Problem 15 - Basic Engineering Mathematics

Question

Find the value of \(6+4 \div(5-3)\)

Step-by-Step Solution

Answer

The value is 8.

Step 1: Calculate the Parentheses

First, solve the expression inside the parentheses \((5-3)\). This gives us the result 2.

Step 2: Perform Division

Next, divide 4 by the result from the parentheses. So we calculate \(4 \div 2\), which equals 2.

Step 3: Addition

Finally, add the result from the division to 6. So the calculation is \(6 + 2\), which gives us 8.

Key Concepts

Parentheses Calculation

Parentheses in math are like a spotlight that tells you which part of a problem to solve first. They are used to group numbers and operations to clarify which calculations should be carried out first in a given expression. In any mathematical expression, operations inside the parentheses need to be solved before anything else to ensure you get the correct outcome. This is crucial because changing the order in which you perform operations could lead to a vastly different result.

Let's look at the example problem:

• The expression inside the parentheses is \(5 - 3\). Calculate this first.
• Here, subtraction is straightforward and yields 2.

Getting the right order here sets the stage for accurately solving the rest of the problem.

Division and Multiplication

After dealing with parentheses, the next step is to perform division and multiplication. These operations have the same precedence and must be handled from left to right as they appear in the expression. Ignoring this order may lead to mistakes and incorrect results.

Continuing with the example, once we obtained the result of 2 from the parentheses, the expression becomes \(6 + 4 \div 2\).

• Division comes before addition in our order of operations, so we perform \(4 \div 2\) first.
• This calculation results in a quotient of 2.

This step narrows down the possible errors we might face if tackled out of order.

Addition and Subtraction

Once you've finished with multiplication and division, it's time for the last operations: addition and subtraction. These operations, just like division and multiplication, possess the same level of precedence and should be executed from left to right.

In the example problem, after calculating the division, you're left with \(6 + 2\).

• The final step is to simply add 6 and 2.
• This addition operation results in 8, which is our final answer.

Understanding this last stage ensures that you've followed the correct sequence and reached the accurate final result. Remember, correctly applying the order of operations is key to solving math problems accurately.