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Are you a ICSE Class 10 student? This is For You!

In ICSE Class 10 mathematics, percentage calculations are a fundamental topic that students must master. Understanding how to calculate percentages is crucial not just for exams but also for real-life applications. This article will guide you through the basic concepts, methods, and applications of percentage calculations relevant to Class 10 ICSE students.

What is a Percentage?

A percentage is a way of expressing a number as a fraction of 100. The term comes from the Latin word “per centum,” which means “by the hundred.” It is a useful mathematical tool for comparing proportions and understanding relative sizes.

The percentage is represented by the symbol % and is calculated using the following formula:

Percentage=(PartWhole)×100\text{Percentage} = \left( \frac{\text{Part}}{\text{Whole}} \right) \times 100 Percent=(WholePart​)×100

Basic Percentage Calculations

1. Finding the Percentage of a Number

To find a specific percentage of a number, use the formula:

Percentage of a Number=(Percentage 100)×Number\text{Percentage of a Number} = \left( \frac{\text{Percentage}}{100} \right) \times \text{Number}Percentage of a Number=(100 Percent​)×Number

Example: What is 25% of 200?

Percentage of a Number=(25100)×200=0.25×200=50\text{Percentage of a Number} = \left( \frac{25}{100} \right) \times 200 = 0.25 \times 200 = 50Percentage of a Number=(10025​)×200=0.25×200=50

So, 25% of 200 is 50.

2. Finding What Percentage One Number is of Another

To determine what percentage one number is of another, use:

Percentage=(PartWhole)×100\text{Percentage} = \left( \frac{\text{Part}}{\text{Whole}} \right) \times 100 Percentage=(WholePart​)×100

Example: What percentage of 80 is 20?

Percentage=(2080)×100=0.25×100=25%\text{Percentage} = \left( \frac{20}{80} \right) \times 100 = 0.25 \times 100 = 25\%Percentage=(8020​)×100=0.25×100=25%

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So, 20 is 25% of 80.

3. Finding the Number when the Percentage is Known

To find the whole number when a part and the percentage are known, use:

Whole=Part×100 Percent\text{Whole} = \frac{\text{Part} \times 100}{\text{Percentage}}Whole=PercentagePart×100​

Example: If 30 is 15% of a number, what is the number?

Whole=30×10015=300015=200\text{Whole} = \frac{30 \times 100}{15} = \frac{3000}{15} = 200Whole=1530×100​=153000​=200

So, the number is 200.

Applications of Percentage Calculations

1. Percentage Increase and Decrease

To calculate percentage increase:

Percentage Increase=(New Value−Original ValueOriginal Value)×100\text{Percentage Increase} = \left( \frac{\text{New Value} - \text{Original Value}}{\text{Original Value}} \right) \times 100 Percent Increase=(Original ValueNew Value−Original Value​)×100

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To calculate percentage decrease:

Percentage Decrease=(Original Value−New ValueOriginal Value)×100\text{Percentage Decrease} = \left( \frac{\text{Original Value} - \text{New Value}}{\text{Original Value}} \right) \times 100 Percent Decrease=(Original ValueOriginal Value−New Value​)×100

Example: If the price of an item increases from $50 to $60, what is the percentage increase?

Percentage Increase=(60−5050)×100=(1050)×100=20%\text{Percentage Increase} = \left( \frac{60 - 50}{50} \right) \times 100 = \left( \frac{10}{50} \right) \times 100 = 20\%Percentage Increase=(5060−50​)×100=(5010​)×100=20%

So, the percentage increase is 20%.

2. Finding the Original Value After a Percentage Increase or Decrease

If you know the new value after a percentage increase or decrease, you can find the original value using:

For increase:

Original Value=New Value1+Percentage Increase100\text{Original Value} = \frac{\text{New Value}}{1 + \frac{\text{Percentage Increase}}{100}}Original Value=1+100 Percentage Increase​New Value​

For decrease:

Original Value=New Value1−Percentage Decrease100\text{Original Value} = \frac{\text{New Value}}{1 - \frac{\text{Percentage Decrease}}{100}}Original Value=1−100 Percentage Decrease​New Value​

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Example: If the new value of a product after a 15% decrease is $85, what was the original price?

