Problem 55 $\frac{x}{5}+\frac{3 x}{5}$... [FREE SOLUTION]

91影视

Elementary Algebra Within Reach

Ron Larson, Kimberly Nolting

$Math Studyset 91影视 Explanations$ Math

6 Edition

Chapter 7: Problem 55

$\frac{x}{5}+\frac{3 x}{5}$

Short Answer

Expert verified

$\frac{4x}{5}$

Step by step solution

Identify Common Denominators

In our case, both fractions have the same denominator which is 5. This makes the process straightforward. We can add the numerators of the fractions without doing any extra work.

Adding the Numerators

When adding the numerators, we get $(1x+3x)/5$.

Simplify the Expression

The expression simplifies to $4x/5$.

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Key Concepts

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

Common Denominators

When adding fractions, having a common denominator is key. A denominator is the bottom part of a fraction that tells us into how many parts the whole is divided. To add fractions, each fraction must have the same denominator.

In the exercise, both fractions have 5 as the denominator: $ \frac{x}{5} $ and $ \frac{3x}{5} $. Since they share this common denominator, adding them becomes straightforward.

If the denominators were different, we would need to find a common denominator by identifying the least common multiple (LCM). Luckily, this step isn't needed here as the denominators are already the same.

Simplifying Expressions

Simplifying an expression means reducing it to its most basic form. After adding fractions with a common denominator, you usually simplify the result.

In our case, after we added $ \frac{x}{5} + \frac{3x}{5} $, we got $ \frac{4x}{5} $. Let's break down this process:

First, add the numerators: $ x + 3x = 4x $.
The denominator remains 5, as it is common to both fractions.

The expression $ \frac{4x}{5} $ is already simple enough in this context. There's no other reduction possible, so $ \frac{4x}{5} $ is our simplified result.

Basic Algebra

Algebra involves working with variables and constants to solve equations or simplify expressions. Let's apply basic algebra concepts to our exercise.

The expression $ \frac{x}{5} + \frac{3x}{5} $ demonstrates how algebra lets us handle unknown values (variables) like $ x $. When dealing with expressions, algebra allows us to regroup terms and perform operations using rules like:

Combine like terms: In this case, $ x $ and $ 3x $ are like terms. Adding them gives $ 4x $.
Work with fractions: Knowing how to deal with common denominators and numerators is essential.

Basic algebra simplifies these tasks and helps form the foundation for solving more complex mathematical problems.

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91影视

\(\frac{x}{5}+\frac{3 x}{5}\)

Short Answer

Step by step solution

Identify Common Denominators

Adding the Numerators

Simplify the Expression

Key Concepts

Common Denominators

Simplifying Expressions

Basic Algebra

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