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Chapter Analysis
Intermediate19 pages • EnglishQuick Summary
The chapter 'Operations with Integers' in Class 7 Math explores the properties and operations of integers, covering addition, subtraction, multiplication, and division. It builds on concepts of additive inverses and introduces the commutative and associative properties of integer multiplication. The chapter also discusses multiplication and division of positive and negative integers through both numerical and graphical models.
Key Topics
- •Addition and Subtraction of Integers
- •Multiplication of Integers
- •Division of Integers
- •Additive Inverses
- •Properties of Integer Operations
- •Commutative Property
- •Associative Property
- •Distributive Property
Learning Objectives
- ✓Understand and perform addition and subtraction operations with integers.
- ✓Learn multiplication and division rules for positive and negative integers.
- ✓Explore properties of integer operations including commutative and associative.
- ✓Apply the distributive property to simplify expressions using integers.
- ✓Use graphical models like the number line for visualizing integer operations.
- ✓Solve practical problems using integer arithmetic.
Questions in Chapter
Find the values of the following expressions: (a) (-5) × (18 + (–3)) (b) (–7) × 4 × (–1) (c) (–2) × (–1) × (–5) × (–3)
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Find the values of the following expressions: (a) (–27) ÷ 9 (b) 84 ÷ (–4) (c) (–56) ÷ (–2)
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Find the integer whose product with (–1) is: (a) 27 (b) –31 (c) –1 (d) 1 (e) 0
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If 47 – 56 + 14 – 8 + 2 – 8 + 5 = –4, then find the value of –47 + 56 – 14 + 8 – 2 + 8 – 5 without calculating the full expression.
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Describe the patterns you observe when trying this with different starting numbers: (–21), (–6), and so on.
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Additional Practice Questions
Calculate the expression (-8) × 3 + (-4).
easyAnswer: (-8) × 3 + (-4) = -24 - 4 = -28.
If the temperature is currently at 12°C and drops by 6°C each hour, what will be the temperature after 5 hours?
mediumAnswer: The temperature after 5 hours will be 12 - (6 × 5) = 12 - 30 = -18°C.
Jane has 15 correct answers on a test with a scoring system that gives +3 points for each correct and -2 points for each wrong answer. Her total score is 33 points. How many questions did she get wrong?
mediumAnswer: Let x be the number of wrong answers. The equation is 3 × 15 - 2 × x = 33. Solving this, 45 - 2x = 33 leads to x = 6.
Explain the distributive property with integers using an example.
hardAnswer: The distributive property is a(b + c) = ab + ac. For example, 2 × (3 + 5) = 2 × 3 + 2 × 5 gives 2 × 8 = 6 + 10 = 16.
Identify the pattern: Start with any integer, if it is even, divide by 2; if odd, multiply by 3 and add 1. What happens if you start with 15?
hardAnswer: For 15, since it's odd, compute 3 × 15 + 1 = 46; then 46 is even, so divide by 2 to get 23, and continue from there.