Complete Exercise 1.3 Class 9 Math Solutions [New Book]
Welcome to the exercise 1.3 class 9 math solutions [New Book]. This guide provides step-by-step solutions to help you master problems involving radicals, algebra, arithmetic, and practical real-life scenarios. You’ll learn how to simplify expressions, calculate areas and lengths, and solve financial word problems like profit, loss, tax, and markup. Each solution connects math concepts to everyday situations, making learning easier and more meaningful.
Along with detailed solutions, this article includes downloadable PDF notes, important formulas, key definitions, real-life applications, and a video lecture to support your understanding. You’ll also find help with practical problems like converting temperatures between Celsius and Fahrenheit, shopping calculations, and other daily-use math skills.
Disclaimer
These solutions are provided for educational purposes only. The book is the property of PCTB, and this article aims to help students understand concepts more easily. For official curriculum updates and the original textbook, please visit the Punjab Curriculum and Textbook Board.
Table of Contents
Download/View PDF Notes
What Students Will Learn
- Solve algebraic equations involving consecutive integers and real-world scenarios.
- Work with radical expressions in geometric contexts (e.g., area and length calculations).
- Convert temperatures between Celsius and Fahrenheit scales.
- Calculate profit/loss percentages, tax amounts, and compound markup.
- Apply formulas to solve practical financial and scientific problems.
If you haven’t already, you can also check the complete solutions for Exercise 1.1 Class 9 Math and Exercise 1.2 Class 9 Math to strengthen your basics. Additionally, the Class 9 Mathematics Textbook PDF is available for download to help you follow along with all exercises.
Common Mistakes to Avoid
1.Consecutive Integers: Confusing consecutive integers (e.g., 5, 6) with consecutive even or odd integers (e.g., 4, 6).
2.Radical Simplification: Mishandling operations like
(a + b)(c + d)
when working with surds.
3.Temperature Conversion: Using the formula
F = (9/5) × C + 32 incorrectly by adding 32 before multiplying.
4.Profit Percentage: Dividing profit by selling price instead of cost price.
5.Tax Calculation: Applying the tax rate to total income instead of taxable income.
6.Compound Markup: Forgetting to include the principal amount when calculating total amount.
Solved Problems
Problem 1:
Question: Find two numbers whose sum is 68 and difference is 22.
Solution:
Let the numbers be x and y.
x + y = 68 (1)
x − y = 22 (2)
Add equations (1) and (2):
2x = 90 ⇒ x = 45
Substitute into (1):
45 + y = 68 ⇒ y = 23
Answer: 45 and 23
Problem 2:
Question: Convert 48°C to Fahrenheit.
Solution:
Use the formula:
F = (9/5) × 48 + 32 = 86.4 + 32 = 118.4°F
Answer: 118.4°F
Key Definitions
Consecutive Integers: Numbers that follow each other without gaps (e.g., 13, 14, 15).
Profit Percentage: The profit percentage is the profit expressed as a percentage of the cost price. It is calculated using the formula:
Profit % = (Profit / Cost Price) × 100 %
Taxable Income: The income amount after removing the exempted amount.
Compound Markup: Interest calculated on the initial principal and on previously added interest.
Important Formulas
Temperature Conversion:
F = (9/5) × C + 32
Profit Percentage:
Profit % = ((SP − CP) / CP) × 100
Tax Calculation:
Tax = Taxable Income × (Rate / 100)
Compound Markup (Annual):
A = P × (1 + r)ᵗ
where
A = Final Amount,
P = Principal,
r = Rate (as a decimal),
t = Time in years
Real-Life Uses
- Financial Management: Calculating business profit/loss.
- Weather Forecasting: Converting temperatures for global reports.
- Engineering & Architecture: Using surds in construction design and calculations.
- Taxation: Computing income tax on salaried earnings.
- Banking: Calculating compound interest and markup on savings or loans.
Short Answer Questions
Q: What are consecutive integers?
A: Numbers that follow one after another without any gap, e.g., 7, 8, 9.
Q: Simplify 3 × √12
A: 3 × √12 = 3 × 2√3 = 6√3
Q: What is the Fahrenheit equivalent of 0°C?
A: F = (9/5) × 0 + 32 = 32°F
Q: Find the profit percentage if CP = 200 and SP = 250
A: Profit =SP – CP
So Profit= 50, Profit % = (Profit / CP) × 100
Profit % = (50 / 200) × 100 = 25%
Q: Simplify (2 + 3√2)(5 − 2√2) and express in form a + b√2
A:
\((2 + 3\sqrt{2})(5 – 2\sqrt{2}) = 10 + 15\sqrt{2} – 4\sqrt{2} – 12\)
\( -2 + 11\sqrt{2}\)
Answer: \(-2 + 11\sqrt{2}\)
Q: What is the compound markup on Rs. 1000 at 10% for 1 year?
A:
A = 1000 × (1 + 0.10)¹ = 1100
Compound markup = 1100 − 1000 = Rs. 100.