Arithmetic | Class 7 Mathematics Notes

Terms in Expressions and Properties of Addition

An expression can be viewed as a sum of terms, where terms are separated by '+' signs. Subtraction is treated as addition of negative numbers to identify terms clearly. For example, 13 - 2 + 6 is written as 13 + (-2) + 6, with terms 13, -2, and 6. The commutative property of addition states that swapping terms does not change the sum, even when terms are negative. For example, 6 + (-4) = (-4) + 6. The associative property states that grouping terms differently does not change the sum, e.g., (−7 + 10) + (−11) = −7 + (10 + (−11)). These properties help simplify calculations and reasoning about expressions. When expressions include multiplication and division, these operations are evaluated first within each term before addition. For example, 30 + 5 × 4 is evaluated as 30 + (5 × 4) = 50. Understanding terms and these properties is essential for evaluating expressions correctly and efficiently.

📊 Diagram: Figures illustrating terms in expressions and token model for integers; Figures showing grouping and swapping of terms in addition.

🧪 Activity: Check if swapping and grouping terms changes the sum; explain using token model.

🔗 Connection: These properties set the foundation for understanding the removal of brackets and distributive property in subsequent sections.