Problem 78 - Algebra 1

Question

Find the difference. $$ -4.1-(-5.1) $$

Step-by-Step Solution

Answer

The difference is 1.0.

Step 1: Understand the Expression

The expression is \(-4.1 - (-5.1)\). This involves subtracting a negative number, which can be tricky. It's important to remember that subtracting a negative is the same as adding a positive.

Step 2: Change the Expression

Change the expression from \(-4.1 - (-5.1)\) to \(-4.1 + 5.1\). When you subtract a negative number, it's the same as adding a positive.

Step 3: Add the Numbers

Now simply add the two numbers together. The result of -4.1 + 5.1 is 1.0.

Key Concepts

Adding Integers

When adding integers, always consider the signs involved. Integers can be positive or negative, and their combination affects the sum. Here are some quick rules for adding integers:

• Adding two positive integers always results in a positive sum. For example, \(3 + 5 = 8\).
• Adding two negative integers results in a more negative number. For instance, \(-3 + (-5) = -8\).
• When adding a positive integer and a negative integer, subtract the smaller from the larger in absolute value. The sign of the sum is the same as the sign of the integer with the larger absolute value.

In the problem \(-4.1 - (-5.1)\), you're transforming it into an addition problem. Subtracting a negative is equivalent to adding a positive. Therefore, it switches to \(-4.1 + 5.1\). This demonstrates the principle of converting subtraction of a negative into addition.

Negative Numbers

Negative numbers represent values less than zero and appear frequently in arithmetic operations. They are essential when working with debts, temperatures below freezing, or elevations below sea level. Here are some tips when dealing with negative numbers:

• Negative numbers can be tricky, but remember that they simply move left from zero on a number line.
• When subtracting negative numbers, you actually add the numbers on the number line.
• A common operation with negative numbers is turning subtraction into addition. It's handy when calculating the difference between numbers.

In our exercise, converting \(-4.1 - (-5.1)\) to \(-4.1 + 5.1\) leverages this transformation. Understanding negative numbers helps in approaching such arithmetic problems with confidence.

Arithmetic Operations

Arithmetic operations form the foundation of mathematics. The primary operations are addition, subtraction, multiplication, and division. Understanding how these operations interact with integers, both positive and negative, is crucial.

• Addition: Combining two numbers to get a sum, as seen in our case converting \(-4.1 - (-5.1)\) to \(-4.1 + 5.1\).
• Subtraction: Generally involves finding the difference between numbers, but subtracting a negative can become addition.
• Multiplication and Division: Include products and quotients, but this problem specifically focused on addition and subtraction.

By familiarizing oneself with these operations and understanding their interactions, you can navigate through most mathematical problems with ease. In our exercise, knowing subtraction can become addition simplified the approach, ultimately resulting in adding \(-4.1 + 5.1\). This arithmetic operation yields a straightforward result of 1.0.