CLASS-6
PERCENTAGE

PERCENTAGE -

IMPORTANT POINTS -

1. Percent:- Out of one hundred, is called percent and it is denoted as (%) e.g. 10%, 15% ….

# Percent can be expressed in fraction and decimal such as given below : -

                1

a)  1% =  -------- Or  0.01

               100

                45

b)  45% = -------- Or  0.45

               100

# A fraction or decimal can be expressed in percent.

# We use percentage in profit and loss and also in finding interest etc.

2. Percentage:- When a quantity is expressed in the percent form, it is called percentage.

3. To convert a given Fraction or Decimal into Percentage (Percent Form):- Multiply the given fraction or the given decimal by 100 and at the same time write the sign of percentage.

4. To convert a given Percentage into a Fraction or Decimal:- Remove the sign of percentage and at the same time divide by 100. Then reduce the fraction obtained to its lowest terms or decimal as required.

5. To Express one Quantity (number) as a percentage of the other:- Divide first quantity by the second and at the same time multiply the result by 100%.

 Keep in Mind:- To find the Increase or Decrease Percent:

         o  Percent or percentage has no unit.

         o  In order to express one quantity as a percentage of another quantity; both the quantities must have same units.6.  

                    Increase in Value

 Increase % = -------------------- X 100%

                     Original Value 


                    Decrease in Value

 Decrease % = -------------------- X 100%

                      Original Value


The percentage increase is equal to the subtraction of original number from a new number, divided by the original number and multiplied by 100.

 % increase = [(New number – Original number)/Original number] x 100

where, increase in number = New number – original number

Similarly, percentage decrease is equal to subtraction of new number from original number, divided by original number and multiplied by 100.

 % decrease = [(Original number – New number)/Original number] x 100

Where, decrease in number = Original number – New number

So basically if the answer is negative then there is percentage decrease.

Here are a few common scenarios where percentages are used:

  1. Discounts and Sales:- When shopping, you might see items on sale with a certain percentage discount, such as "50% off." This means the price has been reduced by half. For instance, a 20% discount on a $100 item means the item now costs $80.
  2. Interest Rates:- In finance, interest rates are often expressed as percentages. For example, a loan with an interest rate of 5% means that you'll pay an extra 5% of the loan amount as interest.
  3. Probability:- Percentages are used to express the likelihood or probability of events. For instance, if there's a 20% chance of rain, it means there's a one in five chance that it will rain.
  4. Grades and Scores:- In education, grades are often given as percentages to reflect a student's performance on assignments, exams, or overall course work.A score of 85 out of 100 would be equivalent to 85%.
  5. Profit and Loss:- As discussed earlier, profit and loss percentages are used to measure financial performance.
  6. Population and Demographics:- Percentages are used to represent the distribution of population, age groups, ethnicities, and other demographic characteristics. When discussing population growth rates, percentages are used to describe how much a population has increased or decreased over a certain period.
  7. Tax Rates:- Tax rates can be given as percentages to indicate the proportion of income or value subject to taxation.
  8. Growth and Decline:- Percentages can be used to express the rate of growth or decline in various contexts, such as population growth, economic growth, or stock market performance.
  9. Stock Market:- Changes in stock prices are often reported as percentages. If a stock's price increases by 10%, it means the price has gone up by 10% from its previous value.

Calculating percentages involves simple arithmetic. To calculate a percentage, you divide the part by the whole (usually expressed as a fraction), and then multiply by 100 to express it as a percentage:

                   Part

Percentage = ---------- X 100%

                  Whole

Example.1) If you have 25 apples out of a total of 100 apples, then find the percentage of apples you have.

And.) The percentage of apple -

                  25    

Percentage = ------- × 100% = 25%

                 100

So, the percentage of the apple is 25%.    (Ans.) 

Percentages are a fundamental concept in mathematics and play a crucial role in various real-world applications.