Class 7 Maths Comparing Quantities Notes

Introduction:

The chapter “Comparing Quantities” in Class 7 Maths introduces students to the concept of comparing two or more quantities. It explains the methods used to find the ratio and percentage of quantities, which are essential in comparing values in real-world scenarios, like sales, discounts, and growth. Understanding how to compare quantities allows students to interpret data effectively and solve everyday problems.

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Key Concepts Covered:

1. What is a Quantity?

• A quantity is a property or amount of something that can be measured.
• Examples include distance, weight, volume, time, etc.

2. What is Comparison?

• Comparison is the process of determining the relationship between two or more quantities to see how much greater or lesser one quantity is than the other.

3. Ratio:

• A ratio is a way of comparing two quantities by showing the relative sizes of two values.
• The ratio is written as $\frac{a}{b}$ba​ or as $a : b$a:b, where $a$a and $b$b are the quantities being compared.

Example:
If a class has 12 boys and 8 girls, the ratio of boys to girls is:$$\text{Ratio} = \frac{12}{8} = 3 : 2$$Ratio=812​=3:2

This means for every 3 boys, there are 2 girls.

4. Percentage:

• A percentage is a way of expressing a number as a fraction of 100. It is denoted by the symbol $\%$%.
• The formula to find the percentage is:

$$\text{Percentage} = \frac{\text{Part}}{\text{Whole}} \times 100$$Percentage=WholePart​×100

Example:
If there are 25 students in a class and 5 students are absent, the percentage of students present is:$$\text{Percentage present} = \frac{20}{25} \times 100 = 80\%$$Percentage present=2520​×100=80%

5. Finding the Percent of a Quantity:

• To find a certain percent of a given quantity, use the formula:

$$\text{Percent of a quantity} = \frac{\text{Percent}}{100} \times \text{Quantity}$$Percent of a quantity=100Percent​×Quantity

Example:
Find 20% of 50.$$\text{20\% of 50} = \frac{20}{100} \times 50 = 10$$20% of 50=10020​×50=10

6. Profit and Loss:

• Profit occurs when the selling price is greater than the cost price.
  • Formula for Profit: $$\text{Profit} = \text{Selling Price} – \text{Cost Price}$$Profit=Selling Price−Cost Price
• Loss occurs when the selling price is less than the cost price.
  • Formula for Loss: $$\text{Loss} = \text{Cost Price} – \text{Selling Price}$$Loss=Cost Price−Selling Price

Example:
If a shopkeeper buys a shirt for ₹300 and sells it for ₹350, the profit is:$$\text{Profit} = 350 – 300 = ₹50$$Profit=350−300=₹50

7. Discount:

• A discount is a reduction in the original price of an item.
• Formula to find the Discount: $$\text{Discount} = \frac{\text{Discount Percentage}}{100} \times \text{Marked Price}$$Discount=100Discount Percentage​×Marked Price

Example:
If an item’s marked price is ₹500 and there is a 10% discount, the discount is:$$\text{Discount} = \frac{10}{100} \times 500 = ₹50$$Discount=10010​×500=₹50

The Selling Price after discount is:$$\text{Selling Price} = \text{Marked Price} – \text{Discount} = 500 – 50 = ₹450$$Selling Price=Marked Price−Discount=500−50=₹450

8. Simple Interest:

• Simple Interest (SI) is the interest calculated on the principal amount for a certain period of time at a given rate.
• Formula for Simple Interest: $$\text{SI} = \frac{P \times R \times T}{100}$$SI=100P×R×T​ Where:
  • $P$P = Principal
  • $R$R = Rate of interest
  • $T$T = Time period (in years)

Example:
If ₹1000 is invested at a rate of 5% per annum for 3 years, the simple interest is:$$\text{SI} = \frac{1000 \times 5 \times 3}{100} = ₹150$$SI=1001000×5×3​=₹150

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Important Questions with Answers:

1. What is a ratio?
   • Answer: A ratio is a way to compare two quantities by dividing one by the other. It is written as $\frac{a}{b}$ba​ or $a : b$a:b.
2. How do you calculate percentage?
   • Answer: The formula for percentage is: $$\text{Percentage} = \frac{\text{Part}}{\text{Whole}} \times 100$$Percentage=WholePart​×100
3. What is the formula for finding the profit?
   • Answer: The formula for profit is: $$\text{Profit} = \text{Selling Price} – \text{Cost Price}$$Profit=Selling Price−Cost Price
4. How do you calculate the selling price after a discount?
   • Answer: The selling price after a discount is: $$\text{Selling Price} = \text{Marked Price} – \text{Discount}$$Selling Price=Marked Price−Discount
5. What is simple interest?
   • Answer: Simple interest is the interest calculated on the principal amount for a given time period at a specified rate. It is calculated using the formula: $$\text{SI} = \frac{P \times R \times T}{100}$$SI=100P×R×T​
6. How do you calculate the percentage of a quantity?
   • Answer: To find the percentage of a quantity, use the formula: $$\text{Percentage of quantity} = \frac{\text{Percent}}{100} \times \text{Quantity}$$Percentage of quantity=100Percent​×Quantity
7. What is the formula for calculating discount?
   • Answer: The formula for discount is: $$\text{Discount} = \frac{\text{Discount Percentage}}{100} \times \text{Marked Price}$$Discount=100Discount Percentage​×Marked Price