$\frac{1}{2}=\frac{\text{ }}{14}$

Question

05-11-2026
Mathematics

Answered

$\frac{1}{2}=\frac{\text{ }}{14}$

Verified Answer :

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GinnyAnswer GinnyAnswer · Answer 1 · 2026-11-05T17:38:14-05:00

The problem asks to find the unknown value $x$ in the equation $\frac{1}{2} = \frac{x}{14}$.
Multiplying both sides by $14$ isolates $x$.
Calculating $14 \times \frac{1}{2}$ results in $7$.
The final answer is $\boxed{7}$.

Explanation

Problem Analysis

We are given the equation $\frac{1}{2} = \frac{x}{14}$, where $x$ represents the unknown value in the box. The objective is to determine the value of $x$ that makes this equation true. This involves solving for $x$ by isolating it on one side of the equation. We can use the concept of equivalent fractions, which states that if $\frac{a}{b} = \frac{c}{d}$, then the equation can be solved by multiplying both sides by a common factor or by using cross-multiplication.

Solving the Equation

To isolate $x$, we multiply both sides of the equation $\frac{1}{2} = \frac{x}{14}$ by $14$. This gives us:
\[14 \times \frac{1}{2} = 14 \times \frac{x}{14}\]
\[\frac{14}{2} = x\]
\[7 = x\]
Thus, the value in the box is $7$.

Examples

Imagine you are following a recipe that calls for 1/2 of a cup of flour, but you only have a measuring tool that measures in 14ths of a cup. To ensure you have the correct amount, you set up the equation $\frac{1}{2} = \frac{x}{14}$. By solving this, you find that you need $x=7$ portions of 1/14 cup to get the equivalent of 1/2 cup of flour. This demonstrates how proportional relationships help in cooking and resource management.