Questions: Solve the following proportion for (v). [ frac7v=frac38 ] Round your answer to the nearest tenth. [ v= ]

$Solve the following proportion for (v). [ frac7v=frac38 ] Round your answer to the nearest tenth. [ v= ]$

Transcript text: Solve the following proportion for $v$. \[ \frac{7}{v}=\frac{3}{8} \] Round your answer to the nearest tenth. \[ v= \]

Solution

Solution Steps

To solve the proportion $\frac{7}{v} = \frac{3}{8}$, we can use cross-multiplication. This involves multiplying the numerator of one fraction by the denominator of the other fraction and setting the products equal to each other. Once we have the equation, we can solve for $v$ by isolating it on one side. Finally, we round the result to the nearest tenth.

Step 1: Set Up the Proportion

We start with the given proportion:

\[ \frac{7}{v} = \frac{3}{8} \]

Step 2: Cross-Multiply

Using cross-multiplication, we can rewrite the equation as:

\[ 7 \cdot 8 = 3 \cdot v \]

This simplifies to:

\[ 56 = 3v \]

Step 3: Solve for $v$

To isolate $v$, we divide both sides by 3:

\[ v = \frac{56}{3} \]

Calculating this gives: