the fixed distance in less amount time. 

 Some of the most important properties of proportion are

• Invertendo

• Alternendo

• Componendo

• Dividendo

• componendo and dividendo

• Addeneo

• Subtrahendo

Ratio and proportion formula

The ratio and proportion formula can be written very easily for two or more different quantities. 

Ratio formula:

a:b = a/b

Here, 

• ‘a’ and ‘c’ are known as antecedents

• ‘b’ and ‘d’ are known as consequents. 

For finding proportions in the terms of two ratios such as a:b and c:d, they can be written as:

a:b::c:d (formula)

• Here the middle terms that are ‘b’ and ‘c’ are termed as mean terms.

• Terms ‘a’ and ‘d’ can be written as extreme terms.

Difference between ratio and proportion 

Some of the most important ratio and proportion tricks

Ratio and proportion tricks can be used while solving mathematical problems related to these methods.  

• Two different quantities that have the same units can only be compared 

• Two ratios are said to be in proportion if both of them are equal 

• To find out whether the two ratios are equal and are in the form of a proportion, the cross-product method can be used. 

A few important notes on ratio and proportion are

• When we divide and multiply each term of a ratio with the same number, the ratio won’t be affected. 

• When there are three quantities, the ratio between the first and second is equal to the ratio between the second and the third quantities, then it is said to be any continued proportion.

• Similarly, in the case of 4 quantities to be in a continued proportion the ratio of the first and second should be equal to the ratio of the third and fourth quantities. 

Conclusion

Therefore, ratio and proportion is a very important topic that tests your problem-solving skills. Ratio and proportion are one of the most important parts of various competitive examinations as well.