Problem 46 Evaluate the expression. $$ 1.... [FREE SOLUTION]

Chapter 2: Problem 46

Evaluate the expression. $$ 1.3+(-1.3)-4.2 $$

Short Answer

Expert verified

-4.2

Step by step solution

Add 1.3 and -1.3

When we add $1.3$ and $-1.3$, we obtain $0$. This is because $-1.3$ is the additive inverse of $1.3$, so adding these two numbers together results in zero.

Subtract 4.2 from the Result

After obtaining $0$ from step 1, we then subtract $4.2$ from $0$. Since subtracting a number is equivalent to adding its additive inverse, and the additive inverse of $4.2$ is $-4.2$, we add $-4.2$ to $0$ and get $-4.2$.

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Key Concepts

These are the key concepts you need to understand to accurately answer the question.

Understanding the Additive Inverse

The additive inverse of a number is a fundamental concept in mathematics. Simply put, the additive inverse is what you would add to a number to get zero. For any given number, its additive inverse is the same number with the opposite sign.
For example:

The additive inverse of 5 is $-5$.
The additive inverse of $-2$ is 2.

When you add a number to its additive inverse, they "cancel out" to zero. This idea is used frequently in simplifying expressions.The original expression in the exercise, $1.3 + (-1.3) - 4.2$, uses the additive inverse of 1.3, which is $-1.3$. Adding these in step 1 results in zero, showing the power of understanding additive inverses.

Subtraction as Addition of the Additive Inverse

Subtraction is often thought of as a more challenging operation than addition. However, it can be simplified by viewing subtraction as the addition of an additive inverse. When you subtract a number, it's the same as adding the opposite of that number.
For instance, when we say we're subtracting 4.2, we're really adding $-4.2$.

Think of subtraction as the addition of the inverse.
This makes calculations more uniform and easier to manage.

In the exercise, after reaching zero in step 1, we subtract 4.2. Instead of complicating things, we simply add $-4.2$ to zero, hence reaching the solution $-4.2$. This approach helps in better understanding subtraction as a familiar addition problem.

Step-by-Step Solutions and Their Role in Learning

Step-by-step solutions are a great way to break down complex problems into more manageable parts. By understanding each piece individually, students can gain a clearer picture of the entire process.
In the given exercise:

Step 1 shows how the additive inverse simplifies two terms to zero.
Step 2 demonstrates subtraction by converting it to an addition problem.

This method doesn't just give you the right answer; it helps you understand why the answer is correct. When you see how each part contributes to the solution, you start to grasp underlying concepts better. Step-by-step solutions are particularly useful for practice and developing problem-solving skills in mathematics.

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91影视

Evaluate the expression. $$ 1.3+(-1.3)-4.2 $$

Short Answer

Step by step solution

Add 1.3 and -1.3

Subtract 4.2 from the Result

Key Concepts

Understanding the Additive Inverse

Subtraction as Addition of the Additive Inverse

Step-by-Step Solutions and Their Role in Learning

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