Percent Proportion

In math, percent proportion is an equation that shows how a percentage is related to a whole number. We mainly use it to determine an unknown value, whether it is the part, the whole number, or the percentage. 

When a student scores 45 marks out of 60 in a test, and we need to find the percentage of the score, we would use percent proportion to find out the percentage of the score. 
 

To calculate percent proportion, we use the formula:

Part/whole = Percent/100

Where,

Part is the portion of the total ( e.g. marks obtained in a test)

Whole is the original amount ( e.g. total marks for a test)

Percent is the percentage given in a problem (out of 100) 

For example, 40 is what percentage of 90?

The first thing to do is identify the key terms “IS” and “OF”. 

IS: It is the part we are looking at, in this case 40.

OF: It is the whole amount; in this example, it is 90. 

So with this information, let's substitute the values. 

Part/whole = Percent/100

Now we need to cross multiply, 

40 × 100 = 90 × whole

4000 = 90 × whole 

4000 / 90 = 44.444%

Whole = 44.444%
 

Percent proportion follows certain mathematical properties to help in solving any kind of percentage-related problem. Here are some key properties: 

• Ratio property: Percent proportion is based on two ratios being equal. This means that the relationship between the part and the whole is always proportional to the percentage out of 100.

• Cross multiplication: Percent proportion is an equation of two equal ratios. We use cross multiplication to solve for any unknown values.
   

Percent proportion allows us to easily compare different quantities, because of which it is used as a tool to understand and interpret data in real-life situations. It also helps solve problems that include percentages.  

With the right approach, it is easy to master percent proportion. Here are some useful tips and tricks to help students quickly and accurately master percent proportion

• Memorize: Memorizing the percent proportion formula can help solve problems faster. Part/Whole = Percent/100.

• Cross multiply: Learning to cross multiply will help you find the missing values without any kind of complex calculations.

• Convert: Sometimes it is easier to convert the percentage into decimals for faster calculations.

Percent proportion is used in many real-life situations like calculating discounts, decision-making, and analyzing different trends. Here are a few real-life situations that we come across every day.

• Calculating tips at restaurants is one of the most common situations where percent proportion is used. It helps customers to quickly calculate the tips without any confusion.

• Trying to find the percentage of test scores is another common situation, especially for students.

• Using percent proportions in cooking recipes and cooking measurements helps to adjust ingredient quantities based on the number of servings.