To simplify the expression \(\frac{1}{6}x + \frac{1}{12}x + \frac{1}{7}x + \frac{1}{2}x\), we need to combine the like terms. 

First, find a common denominator for the fractions:

- The denominators are 6, 12, 7, and 2.
- The least common denominator (LCD) is 84.

Now, rewrite each fraction with the common denominator:

\[
\frac{1}{6}x = \frac{14}{84}x
\]
\[
\frac{1}{12}x = \frac{7}{84}x
\]
\[
\frac{1}{7}x = \frac{12}{84}x
\]
\[
\frac{1}{2}x = \frac{42}{84}x
\]

Next, add the fractions:

\[
\frac{14}{84}x + \frac{7}{84}x + \frac{12}{84}x + \frac{42}{84}x = \frac{75}{84}x
\]

Finally, simplify the fraction \(\frac{75}{84}\) by dividing the numerator and the denominator by their greatest common divisor, which is 3:

\[
\frac{75 \div 3}{84 \div 3}x = \frac{25}{28}x
\]

So, the simplified expression is:

\[
\frac{25}{28}x
\]

Would you like further details or have any questions?

Here are some related questions you might find useful:
1. How do you find the least common denominator (LCD) of multiple fractions?
2. What is the process for simplifying fractions?
3. How do you add algebraic fractions with different denominators?
4. How do you factor the numerator and denominator in a fraction?
5. What are some common mistakes to avoid when adding fractions?

**Tip:** When working with fractions, always ensure to find the correct least common denominator to simplify the addition or subtraction process.

Learn how to simplify the expression (1/6)x + (1/12)x + (1/7)x + (1/2)x using fraction addition with different denominators. This problem involves combining like terms and finding a common denominator to simplify algebraic fractions. Suitable for students in Grades 6-8.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation