Solve the Fractional Equation: 3 1/2y = 21

To solve the equation $3\frac{1}{2} \cdot y = 21$, we'll follow these steps:

• Convert the mixed number to an improper fraction.
• Divide both sides of the equation by the coefficient of $y$.

Let's analyze these steps in detail:

Step 1: Convert the mixed number to an improper fraction.
The coefficient of $y$ is $3\frac{1}{2}$. Converting to an improper fraction, we have:

$3\frac{1}{2} = \frac{7}{2}$

Step 2: Divide both sides of the equation by $\frac{7}{2}$.
The equation becomes:

$\frac{7}{2} \cdot y = 21$

To isolate $y$, divide both sides by $\frac{7}{2}$:

$y = 21 \div \frac{7}{2}$

Dividing by a fraction is equivalent to multiplying by its reciprocal, so:

$y = 21 \cdot \frac{2}{7}$

Carrying out the multiplication, we calculate:

$y = \frac{21 \cdot 2}{7} = \frac{42}{7}$

Dividing the numerator by the denominator gives us:

$y = 6$

Thus, the solution to the equation is $y = 6$.