Solving Mathematical Expressions with BODMAS

To solve the given mathematical expression, we need to follow the order of operations. This rule is commonly known as BODMAS or PEMDAS. It dictates the sequence in which operations should be performed:

• Brackets (Parentheses)
• Orders (Exponents, Square Roots, etc.) or Of
• Division and Multiplication (from left to right)
• Addition and Subtraction (from left to right)

The given expression is:

\(78 + [-4 + (-3) \text{ of } \{27 + (-18 + (-2))\}]\)

Step-by-Step Calculation using Order of Operations

Let's solve the expression step-by-step, starting with the innermost brackets and following the BODMAS rule.

Step 1: Innermost Brackets

First, solve the expression inside the innermost parentheses: \((-18 + (-2))\).

\(-18 + (-2) = -18 - 2 = -20\)

The expression now becomes:

\(78 + [-4 + (-3) \text{ of } \{27 + (-20)\}] \)

Step 2: Next Level Brackets

Next, solve the expression inside the curly braces: \(\{27 + (-20)\}\).

\(27 + (-20) = 27 - 20 = 7\)

The expression now becomes:

\(78 + [-4 + (-3) \text{ of } 7]\)

Step 3: Operation "of"

The term "\((-3) \text{ of } 7\)" means multiplication. So, calculate \((-3) \times 7\).

\(-3 \times 7 = -21\)

The expression now becomes:

\(78 + [-4 + (-21)]\)

Step 4: Remaining Brackets

Solve the expression inside the square brackets: \([-4 + (-21)]\).

\(-4 + (-21) = -4 - 21 = -25\)

The expression now becomes:

\(78 + (-25)\)

Step 5: Addition

Finally, perform the addition:

\(78 + (-25) = 78 - 25\)

\(78 - 25 = 53\)

The value of the expression is 53.

Final Answer Summary

Let's list the steps and results:

The final result of the expression \(78 + [-4 + (-3) \text{ of } \{27 + (-18 + (-2))\}]\) is 53.

Revision Table: Key Concepts for Solving Expressions

Here’s a quick table to review the symbols and operations encountered in this problem:

Additional Information on Order of Operations

Understanding the correct order of operations is fundamental in mathematics. It ensures that everyone gets the same answer when evaluating an expression. While BODMAS is common in some regions, PEMDAS (Parentheses, Exponents, Multiplication and Division, Addition and Subtraction) is used elsewhere. Both rules effectively convey the same hierarchy of operations:

• Brackets/Parentheses first.
• Exponents/Orders/Of next.
• Multiplication and Division have equal priority and are done from left to right.
• Addition and Subtraction have equal priority and are done from left to right.

Mistakes often happen when the left-to-right rule for multiplication/division and addition/subtraction is ignored. For example, in \(10 - 5 + 2\), you perform \(10 - 5 = 5\) first, then \(5 + 2 = 7\), not \(5 + 2 = 7\) first then \(10 - 7 = 3\). Similarly, in \(10 / 2 \times 5\), you perform \(10 / 2 = 5\) first, then \(5 \times 5 = 25\), not \(2 \times 5 = 10\) first then \(10 / 10 = 1\).

Practicing problems with nested brackets and different operations is the best way to master the order of operations.