Problem 120 Simplify. $$ |1.3-(-2.48)| ... [FREE SOLUTION] (2024)

Get started for free

Get started for free Log out

Chapter 5: Problem 120

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

Short Answer

Expert verified

3.78

Step by step solution

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.

Perform the addition

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

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.

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’s 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’s already positive.
So |3.78| = 3.78.
Understanding absolute value is helpful in various mathematical operations, particularly when dealing with negative numbers.

One App. One Place for Learning.

All the tools & learning materials you need for study success - in one app.

Get started for free

Most popular questions from this chapter

Find a linear function whose graph has slope $-\frac{1}{2}$ and contains$(3,7) .$Find the domain of the function $f$ given by each of the following. $$f(x)=\frac{2 x}{5 x^{2}-20}$$Factor completely. $$ 3(x+1)^{2}-9(x+1)-12 $$Factor completely. $$ (x-p)^{2}-p^{2} $$Solve. If $f(x)=3 x^{3}-4 x$ and $g(x)=8 x^{2}+12 x,$ find all $x$ -values for which$f(x)=g(x)$

See all solutions

Recommended explanations on Math Textbooks

Pure Maths

Read Explanation

Applied Mathematics

Read Explanation

Decision Maths

Read Explanation

Discrete Mathematics

Read Explanation

Geometry

Read Explanation

Probability and Statistics

Read Explanation

View all explanations

What do you think about this solution?

We value your feedback to improve our textbook solutions.

Study anywhere. Anytime. Across all devices.

Sign-up for free

This website uses cookies to improve your experience. We'll assume you're ok with this, but you can opt-out if you wish. Accept

Privacy & Cookies Policy

Privacy Overview

This website uses cookies to improve your experience while you navigate through the website. Out of these, the cookies that are categorized as necessary are stored on your browser as they are essential for the working of basic functionalities of the website. We also use third-party cookies that help us analyze and understand how you use this website. These cookies will be stored in your browser only with your consent. You also have the option to opt-out of these cookies. But opting out of some of these cookies may affect your browsing experience.

Necessary

Always Enabled

Necessary cookies are absolutely essential for the website to function properly. This category only includes cookies that ensures basic functionalities and security features of the website. These cookies do not store any personal information.

Non-necessary

Any cookies that may not be particularly necessary for the website to function and is used specifically to collect user personal data via analytics, ads, other embedded contents are termed as non-necessary cookies. It is mandatory to procure user consent prior to running these cookies on your website.

SAVE & ACCEPT