Reading and Evaluating Complex Expressions – Brackets and Terms

Theory: Brackets are used in arithmetic expressions to group terms and indicate that the operations within them should be performed first.
Example:
Question: What is the value of 10 + (5 × 2)?
Solution: Perform the operation in the bracket first: 5 × 2 = 10. Then, 10 + 10 = 20

Theory: To evaluate expressions with brackets, solve the operations inside the brackets first, then proceed according to the order of operations (BODMAS).
Example:
Question: Evaluate 6 + [4 × (3 + 2)].
Solution:
First, inside brackets: (3 + 2) = 5
Then, multiply: 4 × 5 = 20
Add: 6 + 20 = 26

Theory: Terms in an expression are parts separated by plus or minus signs. Each term can be a number, a variable, or a product of numbers and variables.
Example:
Question: Identify the terms in the expression: 5 + 3 – 2
Solution: Terms: 5, 3, and 2 (separated by + and – signs)

Theory: In an arithmetic expression, numbers being added or subtracted are each considered separate terms.
Example:
Question: In the expression 8 + 2 – 5, how many terms are there?
Solution: There are 3 terms: 8, 2, and 5

Theory: Changing the order of terms in addition doesn’t affect the result (commutative), but in subtraction, it does.
Example:
Question: Compare 12 – 4 and 4 – 12
Solution:
12 – 4 = 8,
4 – 12 = –8,
Different results show that order matters in subtraction.

Theory: Grouping terms simplifies evaluation and clarifies which operations to perform first, especially with multiple operations.
Example:
Question: Evaluate: (6 + 4) – (3 + 1)
Solution:
(6 + 4) = 10, (3 + 1) = 4, then 10 – 4 = 6

Theory: Brackets remove confusion in expressions with multiple operations by indicating the priority.
Example:
Question: Simplify: 5 + 2 × 3
Solution: Without brackets, multiplication first: 2 × 3 = 6 → 5 + 6 = 11
With brackets: (5 + 2) × 3 = 7 × 3 = 21

Theory: Brackets help represent practical problems involving grouped actions like repeated purchases or total costs.
Example:
Question: A shopkeeper buys 3 packets each containing 2 pens and 1 eraser. Cost of pen = ₹10, eraser = ₹5.
Solution: Expression: 3 × (2 × 10 + 5) = 3 × (20 + 5) = 3 × 25 = ₹75

Theory: When multiple operations are used, brackets show which operation to solve first for correct results.
Example:
Question: Evaluate: (2 + 3) × (4 – 1)
Solution: (2 + 3) = 5, (4 – 1) = 3 → 5 × 3 = 15

Theory: To remove brackets, apply distributive property if needed or directly simplify inner terms first.
Example:
Question: Simplify: 100 – (25 + 10)
Solution: 25 + 10 = 35, then 100 – 35 = 65