Problem 23 Simplify. $$ -3.8+9.6 $$... [FREE SOLUTION]

Chapter 15: Problem 23

Simplify. $$ -3.8+9.6 $$

Short Answer

Expert verified

5.8

Step by step solution

Identify the Operation

Determine the type of mathematical operation you need to perform. The expression is -3.8 + 9.6 . Here, we need to perform an addition involving both a negative and a positive number.

Add the Numbers

When adding a negative number and a positive number, subtract the smaller absolute value from the larger absolute value. Here, |3.8| = 3.8 and |9.6| = 9.6 . Since 9.6 > 3.8 , we subtract 3.8 from 9.6.

Calculate the Result

Perform the subtraction 9.6 - 3.8 = 5.8. Since 9.6 has the larger absolute value and it's positive, the result of the expression is positive.

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Key Concepts

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

Addition of Positive and Negative Numbers

Adding positive and negative numbers can sometimes be tricky, but it follows basic rules that make it easy. When you add a positive number and a negative number, what you're really doing is finding the difference between their absolute values.
If the positive number has a larger absolute value, the result will be positive.
If the negative number has a larger absolute value, the result will be negative.
For example, in our exercise, we add -3.8 and 9.6. Here, you subtract the smaller absolute value from the larger one, which is: 9.6 - 3.8 = 5.8. Since 9.6 is positive and has a larger absolute value, our final result is positive 5.8.

Absolute Value

The absolute value of a number is how far it is from zero on the number line, regardless of direction. It鈥檚 always a non-negative number.
For example, the absolute value of -3.8 is written as | -3.8 | and equals 3.8.
Similarly, the absolute value of 9.6 is | 9.6 |, which is just 9.6.
Absolute values are helpful when adding or subtracting positive and negative numbers because they simplify the process to just dealing with magnitudes without signs.
In our exercise, we used absolute values to correctly perform subtraction: |9.6| - |3.8| results in 5.8. Because the original larger number was positive, our answer is positive.

Subtraction

Even though it might look like we鈥檙e just adding numbers, when you add a negative number, you are effectively subtracting.
Subtraction can be thought of as finding the difference between two numbers.
In the exercise -3.8 + 9.6. We subtract the smaller absolute value (3.8) from the larger absolute value (9.6).
Therefore, 9.6 - 3.8 = 5.8.
Since we subtracted a smaller positive number from a larger positive number, our result remains positive.
Subtraction simplifies any addition problem involving negative numbers by focusing only on the absolute values.

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91影视

Simplify. $$ -3.8+9.6 $$

Short Answer

Step by step solution

Identify the Operation

Add the Numbers

Calculate the Result

Key Concepts

Addition of Positive and Negative Numbers

Absolute Value

Subtraction

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