What is the value of x in the proportion below?

StartFraction One-half over 4 EndFraction = StartFraction x over 28 EndFraction
3 and one-half
7 and one-half
14
56

We are given the proportion:

\[
\frac{\frac{1}{2}}{4} = \frac{x}{28}
\]

To solve for \( x \), follow these steps:

1. Simplify the left-hand side:
   \[
   \frac{\frac{1}{2}}{4} = \frac{1}{2} \times \frac{1}{4} = \frac{1}{8}
   \]
   So, the equation becomes:
   \[
   \frac{1}{8} = \frac{x}{28}
   \]

2. To solve for \( x \), cross-multiply:
   \[
   1 \times 28 = 8 \times x
   \]
   \[
   28 = 8x
   \]

3. Now, solve for \( x \) by dividing both sides by 8:
   \[
   x = \frac{28}{8} = 3.5
   \]

Thus, the value of \( x \) is \( 3 \frac{1}{2} \), or \( 3.5 \).

The correct answer is: **3 and one-half**.

Would you like more details or have any questions?

Here are five questions to expand on this concept:
1. How do you simplify complex fractions like in this proportion?
2. What does cross-multiplying achieve when solving proportions?
3. Can proportions be used to solve word problems? How?
4. What happens when both numerators or both denominators are variables?
5. How do proportions relate to similar triangles in geometry?

**Tip:** Always simplify fractions in proportions before solving to make calculations easier.

What is the value of x in the proportion below? StartFraction One-half over 4 EndFraction = StartFraction x over 28 EndFraction 3 and one-half 7 and one-half 14 56

Learn how to solve the proportion (1/2)/4 = x/28 using cross-multiplication and fraction simplification. This step-by-step solution covers key concepts such as simplifying complex fractions and solving for variables in proportions. Ideal for students in Grades 6-8.

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