Symbols of inclusion
Symbols of inclusion such as parentheses (), brackets [], and braces {} indicate which parts of a mathematical expression to evaluate first. When multiple symbols are nested, simplify from the innermost set outward. For example, 50 - [20 + (10 - 5)] becomes 50 - [20 + 5] = 50 - 25 = 25. This skill is covered in Chapter 7 of Saxon Math Course 2 for 7th grade math and is essential for correctly evaluating complex expressions, following order of operations, and preparing for algebraic simplification.
Key Concepts
Property When an expression contains multiple symbols of inclusion, such as parentheses (), brackets [], or braces {}, we simplify within the innermost symbols first.
Examples $50 [20 + (10 5)] = 50 [20 + 5] = 50 25 = 25$ $100 3[2(6 2)] = 100 3[2(4)] = 100 3[8] = 100 24 = 76$ $30 [40 (10 2)] = 30 [40 8] = 30 32 = 2$.
Explanation Think of these symbols as nested secret boxes. You must always unlock and solve the calculation in the innermost box first before moving outward. Tackling problems from the inside out is the key to getting the right answer without getting lost in all the numbers and operations.
Common Questions
What are symbols of inclusion in math?
Symbols of inclusion are grouping symbols like parentheses (), brackets [], and braces {} that tell you which part of an expression to evaluate first. They override the standard order of operations for the enclosed portion.
How do you simplify expressions with nested symbols of inclusion?
Start with the innermost grouping symbol and work outward. For 50 - [20 + (10 - 5)], first simplify (10 - 5) = 5, then [20 + 5] = 25, then 50 - 25 = 25.
What is the order for parentheses, brackets, and braces?
Parentheses () are typically innermost, brackets [] go around them, and braces {} go on the outside. However, the important rule is always to simplify the innermost grouping first, regardless of which symbol is used.
How do you handle a number multiplied in front of brackets?
Multiply that number by the result inside the brackets. For 100 - 3[2(6 - 2)], first simplify inside: (6 - 2) = 4, then 2(4) = 8, then 3[8] = 24, so 100 - 24 = 76.
What happens when the result inside brackets is negative?
Proceed normally with the negative value. For 30 - [40 - (10 - 2)] = 30 - [40 - 8] = 30 - 32 = -2. A negative result is perfectly valid when subtracting a larger number.
When do students learn about symbols of inclusion?
Symbols of inclusion are taught in 7th grade math as part of order of operations. Saxon Math Course 2 covers them in Chapters 6 and 7, where students practice with increasingly complex nested expressions.