Arithmetic | Class 7 Mathematics Notes

2.2 Reading and Evaluating Complex Expressions

Complex arithmetic expressions may contain multiple operations and can be ambiguous without clear rules for evaluation. Just as punctuation clarifies meaning in language, brackets in mathematics specify the order of operations. For example, the expression 30 + 5 × 4 can be evaluated differently depending on whether addition or multiplication is done first. According to the order of operations, multiplication is done before addition, so 5 × 4 is evaluated first, then added to 30, giving 50. Using brackets, this is written as 30 + (5 × 4). Expressions can be broken into terms, which are parts separated by '+' signs. Subtraction is treated as addition of negative numbers to identify terms clearly. For example, 83 - 14 is written as 83 + (-14), making the terms 83 and -14. Understanding terms helps in evaluating expressions correctly. The commutative property of addition states that changing the order of terms does not change the sum, and the associative property states that grouping terms differently does not change the sum. These properties hold even when terms are negative. When expressions include multiplication and division, these operations are evaluated first within each term before addition. This section also introduces the distributive property, which relates multiplication over addition or subtraction inside brackets.

📊 Diagram: Figures showing different interpretations of sentences with and without commas; Figures illustrating the drone's movement and arithmetic terms; Figure showing token model of integers for addition.

🧪 Activity: Identify terms in expressions; rewrite subtraction as addition of negatives; verify commutative and associative properties with positive and negative terms.

🔗 Connection: This section prepares students to handle complex expressions with multiple operations, leading to the next section on properties of operations and removing brackets.