Simplify 2/(1/3+1/5)

$\frac{2}{\frac{1}{3} + \frac{1}{5}}$

Step 1

Simplify the denominator.

To write $\frac{1}{3}$ as a fraction with a common denominator, multiply by $\frac{5}{5}$ .

$\frac{2}{\frac{1}{3} \cdot \frac{5}{5} + \frac{1}{5}}$

To write $\frac{1}{5}$ as a fraction with a common denominator, multiply by $\frac{3}{3}$ .

$\frac{2}{\frac{1}{3} \cdot \frac{5}{5} + \frac{1}{5} \cdot \frac{3}{3}}$

Write each expression with a common denominator of $15$ , by multiplying each by an appropriate factor of $1$ .

Multiply $\frac{1}{3}$ by $\frac{5}{5}$ .

$\frac{2}{\frac{5}{3 \cdot 5} + \frac{1}{5} \cdot \frac{3}{3}}$

Multiply $3$ by $5$ .

$\frac{2}{\frac{5}{15} + \frac{1}{5} \cdot \frac{3}{3}}$

Multiply $\frac{1}{5}$ by $\frac{3}{3}$ .

$\frac{2}{\frac{5}{15} + \frac{3}{5 \cdot 3}}$

Multiply $5$ by $3$ .

$\frac{2}{\frac{5}{15} + \frac{3}{15}}$

Combine the numerators over the common denominator.

$\frac{2}{\frac{5 + 3}{15}}$

Add $5$ and $3$ .

$\frac{2}{\frac{8}{15}}$

Step 2

Multiply the numerator by the reciprocal of the denominator.

$2 (\frac{15}{8})$

Step 3

Cancel the common factor of $2$ .

Factor $2$ out of $8$ .

$2 \frac{15}{2 (4)}$

Cancel the common factor.

$2 \frac{15}{2 \cdot 4}$

Rewrite the expression.

$\frac{15}{4}$

Step 4

The result can be shown in multiple forms.

Exact Form:

$\frac{15}{4}$

Decimal Form:

$3.75$

Mixed Number Form:

$3 \frac{3}{4}$