Problem 40 - Fundamentals of Mathematics

Question

For the following 4 problems, perform the indica ted operations $$ -104-(-216)-(-52) $$

Step-by-Step Solution

Answer

The result is 164.

Step 1: Identify the Expression

The expression we need to solve is \[ -104 - (-216) - (-52) \] .This involves subtracting negative numbers, which is equivalent to adding their positive counterparts.

Step 2: Convert Subtraction of Negatives to Addition

Recognize that subtracting a negative number is the same as adding its positive form. So, the expression becomes \[ -104 + 216 + 52 \] .

Step 3: Perform the Addition Step-by-Step

First, add the numbers in order:1. Add \[ -104 + 216 \] . - The difference between these numbers can be calculated by subtracting 104 from 216, which equals 112.2. Add this result to 52: - \[ 112 + 52 = 164 \] .

Step 4: Verify the Calculation

Re-check the addition of 112 and 52 by ensuring all steps follow basic arithmetic rules: - Adding 112 and 52 equals 164, confirming that our calculation is correct.

Key Concepts

Subtraction of Negative Numbers

Subtracting negative numbers can initially seem confusing, but there's a simple rule to follow. When you subtract a negative number, it's the same as adding the positive value of that number.

Consider the original expression:

• \[-104 - (-216) - (-52)\]

Each of those negative signs in front of the parentheses becomes a plus sign.

For example:

• Subtracting \(-216\) actually means adding \(216\).
• Subtracting \(-52\) actually means adding \(52\).

Once you convert the expression using this rule, what looks like a complicated subtraction problem becomes a straightforward addition.

Addition of Integers

Once we have turned the subtractions into additions, we're left with adding integers, which is much simpler. With the expression:

• \[-104 + 216 + 52\]

We add each number step by step.

When dealing with different signs, as in \(-104 + 216\), we subtract the smaller absolute value from the larger and keep the sign of the larger. Here,

• \(216\) is greater than \(104\), so the result is positive, and the difference is \(112\).

Next, we simply add \(52\) to \(112\) because they are both positive, making calculation straightforward.

Simply add them like this:

• \(112 + 52 = 164\).

Make sure each step follows the simple integer addition rules to arrive at the correct solution.

Basic Arithmetic Rules

Mastering arithmetic operations requires understanding a few basic rules. In this example, these rules help ensure accurate addition and subtraction:

• Order of Operations: Always perform operations from left to right when dealing with simple additions and subtractions.
• Same Sign Addition: Add like you normally would and keep the sign (i.e., positive + positive or negative + negative).
• Different Sign Addition: Subtract the smaller absolute value from the larger one and use the sign of the larger number.

For example, in the arithmetic problem provided, we utilized the switching of subtraction of negatives into addition.

Then we applied the rules of integer addition, ensuring every step was correctly followed, which highlighted the importance of careful calculation. By sticking to these basic rules, solving such types of arithmetic problems becomes easier and more intuitive.