What is Comparing Quantities Class 7: A Clear NCERT Guide

Understanding Comparing Quantities in Class 7 Mathematics

In Class 7 NCERT Mathematics, "Comparing Quantities" means examining two or more quantities to find their relation or difference. This chapter helps you learn how to express one quantity in terms of another using ratios and percentages.

Key points:

• Quantities must be of the same kind to compare directly.
• Ratios show how many times one quantity is of another.
• Percentages express a quantity as a part of 100.

For example, if you have 40 apples and 50 oranges, comparing these quantities means finding the ratio or percentage difference between them.

What is Ratio? Basics and Examples

A ratio compares two quantities of the same kind by division.

Formula:

$$\text{Ratio} = \frac{\text{Quantity 1}}{\text{Quantity 2}}$$

Ratios can be written in three ways: $a:b$, $\frac{a}{b}$, or "a to b".

Example:

If a classroom has 20 boys and 15 girls, the ratio of boys to girls is:

$$20:15 = \frac{20}{15} = \frac{4}{3}$$

So, the ratio is 4:3.

Ratios help compare quantities directly and are the foundation for understanding percentages and other comparison methods.

What is Percentage? Definition and Calculation

Percentage means "per hundred" and is a way to express a number as a fraction of 100.

Formula:

$$\text{Percentage} = \left( \frac{\text{Part}}{\text{Whole}} \right) \times 100$$

Example:

If you scored 45 marks out of 50 in a test, your percentage is:

$$\left( \frac{45}{50} \right) \times 100 = 90\%$$

Percentages are widely used in daily life, such as calculating discounts, interest rates, and exam scores.

Comparing Quantities Using Percentage Increase and Decrease

When quantities change, we often want to find how much they have increased or decreased in percentage terms.

Percentage Increase Formula:

$$\text{Percentage Increase} = \left( \frac{\text{New Quantity} - \text{Original Quantity}}{\text{Original Quantity}} \right) \times 100$$

Percentage Decrease Formula:

$$\text{Percentage Decrease} = \left( \frac{\text{Original Quantity} - \text{New Quantity}}{\text{Original Quantity}} \right) \times 100$$

Example:

A shirt price rises from ₹500 to ₹600.

Percentage increase = $$\left( \frac{600 - 500}{500} \right) \times 100 = 20\%$$

This means the price increased by 20%.

Profit and Loss: Applying Comparing Quantities

Profit and loss are practical examples of comparing quantities in business.

• Profit occurs when the selling price (SP) is more than the cost price (CP).
• Loss occurs when SP is less than CP.

Formulas:

$$\text{Profit} = \text{SP} - \text{CP}$$

$$\text{Loss} = \text{CP} - \text{SP}$$

Profit Percentage:

$$\left( \frac{\text{Profit}}{\text{CP}} \right) \times 100$$

Loss Percentage:

$$\left( \frac{\text{Loss}}{\text{CP}} \right) \times 100$$

Example:

If a toy costs ₹200 and sells for ₹250:

Profit = ₹250 - ₹200 = ₹50

Profit % = $$\left( \frac{50}{200} \right) \times 100 = 25\%$$

This means a 25% profit was made.

Summary Table: Ratio, Percentage, and Profit/Loss

Here is a quick comparison table to summarize key formulas: