Problem 27 - Algebra 1

Question

Find the difference. $$ -6.6-(-16.1) $$

Step-by-Step Solution

Answer

The difference of -6.6 and -16.1 is 9.5.

Step 1: Understanding Negative Number Rules

Recall one of the rules of negative numbers: subtracting a negative number is the same as adding a positive number. So, the equation can be rewritten using this rule from \(-6.6 - (-16.1)\) to \(-6.6 + 16.1\).

Step 2: Perform the Addition

Now, simply add these two numbers. So, when you add -6.6 to 16.1, you get 9.5.

Key Concepts

Negative Number Rules

In arithmetic, negative numbers are used to represent values that are less than zero, such as debts or temperatures below freezing. The rules for negative numbers might initially seem counterintuitive, but they are vital for understanding how arithmetic operations work with all numbers.

Here's a fundamental rule that often confuses students: when you subtract a negative number, it is equivalent to adding a positive number. This is because subtraction is the inverse operation of addition. For example, if you have \( -6.6 - (-16.1) \), this is the same as saying \( -6.6 + 16.1 \). This use of double negatives flips the operation:

• \( - (-x) = +x \)
• \( -x - (-y) = -x + y \)

Remember, two negatives make a positive, which is a core foundation in arithmetic operations involving negative numbers.

Arithmetic Operations

Arithmetic operations include addition, subtraction, multiplication, and division. These are the building blocks of most mathematical concepts. Each operation follows specific rules and properties, which are important to comprehend for manipulating numbers effectively.

When dealing with addition or subtraction of negative numbers, the signs of the numbers guide you on the operation to perform. Positive and negative signs indicate direction on a number line—positives move to the right and negatives to the left. So, adding a negative number moves you left (decreasing the value), and subtracting a negative number moves you right (increasing the value).

Always line up decimals when performing these operations and combine like signs while treating different signs as a cue to perform subtraction, essentially finding the numerical difference between the two values.

Adding Positive Numbers

Adding positive numbers is a fundamental mathematical skill. Whenever you're adding a positive number to another number, it's as simple as moving to the right on a number line. If you're combining a positive number with a negative one, consider the absolute values: subtract the smaller absolute value from the larger one and then apply the sign of the larger absolute value number.

From our exercise example, \( -6.6 + 16.1 \), even though we're adding a negative number to a positive number, we're essentially dealing with their absolute values, subtracting the smaller from the larger, and keeping the sign of the larger value. This results in a positive outcome since the positive number has a greater absolute value. Simple number line visualizations or counting up methods can often assist in grasping this concept.