Solve for $k$ in the proportion.
$\begin{aligned}
\frac{1}{4} & =\frac{8}{k} \\
k & =\square
\end{aligned}$
Answer (1)
Cross-multiply the proportion: 1 × k = 4 × 8 .
Simplify the equation: k = 32 .
The value of k is 32 .
Explanation
Understanding the Proportion We are given the proportion 4 1 = k 8 . Our goal is to find the value of k that makes this proportion true. To do this, we can use cross-multiplication. This means we multiply the numerator of the first fraction by the denominator of the second fraction, and set it equal to the product of the denominator of the first fraction and the numerator of the second fraction.
Cross-Multiplication Cross-multiplying, we get 1 ⋅ k = 4 ⋅ 8 . This simplifies to k = 32 .
Finding the Value of k Therefore, the value of k that satisfies the proportion is 32.
Examples
Proportions are useful in everyday life. For example, if you know that 1 apple costs 0.50 , yo u c an u se a p ro p or t i o n t o f in d o u t h o w m u c h 10 a ppl escos t . I f \frac{1}{0.50} = \frac{10}{x} , t h e n x = 10 \cdot 0.50 = 5$. So, 10 apples cost $5.00.
