Problem 19 - Basic Engineering Mathematics

Question

Find the value of $$ 23.4-17.83-57.6+32.68 $$

Step-by-Step Solution

Answer

The value of the expression is -19.35.

Step 1: Rearrange the Expression

Reorder the expression for clarity in calculation: \[ 23.4 - 17.83 - 57.6 + 32.68 \]can be rearranged to: \[ (23.4 - 17.83) + (32.68 - 57.6) \]. This rearrangement helps in breaking down the expression into simpler parts.

Step 2: Solve the First Part

Calculate the first part of the expression: \[ 23.4 - 17.83 \].Subtract 17.83 from 23.4. This yields:\[ 23.4 - 17.83 = 5.57 \].

Step 3: Solve the Second Part

Calculate the second part of the expression: \[ 32.68 - 57.6 \].Subtract 57.6 from 32.68. This results in:\[ 32.68 - 57.6 = -24.92 \].

Step 4: Combine the Results

Add the results from the previous steps:\[ 5.57 + (-24.92) \].Perform the addition:\[ 5.57 - 24.92 = -19.35 \].

Step 5: Write the Final Answer

The value of the given expression is:\[ -19.35 \].

Key Concepts

Order of Operations

When solving math problems, especially those that include multiple operations like addition and subtraction, it's important to follow a specific set of rules known as the order of operations. This ensures that every mathematician will get the same answer. When we look at our exercise, you notice how we rearranged the numbers into parts. This is where the order of operations becomes super helpful. Whenever you have a problem like \[23.4 - 17.83 - 57.6 + 32.68\] you should always work from left to right, focusing on the operations inside parenthesis first if there are any.

• First, tackle what's in parentheses.
• Next, handle multiplications and divisions.
• Finally, do additions and subtractions.

In this problem, we only have subtraction and addition. Grouping subtractions can make solving easier and prevent mistakes.

Subtraction

Subtraction can seem tricky at times, but it’s essentially finding out how much something reduces by when something is taken away. For example, in our exercise, we need to solve \[23.4 - 17.83\]. This means starting from 23.4 and removing or subtracting 17.83 from it. This process gives us an answer of 5.57. Subtraction involves understanding two main things:

• The minuend is the number from which you subtract, here it’s 23.4.
• The subtrahend is the number you’re subtracting, which is 17.83 in this case.

Once mastered, subtraction becomes an enjoyable task as you get to reduce numbers step by step.

Negative Numbers

Working with negative numbers can feel intimidating, but it's all about understanding what these numbers represent. In our exercise, we encountered \[32.68 - 57.6\], which resulted in \[-24.92\]. Negative numbers are numbers less than zero and often signify a loss or deficit. When you subtract a larger number from a smaller number, the result is negative.

• Think of it as owing money. If you have \(32.68 and owe \)57.6, you are short by $24.92.
• To add a negative number, like in step 4 \[5.57 + (-24.92)\], you think of it as continuing the subtraction, turning it into \[5.57 - 24.92\].

Practicing with negative numbers can enhance your ability to solve real-world problems involving gains and losses.