Solve for y y+2/7=7/14

$y + \frac{2}{7} = \frac{7}{14}$

Step 1

Cancel the common factor of $7$ and $14$ .

Factor $7$ out of $7$ .

$y + \frac{2}{7} = \frac{7 (1)}{14}$

Cancel the common factors.

Factor $7$ out of $14$ .

$y + \frac{2}{7} = \frac{7 \cdot 1}{7 \cdot 2}$

Cancel the common factor.

$y + \frac{2}{7} = \frac{7 \cdot 1}{7 \cdot 2}$

Rewrite the expression.

$y + \frac{2}{7} = \frac{1}{2}$

Step 2

Move all terms not containing $y$ to the right side of the equation.

Subtract $\frac{2}{7}$ from both sides of the equation.

$y = \frac{1}{2} - \frac{2}{7}$

To write $\frac{1}{2}$ as a fraction with a common denominator, multiply by $\frac{7}{7}$ .

$y = \frac{1}{2} \cdot \frac{7}{7} - \frac{2}{7}$

To write $- \frac{2}{7}$ as a fraction with a common denominator, multiply by $\frac{2}{2}$ .

$y = \frac{1}{2} \cdot \frac{7}{7} - \frac{2}{7} \cdot \frac{2}{2}$

Write each expression with a common denominator of $14$ , by multiplying each by an appropriate factor of $1$ .

Multiply $\frac{1}{2}$ by $\frac{7}{7}$ .

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

Multiply $2$ by $7$ .

$y = \frac{7}{14} - \frac{2}{7} \cdot \frac{2}{2}$

Multiply $\frac{2}{7}$ by $\frac{2}{2}$ .

$y = \frac{7}{14} - \frac{2 \cdot 2}{7 \cdot 2}$

Multiply $7$ by $2$ .

$y = \frac{7}{14} - \frac{2 \cdot 2}{14}$

Combine the numerators over the common denominator.

$y = \frac{7 - 2 \cdot 2}{14}$

Simplify the numerator.

Multiply $- 2$ by $2$ .

$y = \frac{7 - 4}{14}$

Subtract $4$ from $7$ .

$y = \frac{3}{14}$

Step 3

The result can be shown in multiple forms.

Exact Form:

$y = \frac{3}{14}$

Decimal Form:

$y = 0.2\overline{142857}$