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Chapter 5: Problem 120

Simplify. $$ |1.3-(-2.48)| $$

Short Answer

Expert verified
3.78

Step by step solution

01

Simplify the expression inside the absolute value

First, simplify the expression inside the absolute value brackets. The expression is 1.3 - (-2.48). When we subtract a negative number, it is the same as adding the positive value of that number. So, 1.3 - (-2.48) = 1.3 + 2.48.
02

Perform the addition

Now, add the numbers together: 1.3 + 2.48 = 3.78. So the expression inside the absolute value becomes 3.78.
03

Apply the absolute value

Finally, apply the absolute value. The absolute value of 3.78 is 3.78, because it is already a positive number: |3.78| = 3.78.

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Key Concepts

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

Simplifying Expressions
To simplify an expression, you need to perform all the arithmetic operations inside it.
Start by simplifying the innermost expressions and work your way out.
In this problem, we start by simplifying what's inside the absolute value brackets.
For our example, the expression inside the brackets is 1.3 - (-2.48).
Subtracting a negative number is the same as adding its positive counterpart.
So, 1.3 - (-2.48) becomes 1.3 + 2.48.
Now you've simplified the expression inside the absolute value brackets, making it easier to handle.
Addition of Decimals
Adding decimals might seem tricky, but it's just like adding whole numbers if you keep a few things in mind.
Always align the decimal points before starting the addition.
In our example, we add 1.3 and 2.48.
Here鈥檚 a quick way to do it:
  • Align the decimal points: 1.30 (Add a zero to keep the decimal places consistent) + 2.48
  • Add like you would with whole numbers: 0.30 + 0.48 = 0.78 and 1 + 2 = 3
Combine the results: 3 + 0.78 = 3.78.
Now, the expression inside the absolute value bracket is simplified to 3.78.
It's straightforward if you keep decimals lined up!
Absolute Value Properties
The absolute value of a number is its distance from zero on the number line, always a non-negative number.
Here are a few key points about absolute values:
  • It makes any negative number positive.
  • If the number is already positive or zero, it remains unchanged.
In our example, we have the number 3.78.
The absolute value of 3.78 is simply 3.78, because it鈥檚 already positive.
So |3.78| = 3.78.
Understanding absolute value is helpful in various mathematical operations, particularly when dealing with negative numbers.

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