Solve for a 1/3+a=5/4

$\frac{1}{3} + a = \frac{5}{4}$

Subtract $\frac{1}{3}$ from both sides of the equation.

$a = \frac{5}{4} - \frac{1}{3}$

To write $\frac{5}{4}$ as a fraction with a common denominator, multiply by $\frac{3}{3}$ .

$a = \frac{5}{4} \cdot \frac{3}{3} - \frac{1}{3}$

To write $- \frac{1}{3}$ as a fraction with a common denominator, multiply by $\frac{4}{4}$ .

$a = \frac{5}{4} \cdot \frac{3}{3} - \frac{1}{3} \cdot \frac{4}{4}$

Write each expression with a common denominator of $12$ , by multiplying each by an appropriate factor of $1$ .

Multiply $\frac{5}{4}$ by $\frac{3}{3}$ .

$a = \frac{5 \cdot 3}{4 \cdot 3} - \frac{1}{3} \cdot \frac{4}{4}$

Multiply $4$ by $3$ .

$a = \frac{5 \cdot 3}{12} - \frac{1}{3} \cdot \frac{4}{4}$

Multiply $\frac{1}{3}$ by $\frac{4}{4}$ .

$a = \frac{5 \cdot 3}{12} - \frac{4}{3 \cdot 4}$

Multiply $3$ by $4$ .

$a = \frac{5 \cdot 3}{12} - \frac{4}{12}$

Combine the numerators over the common denominator.

$a = \frac{5 \cdot 3 - 4}{12}$

Simplify the numerator.

Multiply $5$ by $3$ .

$a = \frac{15 - 4}{12}$

Subtract $4$ from $15$ .

$a = \frac{11}{12}$

The result can be shown in multiple forms.

Exact Form:

$a = \frac{11}{12}$

Decimal Form:

$a = 0.91\overline{6}$