Operations | Class 7 Mathematics Notes

2.2 Multiplication of Integers

This section explores multiplication of integers using the token model, extending the addition and subtraction concepts from earlier. Starting with positive integers, multiplication is interpreted as repeated addition of positive tokens. For example, 4 × 2 means placing 2 positive tokens into an empty bag 4 times, resulting in 8 positive tokens. The section then extends this to multiplication involving negative integers. For 4 × (-2), 2 negative tokens are placed 4 times, resulting in 8 negative tokens, i.e., -8. When the multiplier is negative, such as (-4) × 2, it is interpreted as removing 2 positive tokens 4 times from the bag. Since the bag starts empty, zero pairs are added to allow removal, leaving 8 negative tokens, i.e., -8. For (-4) × (-2), removing 2 negative tokens 4 times from an empty bag requires adding zero pairs first, resulting in 8 positive tokens, i.e., +8. These token manipulations provide a concrete understanding of multiplication rules involving signs. The section also examines patterns in integer multiplication by constructing sequences and observing how the product changes with increments or decrements in multiplier and multiplicand, confirming that multiplication rules for positive integers extend naturally to negative integers. The commutative property of multiplication is verified for integers, showing that swapping multiplier and multiplicand does not change the product. Brahmagupta’s ancient rules for multiplication and division of positive and negative numbers are introduced, highlighting historical significance. Real-world examples such as exam scoring and elevator movement illustrate the application of integer multiplication and addition in practical contexts. The section concludes with a magic grid activity involving integers, encouraging exploration of integer multiplication properties.

📊 Diagram: Diagrams show bags with green (positive) and red (negative) tokens being added or removed to model multiplication of integers with different sign combinations. Number line patterns illustrate multiplication sequences with positive and negative multiplicands and multipliers.

🧪 Activity: Magic Grid of Integers: Students follow steps to strike out numbers in a grid and multiply circled numbers, exploring properties of integer multiplication.

🔗 Connection: This section prepares students for understanding division of integers and properties of integer operations, which are covered in subsequent sections.