Solving the Mathematical Expression

We need to solve the given mathematical expression: \(-1/4 \times \{-45 – (-96) \div (-32)\}\).

To solve such expressions, we must follow the standard order of operations, often remembered by acronyms like BODMAS or PEMDAS.

Understanding the Order of Operations (BODMAS/PEMDAS)

The order dictates the sequence in which operations should be performed:

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

In the given expression, we have brackets, subtraction, division, and multiplication. We will start with the operations inside the innermost brackets.

Step-by-Step Solution Process

Let's break down the solution into simple steps:

The expression is: \(-1/4 \times \{-45 – (-96) \div (-32)\}\)

Step 1: Solve the operations inside the curly brackets \(\{\}\).

Inside the brackets, we have \(-45 – (-96) \div (-32)\). According to BODMAS, division comes before subtraction. So, we first calculate \((-96) \div (-32)\).

Remember that when dividing two negative numbers, the result is positive.

Calculate \((-96) \div (-32)\):

\(\frac{-96}{-32} = \frac{96}{32} = 3\)

Now, substitute this result back into the expression inside the curly brackets:

\(\{-45 – 3\}\)

Next, perform the subtraction inside the brackets:

\(-45 – 3 = -48\)

So, the expression inside the curly brackets simplifies to \(-48\).

Step 2: Perform the multiplication outside the brackets.

The original expression now becomes:

\(-1/4 \times -48\)

We are multiplying a negative fraction \(-1/4\) by a negative integer \(-48\). When multiplying two negative numbers, the result is positive.

Calculate \(-1/4 \times -48\):

\(= \frac{-1}{4} \times -48\)

\(= \frac{1}{4} \times 48\)

\(= \frac{48}{4}\)

\(= 12\)

The final result of the expression is \(12\).

Summary of Calculation

Here is the complete calculation:

\(-1/4 \times \{-45 – (-96) \div (-32)\}\)

\(= -1/4 \times \{-45 – (3)\}\)
(Performing division inside brackets)

\(= -1/4 \times \{-48\}\)
(Performing subtraction inside brackets)

\(= -1/4 \times -48\)

\(= 12\)
(Performing multiplication)

The value of the expression is \(12\).

Revision Table: Integer Arithmetic Rules

Additional Information: Mastering BODMAS

Consistently applying the BODMAS or PEMDAS rule is key to accurately solving mathematical expressions, especially those involving different operations and brackets.

Always work from the innermost brackets outwards.

Perform division and multiplication from left to right as they appear in the expression.

Perform addition and subtraction from left to right as they appear.

Pay close attention to the signs of the numbers, particularly when dealing with negative numbers.