Solve for a a/2+1/5=21/10

$\frac{a}{2} + \frac{1}{5} = \frac{21}{10}$

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

Subtract $\frac{1}{5}$ from both sides of the equation.

$\frac{a}{2} = \frac{21}{10} - \frac{1}{5}$

To write $- \frac{1}{5}$ as a fraction with a common denominator, multiply by $\frac{2}{2}$ .

$\frac{a}{2} = \frac{21}{10} - \frac{1}{5} \cdot \frac{2}{2}$

Write each expression with a common denominator of $10$ , by multiplying each by an appropriate factor of $1$ .

Multiply $\frac{1}{5}$ by $\frac{2}{2}$ .

$\frac{a}{2} = \frac{21}{10} - \frac{2}{5 \cdot 2}$

Multiply $5$ by $2$ .

$\frac{a}{2} = \frac{21}{10} - \frac{2}{10}$

Combine the numerators over the common denominator.

$\frac{a}{2} = \frac{21 - 2}{10}$

Subtract $2$ from $21$ .

$\frac{a}{2} = \frac{19}{10}$

Multiply both sides of the equation by $2$ .

$2 \frac{a}{2} = 2 (\frac{19}{10})$

Simplify both sides of the equation.

Simplify the left side.

Cancel the common factor of $2$ .

Cancel the common factor.

$2 \frac{a}{2} = 2 (\frac{19}{10})$

Rewrite the expression.

$a = 2 (\frac{19}{10})$

Simplify the right side.

Cancel the common factor of $2$ .

Factor $2$ out of $10$ .

$a = 2 \frac{19}{2 (5)}$

Cancel the common factor.

$a = 2 \frac{19}{2 \cdot 5}$

Rewrite the expression.

$a = \frac{19}{5}$

The result can be shown in multiple forms.

Exact Form:

$a = \frac{19}{5}$

Decimal Form:

$a = 3.8$

Mixed Number Form:

$a = 3 \frac{4}{5}$