Questions: Solve for (n). [ fracn24=frac832 ] (n=) (square) (Type an integer or a simplified fraction.)

$Solve for (n). [ fracn24=frac832 ] (n=) (square) (Type an integer or a simplified fraction.)$

Transcript text: Solve for $n$. \[ \frac{n}{24}=\frac{8}{32} \] $n=$ $\square$ (Type an integer or a simplified fraction.)

Solution

Solution Steps

To solve for $ n $ in the equation $\frac{n}{24} = \frac{8}{32}$, we can use cross-multiplication to eliminate the fractions and then solve for $ n $.

Step 1: Set Up the Equation

Given the equation: \[ \frac{n}{24} = \frac{8}{32} \]

Step 2: Simplify the Right-Hand Side

Simplify $\frac{8}{32}$: \[ \frac{8}{32} = \frac{1}{4} \] So the equation becomes: \[ \frac{n}{24} = \frac{1}{4} \]

Step 3: Cross-Multiply to Solve for $ n $

Cross-multiplying to eliminate the fractions: \[ n \cdot 4 = 1 \cdot 24 \] \[ 4n = 24 \]

Step 4: Solve for $ n $

Divide both sides by 4: \[ n = \frac{24}{4} = 6 \]

Final Answer

\[ \boxed{n = 6} \]

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