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135 LearnersLast updated on September 25, 2025
Math Formula for Comparing Quantities
In Class 8 mathematics, comparing quantities involves understanding ratios, percentages, profit and loss, and simple and compound interest. These concepts are essential for solving problems related to real-life scenarios. In this topic, we will learn the formulas for comparing quantities.
Math Formula for Ratios
A ratio represents the relationship between two quantities. It is expressed as a:b, where a and b are any two quantities to be compared.
The formula for calculating a ratio is simple: Ratio = a/b
Math Formula for Percentages
Percentage is a way to express a number as a part of a whole.
The percentage formula is used to convert a ratio or fraction into a percentage: Percentage = (Part/Whole) × 100
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Math Formula for Profit and Loss
Profit and loss are financial concepts used to determine gain or loss from a transaction.
Profit = Selling Price - Cost Price Loss = Cost Price - Selling Price
Profit Percentage = (Profit/Cost Price) × 100
Loss Percentage = (Loss/Cost Price) × 100
Math Formula for Simple Interest
Simple interest is calculated on the original principal over time.
The formula for simple interest is: Simple Interest (SI) = (Principal × Rate × Time)/100
Math Formula for Compound Interest
Compound interest is calculated on the principal and the accumulated interest.
The formula for compound interest is: Compound Interest = Principal × (1 + Rate/100)^Time - Principal
Common Mistakes and How to Avoid Them While Using Comparing Quantities Math Formulas
Students make errors when calculating ratios, percentages, profit and loss, and interest. Here are some mistakes and the ways to avoid them.
Mistake 1
Confusing Ratios with Fractions
Students sometimes confuse ratios with fractions.
To avoid this error, ensure that you understand that a ratio is a comparison between two quantities, whereas a fraction represents a part of a whole.
Mistake 2
Incorrect Conversion to Percentage
Errors occur when converting fractions or ratios to percentages.
Always multiply by 100 to convert to a percentage.
Mistake 3
Mixing Profit and Loss Formulas
Students often mix up the profit and loss formulas.
Remember, profit is when selling price exceeds cost price, and loss is when cost price exceeds selling price.
Mistake 4
Misunderstanding Simple and Compound Interest
Students sometimes confuse simple and compound interest.
Remember, simple interest is calculated on the original principal, while compound interest includes interest on accumulated interest.
Mistake 5
Forgetting to Use the Correct Time Period in Interest Calculations
Errors occur by not using the correct time period for interest calculations.
Always ensure that the time matches the rate's time unit.
Examples of Problems Using Comparing Quantities Math Formulas
Problem 1
A bag has 6 red balls and 4 blue balls. What is the ratio of red balls to blue balls?
The ratio is 3:2
Explanation
To find the ratio, divide the number of red balls by the number of blue balls: 6/4 = 3/2.
Thus, the ratio is 3:2.
Problem 2
A dress originally costs $200 and is sold at a 20% discount. What is the sale price?
The sale price is $160
Explanation
To find the sale price, calculate the discount: 20% of $200 = (20/100) × 200 = $40.
Subtract the discount from the original price: $200 - $40 = $160.
Problem 3
A person bought a bike for $500 and sold it for $450. What is the loss percentage?
The loss percentage is 10%
Explanation
Calculate the loss: $500 - $450 = $50.
Then find the loss percentage: (50/500) × 100 = 10%.
Problem 4
If $1000 is invested at an annual simple interest rate of 5% for 3 years, what is the simple interest earned?
The simple interest earned is $150
Explanation
Use the simple interest formula:
SI = (Principal × Rate × Time)/100 = (1000 × 5 × 3)/100 = $150.
Problem 5
What is the compound interest on $6000 at 10% per annum for 2 years?
The compound interest is $1260
Explanation
Use the compound interest formula:
CI = 6000 × (1 + 10/100)^2 - 6000 = 6000 × (1.1)^2 - 6000 = 6000 × 1.21 - 6000 = $1260.
FAQs on Comparing Quantities Math Formulas
1.What is the formula for calculating a ratio?
2.How do you convert a fraction to a percentage?
3.What is the difference between simple and compound interest?
4.How do you calculate profit percentage?
5.What is the formula for calculating loss?
Glossary for Comparing Quantities Math Formulas
- Ratio: A comparison of two quantities by division, expressed as a:b or a/b.
- Percentage: A fraction or ratio expressed as a part of 100.
- Profit: The financial gain when the selling price exceeds the cost price.
- Loss: The financial loss when the cost price exceeds the selling price.
- Interest: The cost of borrowing money or the return on investment, calculated as simple or compound interest.
Jaskaran Singh Saluja
About the Author
Jaskaran Singh Saluja is a math wizard with nearly three years of experience as a math teacher. His expertise is in algebra, so he can make algebra classes interesting by turning tricky equations into simple puzzles.
Fun Fact
: He loves to play the quiz with kids through algebra to make kids love it.
