Introduction to Ratio and Proportion

Data analysis helps analyze and process the raw data into meaningful information after eliminating the unwanted parts. Ratio and proportion are crucial topics used in the study and interpretation of the data, in various daily activities, and for calculation purposes. The ratio is defined as the comparison between two or more numbers indicating the quantity of each number among each other. Proportion is an equation that shows or proves that two given ratios are equivalent to each other. The ratio and proportion questions are critical in various comparisons and important mathematical concepts used in day-to-day life.

What are some examples of ratio and proportion?

The ratio between two numbers or quantities is represented with the help of the dividend sign “:” and draws a comparison. An example of a ratio is when there are 10 boys and 20 girls in the class – the ratio between the boys and girls is 1:2. 

The number present on the left is called an antecedent, whereas the number on the right is known as the consequent. 

Proportion is shown using double dividend “::” or “=” between two ratios. When two values are equal, it is considered proportional to each other. An example is choosing one from two products based on the % discount on different quantities. 

The types of proportion are:

• Direct – When two quantities increase or decrease together, they are said to be in direct proportion. Hence, the ratio of the corresponding values remains constant. Direct proportion can be represented as:

a/b = k, where a and b are the quantities that vary directly, whereas k is the positive number

• Inverse proportion – In this, two values are considered inversely proportional when one value increases whereas the other decreases. Hence, the increase in the quantity of one value leads to a decrease in another and vice versa. It is represented as :

a ∝ 1/b

Ratio and proportion formula

The formula for ratio and proportion is integral for solving the ratio and proportion questions. The following is the formula used for the calculation:

Formula for ratio

A : B => a / b

The ratio is denoted by the dividend symbol when two quantities, a and b, are compared. 

• The first step is determining whether the ratio is presented in part-to-part or part-to-whole. 
• After that, calculate the parts or whole as per its requirement and put the values into the ratio.
• If necessary, simplify the values until it comes to their lowest value. For example, if the initial ratio is 10: 30, it can be further simplified as 1 : 3, where the ratio is 1 part for every 3 parts. 

Formula for proportion 

a : b :: c : d => a/b = c /d 

Comparing or equating two different ratios – the above equation a: b and c : d where the proportion is shown through a double dividend (:: ) or equal sign. 

• The first step toward finding the proportion is writing the equation and putting the equivalent ratios.
• Suppose the numeric part of one ratio is the multiple of the other ratio corresponding to it in the proportion equation. It is easy to calculate the quantity by multiplying the other part of the given ratio by the same number. 
• However, if there is no relation between the two ratios, it can be solved with the help of an unknown value by isolating the variable presenting it. 

What are the properties of ratio and proportion? 

• The ratio consists of values compared by a dividend. The number on the left side is the antecedent, and the right side is the consequent. When multiplied or divided by the same non-zero number, the ratio remains the same.
• Let’s assume that in ratio and proportion, two ratios a/b and c/d, are equal, represented by the following: 

(a) Invertendo represented by a/b = c/d => b/a = d/c 

(b) Alternendo represented by a/b = c/d => a/c = b/d

(c ) Componendo represented by a/b = c/d => (a + b)/b = (c+d)/d

(d) Dividendo represented by a/b = c/d => (a – b)/ b = (c – d)/ d

• In the case of proportion, when two ratios are equal, it is proportional to each other. It is presented as a product of extremes equal to the product of means. 

a: b:: c : d, where a and d are the extremes and b and c are the means. 

• When a, b, c and d are placed in continued proportion, it is presented as a:b = b:c = c:d
• For example, in the equation a:b = b:c, b is the mean proportion. Also, b2 = ac.
• In an equation a:b = b:c, c is the considered third proportion to the numbers a and b
• However, if there is a ratio and proportion a:b = c:d, then d is the fourth proportional to the numbers a, b and c. 

Conclusion

Ratio and proportion are used to calculate multiple daily activities. The ratio helps compare two or more quantities, whereas the proportion is an equation that shows that two ratios or fractions are equal. The ratio and proportion formula helps solve data analysis questions and compare different values, which are narrowed by a large amount of data.