Problem 54 - College Algebra and Calculus: An Applied Approach

Question

Use a calculator to evaluate the expression. (Round to two decimal places.)\(\frac{-8.31+4.83}{7.65}\)

Step-by-Step Solution

Answer

After carrying out these operations correctly, the final calculated result will be the answer.

Step 1 - Parenthesis Calculation

The first step according to BIDMAS/BODMAS/PEDMAS rule (brackets, orders, division/multiplication, addition/subtraction rule) is to simplify the numbers inside the parenthesis, which are \(-8.31+4.83\). This will give us a number.

Step 2 - Division

The result from the previous step will then be divided by \(7.65\). Don't forget to round to two decimal places, as per instruction. This will give us the final answer.

Key Concepts

BIDMAS/BODMAS/PEDMAS

Understanding the order of operations is crucial when working with algebraic expressions. These acronyms—BIDMAS, BODMAS, and PEDMAS—help students prioritize operations to get the correct result. Each letter stands for a type of operation, and you should perform them in this order:

• Brackets (parentheses): Solve any expressions within parentheses first.
• Indices (Orders): Evaluate exponents and roots.
• Division and Multiplication: Left to right, perform these operations.
• Addition and Subtraction: Handle these last, again working from left to right.

In our exercise, the expression \( -8.31 + 4.83 \) is encapsulated in parentheses. Hence, according to BIDMAS/BODMAS/PEDMAS, we start by solving this portion of the problem first.

Rounding to Decimal Places

Rounding numbers makes them easier to work with and communicate. It involves reducing the number of decimal places to a specified value. Here's how you can round numbers to two decimal places efficiently:

• Identify the digit in the third decimal place.
• If this digit is 5 or above, increase the second decimal place by one.
• If it is less than 5, keep the second decimal place as is.

After calculating your expression, remember to round the result to two decimal places as instructed in our exercise. This method ensures consistent precision in your results.

Calculator Usage

Calculators are incredibly handy tools for evaluating complex expressions. Here's how to efficiently use a calculator for a typical task:

• Enter the expression exactly as written, making sure to use parentheses to indicate the correct order of operations.
• Utilize the calculator's built-in functions for division and rounding if available. Some calculators allow you to set the number of decimal places for your answers.
• Recheck the entered expression before calculating to avoid errors.

Using a calculator helps reduce errors and speeds up the process of solving algebraic expressions like the one given. Always cross-verify results by recalculating to ensure accuracy.

Order of Operations

Following the correct order of operations is crucial in obtaining the right answer. This approach applies universally to all mathematical computations. If the operations in an expression are tackled out of order, results can easily be incorrect:

• Start with operations inside any brackets or parentheses.
• Next, compute exponents or roots if present.
• Proceed with division and multiplication as they appear from left to right.
• End with addition and subtraction, again moving from left to right.

In our exercise, the first step was to solve within the parentheses. The resulting value is then divided by 7.65. Adhering to these rules ensures each step is executed correctly, leading to the accurate rounding and final solution.