Solve for a a-1/5=-1/7

$a - \frac{1}{5} = - \frac{1}{7}$

Step 1

Add $\frac{1}{5}$ to both sides of the equation.

$a = - \frac{1}{7} + \frac{1}{5}$

Step 2

To write $- \frac{1}{7}$ as a fraction with a common denominator, multiply by $\frac{5}{5}$ .

$a = - \frac{1}{7} \cdot \frac{5}{5} + \frac{1}{5}$

Step 3

To write $\frac{1}{5}$ as a fraction with a common denominator, multiply by $\frac{7}{7}$ .

$a = - \frac{1}{7} \cdot \frac{5}{5} + \frac{1}{5} \cdot \frac{7}{7}$

Step 4

Write each expression with a common denominator of $35$ , by multiplying each by an appropriate factor of $1$ .

Multiply $\frac{1}{7}$ by $\frac{5}{5}$ .

$a = - \frac{5}{7 \cdot 5} + \frac{1}{5} \cdot \frac{7}{7}$

Multiply $7$ by $5$ .

$a = - \frac{5}{35} + \frac{1}{5} \cdot \frac{7}{7}$

Multiply $\frac{1}{5}$ by $\frac{7}{7}$ .

$a = - \frac{5}{35} + \frac{7}{5 \cdot 7}$

Multiply $5$ by $7$ .

$a = - \frac{5}{35} + \frac{7}{35}$

Step 5

Combine the numerators over the common denominator.

$a = \frac{- 5 + 7}{35}$

Step 6

Add $- 5$ and $7$ .

$a = \frac{2}{35}$

Step 7

The result can be shown in multiple forms.

Exact Form:

$a = \frac{2}{35}$

Decimal Form:

$a = 0.0\overline{571428}$