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Chapter Analysis
Intermediate20 pages • EnglishQuick Summary
This chapter covers arithmetic expressions, focusing on understanding and manipulating them using the properties of arithmetic operations like addition, subtraction, multiplication, and division. The chapter emphasizes using brackets to clarify the order of operations and introduces concepts like evaluating complex expressions and the associative, commutative, and distributive properties. Through examples and exercises, students learn to interpret, compare, and evaluate expressions confidently.
Key Topics
- •Arithmetic expressions
- •Order of operations
- •Use of brackets
- •Commutative property
- •Associative property
- •Distributive property
- •Evaluating complex expressions
- •Comparing expressions
Learning Objectives
- ✓Understand and evaluate arithmetic expressions
- ✓Use brackets to correctly interpret mathematical expressions
- ✓Apply the commutative, associative, and distributive properties
- ✓Solve practical problems using expressions
- ✓Compare different arithmetic expressions without computation
- ✓Develop reasoning skills in interpreting expressions
Questions in Chapter
Find different ways of evaluating the following expressions: (a) 1 – 2 + 3 – 4 + 5 – 6 + 7 – 8 + 9 – 10 (b) 1 – 1 + 1 – 1 + 1 – 1 + 1 – 1 + 1 – 1
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Compare the following pairs of expressions using '<', '>' or '=' or by reasoning.
Answer: This requires understanding the expressions without computation, relying on properties like the commutative and associative properties.
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Identify which of the following expressions are equal to the given expression without computation.
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Additional Practice Questions
Create an expression using four 4's to get the value of 20.
mediumAnswer: An example expression could be (4/4) + 4 + 4 + 4 = 20.
If a metro ticket costs ₹40 for adults and ₹20 for children, find the total cost for two adults and three children.
easyAnswer: The total cost is (2 * 40) + (3 * 20) = 80 + 60 = ₹140.
Using the numbers 3, 6, and 9, form an expression that equals 18 using addition and multiplication.
easyAnswer: One possible expression is 3 * 6 = 18.
A snail climbs 3 cm during the day and slips 2 cm at night on a 12 cm pole. How many days does it take to reach the top?
mediumAnswer: The snail climbs 1 cm per day net. It will take 12 days to reach the top.
Explain why 5 * (6 + 4) and (5 * 6) + (5 * 4) are equal using the distributive property.
mediumAnswer: According to the distributive property, multiplication distributed over addition yields the same result: 5*(6+4) = 5*6 + 5*4 = 50.