To find the value of \( x \) in the proportion \(\frac{1}{2} : \frac{2}{3} = x : 1\), we need to solve for \( x \) using the properties of proportions. 

A proportion states that two ratios are equal, so we can write:

\[
\frac{\frac{1}{2}}{\frac{2}{3}} = \frac{x}{1}
\]

### Step-by-Step Solution

1. **Rewrite the proportion:**

   \[
   \frac{\frac{1}{2}}{\frac{2}{3}} = x
   \]

2. **Simplify the fraction on the left-hand side:**

   To simplify \(\frac{\frac{1}{2}}{\frac{2}{3}}\), we multiply by the reciprocal of \(\frac{2}{3}\):

   \[
   \frac{1}{2} \times \frac{3}{2} = \frac{1 \cdot 3}{2 \cdot 2} = \frac{3}{4}
   \]

3. **Set the simplified expression equal to \(x\):**

   \[
   x = \frac{3}{4}
   \]

### Conclusion

The value of \( x \) is:

\[
\boxed{\frac{3}{4}}
\]

Would you like more details on this problem, or do you have any other questions?

### Related Questions

1. How do you solve proportions with variables on both sides?
2. What are some real-life applications of proportions?
3. How do you convert a fraction to a percentage?
4. How can you check if two ratios are proportional?
5. How do you solve complex fractions?

### Tip

When working with proportions, remember to cross-multiply to find the unknown variable quickly.

Learn how to calculate the value of x in the proportion 1/2 : 2/3 = x : 1 with a detailed step-by-step solution. This problem covers key concepts in proportions and includes a simplified explanation and solution method. 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