Problem 62 Simplify each expression. $$ ... [FREE SOLUTION]

Chapter 1: Problem 62

Simplify each expression. $$ w+(-w)+\frac{1}{4}(4) $$

Short Answer

Expert verified

Step by step solution

Combine Like Terms

Look at the expression: $w + (-w) + \frac{1}{4}(4)$. Notice that there is $w$ and $-w$ in the expression. Combining these terms yields 0 since $w - w = 0$. This simplifies the expression to $0 + \frac{1}{4}(4)$.

Simplify the Fraction

Now, simplify $\frac{1}{4} \cdot 4$. Multiply $\frac{1}{4}$ by 4: $\frac{1}{4} \cdot 4 = 1$. This gives us: $0 + 1$.

Combine Final Terms

Combine 0 and 1: $0 + 1 = 1$. Therefore, the simplified expression is 1.

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

When simplifying algebraic expressions, it's crucial to combine like terms. Like terms are terms that have the same variable raised to the same power. For instance, in the expression $w + (-w) + \frac{1}{4}(4)$, the terms $w$ and $-w$ are like terms because they both contain the variable $w$.
Combining these terms simplifies the expression:

$w - w = 0$

Now the expression becomes:
$0 + \frac{1}{4}(4)$.
Combining like terms helps in reducing complex expressions to simpler forms, making them easier to work with.

Simplifying Fractions

Simplifying fractions involves reducing the fraction to its simplest form where the numerator and the denominator are as small as possible. This makes the fraction easier to understand and work with. In our example, the term $\frac{1}{4}(4)$ needs to be simplified.
Multiply the fraction by the number:

$\frac{1}{4} \cdot 4 = 1$

Hence, the simplified term is 1.
Simplifying fractions is essential in algebra as it streamlines calculations and helps in better comprehension of the expressions.

Algebra Basics

Understanding the basics of algebra is essential in solving and simplifying expressions. Algebra involves using symbols and letters to represent numbers and quantities in formulas and equations.
In this exercise, we used foundational concepts:

Combining like terms: Reducing terms with the same variable.
Simplifying fractions: Making fractions as simple as possible.

After combining like terms and simplifying fractions, our final step is to combine the remaining simplified terms: $0 + 1 = 1$.
Therefore, the final simplified expression is 1. Mastering these basics ensures a strong foundation for tackling more complex algebraic problems.
Remember to always break down the problem step by step, which makes solving easier and less error-prone.

One App. One Place for Learning.

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

Get started for free

Recommended explanations on Math Textbooks

View all explanations

What do you think about this solution?

We value your feedback to improve our textbook solutions.

91影视

Simplify each expression. $$ w+(-w)+\frac{1}{4}(4) $$

Short Answer

Step by step solution

Combine Like Terms

Simplify the Fraction

Combine Final Terms

Key Concepts

Combining Like Terms

Simplifying Fractions

Algebra Basics

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Theoretical and Mathematical Physics

Pure Maths

Geometry

Discrete Mathematics

Statistics

Probability and Statistics

Study anywhere. Anytime. Across all devices.