Original Value=851−15100=850.85=100\text{Original Value} = \frac{85}{1 - \frac{15}{100}} = \frac{85}{0.85} = 100 Original Value=1−10015​85​=0.8585​=100

So, the original price was $100.

Common Mistakes and Tips

1. Confusing the Percentage with the Whole Number: Always remember that the percentage is a part of 100. Ensure you are clear about which number is the part and which is the whole.
2. Incorrect Use of Formulas: Double-check the formulas you use to ensure they are appropriate for the problem you are solving.
3. Misinterpreting the Result: Sometimes students misinterpret what their percentage result means. Always contextualise your percentage results in relation to the problem.

(Know More: How to convert SGPAto CGPA percentage?)

Practice Problems

1. What is 12% of 250?
2. A student scored 45 out of 60 in a test. What percentage did they score?
3. If a shirt’s price is reduced by 20% and the sale price is $40, what was the original price?
4. A company’s revenue increased from $200,000 to $250,000. What was the percentage increase?

Conclusion

Percentage calculations are a crucial part of Class 10 ICSE mathematics. By understanding how to find percentages, calculate increases and decreases, and apply these concepts to real-world scenarios, you can improve your mathematical skills and problem-solving abilities. Practise regularly with a variety of problems to strengthen your understanding and proficiency in working with percentages.

Frequently Asked Questions (FAQs) on Percentage Calculation for ICSE Class 10

1. What is a percentage?

A percentage is a way of expressing a number as a fraction of 100. It represents a portion of a whole and is denoted by the symbol %. For example, 25% means 25 out of every 100 parts.

2. How do you calculate a percentage of a number?

To find a percentage of a number, use the formula:

Percentage of a Number=(Percentage 100)×Number\text{Percentage of a Number} = \left( \frac{\text{Percentage}}{100} \right) \times \text{Number}Percentage of a Number=(100 Percent​)×Number

For example, to find 20% of 150:

Percentage of a Number=(20100)×150=0.20×150=30\text{Percentage of a Number} = \left( \frac{20}{100} \right) \times 150 = 0.20 \times 150 = 30 Percentage of a Number=(10020​)×150=0.20×150=30

3. How do you find what percentage one number is of another?

Use the formula:

Percentage=(PartWhole)×100\text{Percentage} = \left( \frac{\text{Part}}{\text{Whole}} \right) \times 100 Percent=(WholePart​)×100

For example, to find what percentage 30 is of 120:

Percentage=(30120)×100=0.25×100=25%\text{Percentage} = \left( \frac{30}{120} \right) \times 100 = 0.25 \times 100 = 25\%Percentage=(12030​)×100=0.25×100=25%

4. How do you calculate the percentage increase or decrease?

To find the percentage increase:

Percentage Increase=(New Value−Original ValueOriginal Value)×100\text{Percentage Increase} = \left( \frac{\text{New Value} - \text{Original Value}}{\text{Original Value}} \right) \times 100 Percent Increase=(Original ValueNew Value−Original Value​)×100

To find the percentage decrease:

Percentage Decrease=(Original Value−New ValueOriginal Value)×100\text{Percentage Decrease} = \left( \frac{\text{Original Value} - \text{New Value}}{\text{Original Value}} \right) \times 100 Percent Decrease=(Original ValueOriginal Value−New Value​)×100

For example, if the price of an item increases from $50 to $60, the percentage increase is:

Percentage Increase=(60−5050)×100=20%\text{Percentage Increase} = \left( \frac{60 - 50}{50} \right) \times 100 = 20\%Percentage Increase=(5060−50​)×100=20%