Finding the Value of Mathematical Expressions with Nested Brackets

We are asked to find the value of the given mathematical expression: $27 – [38 – {46 – (15 – 13 – 2)}]$. This expression involves several levels of grouping symbols: parentheses $(\,)$, curly braces $\{\,\}$, and square brackets $[\,]$. To solve this correctly, we must follow the order of operations.

Understanding the Order of Operations (BODMAS/PEMDAS)

The order of operations is a rule that tells us the sequence in which we should perform mathematical operations in an expression to ensure a unique result. Common acronyms for this order are BODMAS or PEMDAS.

• Brackets (or Parentheses)
• Orders (or Exponents)
• Division and Multiplication (from left to right)
• Addition and Subtraction (from left to right)

In expressions with nested grouping symbols, we always start with the innermost set of symbols and work our way outwards.

Step-by-Step Solution to Find the Value

Let's solve the expression $27 – [38 – {46 – (15 – 13 – 2)}]$ by following the order of operations:

Step 1: Solve the innermost parentheses $(\,)$

The innermost part is $(15 – 13 – 2)$.

$15 – 13 = 2$

Then, $2 – 2 = 0$

So, $(15 – 13 – 2) = 0$.

The expression now becomes: $27 – [38 – {46 – 0}]$

Step 2: Solve the curly braces $\{\,\}$

Next, we solve the part inside the curly braces: $\{46 – 0\}$.

$46 – 0 = 46$

The expression now becomes: $27 – [38 – 46]$

Step 3: Solve the square brackets $[\,]$

Now, we solve the part inside the square brackets: $[38 – 46]$.

$38 – 46 = -8$

The expression now becomes: $27 – (-8)$

Step 4: Perform the final subtraction

Finally, we perform the remaining operation: $27 – (-8)$.

Subtracting a negative number is the same as adding the positive number.

$27 – (-8) = 27 + 8 = 35$

So, the value of the expression $27 – [38 – {46 – (15 – 13 – 2)}]$ is 35.

Summary of Calculation Steps

Conclusion on Finding the Expression Value

By carefully applying the order of operations, starting from the innermost brackets and moving outwards, we determined the value of the complex mathematical expression. The value is 35.

Revision Table: Key Concepts

Additional Information: Mastering Arithmetic Calculations

Mastering arithmetic calculations, especially with grouping symbols, is fundamental for higher mathematics. Practice with different types of expressions, including those with exponents, multiplication, and division, to build confidence.

• Always identify the grouping symbols first.
• Work from inside out for nested symbols.
• Perform multiplication and division before addition and subtraction if they are at the same level.
• Perform operations at the same level (like addition and subtraction) from left to right.
• Be careful with negative signs, especially when distributing or subtracting.

Regular practice with mathematical expressions helps in developing strong problem-solving skills.