/*! This file is auto-generated */ .wp-block-button__link{color:#fff;background-color:#32373c;border-radius:9999px;box-shadow:none;text-decoration:none;padding:calc(.667em + 2px) calc(1.333em + 2px);font-size:1.125em}.wp-block-file__button{background:#32373c;color:#fff;text-decoration:none} Problem 100 Simplify each expression, if pos... [FREE SOLUTION] | 91影视

91影视

Log out

Learning Materials

Features

Discover

Chapter 1: Problem 100

Simplify each expression, if possible. $$ -1.1 m-(-2.4 m) $$

Short Answer

Expert verified
The simplified expression is \(1.3m\).

Step by step solution

01

Rewrite the Expression to Remove the Parentheses

The expression is given as \(-1.1m - (-2.4m)\). According to the rules of arithmetic, subtracting a negative is the same as adding a positive. So we rewrite the expression as \(-1.1m + 2.4m\).
02

Combine Like Terms

Now, we need to combine \(-1.1m\) and \(2.4m\). These are like terms because they both include the variable \(m\). To combine them, simply add the coefficients: \(-1.1 + 2.4 = 1.3\). Therefore, the expression simplifies to \(1.3m\).

Unlock Step-by-Step Solutions & Ace Your Exams!

  • Full Textbook Solutions

    Get detailed explanations and key concepts

  • Unlimited Al creation

    Al flashcards, explanations, exams and more...

  • Ads-free access

    To over 500 millions flashcards

  • Money-back guarantee

    We refund you if you fail your exam.

Over 30 million students worldwide already upgrade their learning with 91影视!

Key Concepts

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

Combining Like Terms
In algebra, combining like terms is an essential skill. It helps simplify expressions to make them more manageable and easier to understand. Like terms are terms that have the same variable raised to the same power. This means that only the coefficients of such terms can be combined.
  • For instance, in the expression \(-1.1m + 2.4m\), both terms have the variable \(m\), making them like terms.
  • You can add their coefficients, which are \(-1.1\) and \(2.4\), to simplify the expression.
This strategy is particularly helpful for simplifying longer and more complex expressions by effectively reducing the number of terms to work with. It's like cleaning up a messy desk; once you've cleared away the unnecessary clutter, everything becomes a lot clearer!
Arithmetic Operations
Understanding arithmetic operations is important in simplifying algebraic expressions. The basic operations are addition, subtraction, multiplication, and division. Each has specific rules, especially when it involves variables.
  • Addition and subtraction are straightforward, but remember: subtracting a negative is the same as adding a positive. This rule changes the expression from \(-1.1m - (-2.4m)\) to \(-1.1m + 2.4m\).
  • Multiplication and division involve coefficients and should respect the order of operations, also known by the acronym PEMDAS (Parentheses, Exponents, Multiplication and Division, Addition and Subtraction).
When applying these operations, always pay close attention to the signs and terms to avoid errors, as arithmetic is the backbone of algebraic simplification.
Negative Numbers in Algebra
Negative numbers often seem intimidating, but they are friendly once you get to know them. In algebra, handling negative numbers correctly is crucial.
  • A negative sign indicates a value less than zero, and often represents subtraction or the opposite of a positive value.
  • Key thing to remember is that subtracting a negative number is the same as adding its positive counterpart. For example, the negative of \( -2.4m \) becomes \( +2.4m \) when subtracted from another term.
When dealing with negative coefficients, it's important to accurately reflect their effect on the expression. Mistakes with signs can lead to errors in calculations. Practice and familiarity with these rules will help refine your algebra skills.

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

Explain why we know that the answer to \(4-10\) is negative without having to do any computation.

Law Enforcement. A burglar scored \(-18\) on a lie detector test, a score that indicates deception. However, on a second test, he scored \(+3,\) a score that is inconclusive. Find the change in the scores.

Simplify. $$ 12(m+11)-11+m $$

Find the LCD for \(\frac{5}{12}\) and \(\frac{1}{15}\)

Geography. The elevation of Death Valley, California, is 282 feet below sea level. The elevation of the Dead Sea in Israel is \(1,312\) feet below sea level. Find the difference in their elevations.
See all solutions

Recommended explanations on Math Textbooks

Decision Maths

Read Explanation

Statistics

Read Explanation

Pure Maths

Read Explanation

Calculus

Read Explanation

Probability and Statistics

Read Explanation

Discrete Mathematics

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.