Solve for y 7/17y=3 12/17

$\frac{7}{17} y = 3 \frac{12}{17}$

Step 1

Simplify the left side.

Combine $\frac{7}{17}$ and $y$ .

$\frac{7 y}{17} = 3 \frac{12}{17}$

Step 2

Simplify the right side.

Convert $3 \frac{12}{17}$ to an improper fraction.

A mixed number is an addition of its whole and fractional parts.

$\frac{7 y}{17} = 3 + \frac{12}{17}$

Add $3$ and $\frac{12}{17}$ .

To write $3$ as a fraction with a common denominator, multiply by $\frac{17}{17}$ .

$\frac{7 y}{17} = 3 \cdot \frac{17}{17} + \frac{12}{17}$

Combine $3$ and $\frac{17}{17}$ .

$\frac{7 y}{17} = \frac{3 \cdot 17}{17} + \frac{12}{17}$

Combine the numerators over the common denominator.

$\frac{7 y}{17} = \frac{3 \cdot 17 + 12}{17}$

Simplify the numerator.

Multiply $3$ by $17$ .

$\frac{7 y}{17} = \frac{51 + 12}{17}$

Add $51$ and $12$ .

$\frac{7 y}{17} = \frac{63}{17}$

Step 3

Since the expression on each side of the equation has the same denominator, the numerators must be equal.

$7 y = 63$

Step 4

Divide each term in $7 y = 63$ by $7$ and simplify.

Divide each term in $7 y = 63$ by $7$ .

$\frac{7 y}{7} = \frac{63}{7}$

Simplify the left side.

Cancel the common factor of $7$ .

Cancel the common factor.

$\frac{7 y}{7} = \frac{63}{7}$

Divide $y$ by $1$ .

$y = \frac{63}{7}$

Simplify the right side.

Divide $63$ by $7$ .

$y = 9$