Evaluate (1/3)÷(3/5)-1/2*3/5

$\frac{1}{3} \div \frac{3}{5} - \frac{1}{2} \cdot \frac{3}{5}$

Step 1

Simplify each term.

To divide by a fraction, multiply by its reciprocal.

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

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

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

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

Multiply $3$ by $3$ .

$\frac{5}{9} - \frac{1}{2} \cdot \frac{3}{5}$

Multiply $- \frac{1}{2} \cdot \frac{3}{5}$ .

Multiply $\frac{3}{5}$ by $\frac{1}{2}$ .

$\frac{5}{9} - \frac{3}{5 \cdot 2}$

Multiply $5$ by $2$ .

$\frac{5}{9} - \frac{3}{10}$

Step 2

To write $\frac{5}{9}$ as a fraction with a common denominator, multiply by $\frac{10}{10}$ .

$\frac{5}{9} \cdot \frac{10}{10} - \frac{3}{10}$

Step 3

To write $- \frac{3}{10}$ as a fraction with a common denominator, multiply by $\frac{9}{9}$ .

$\frac{5}{9} \cdot \frac{10}{10} - \frac{3}{10} \cdot \frac{9}{9}$

Step 4

Write each expression with a common denominator of $90$ , by multiplying each by an appropriate factor of $1$ .

Multiply $\frac{5}{9}$ by $\frac{10}{10}$ .

$\frac{5 \cdot 10}{9 \cdot 10} - \frac{3}{10} \cdot \frac{9}{9}$

Multiply $9$ by $10$ .

$\frac{5 \cdot 10}{90} - \frac{3}{10} \cdot \frac{9}{9}$

Multiply $\frac{3}{10}$ by $\frac{9}{9}$ .

$\frac{5 \cdot 10}{90} - \frac{3 \cdot 9}{10 \cdot 9}$

Multiply $10$ by $9$ .

$\frac{5 \cdot 10}{90} - \frac{3 \cdot 9}{90}$

Step 5

Combine the numerators over the common denominator.

$\frac{5 \cdot 10 - 3 \cdot 9}{90}$

Step 6

Simplify the numerator.

Multiply $5$ by $10$ .

$\frac{50 - 3 \cdot 9}{90}$

Multiply $- 3$ by $9$ .

$\frac{50 - 27}{90}$

Subtract $27$ from $50$ .

$\frac{23}{90}$

Step 7

The result can be shown in multiple forms.

Exact Form:

$\frac{23}{90}$

Decimal Form:

$0.2\overline{5}$

Evaluate (1/3)÷(3/5)-1/2*3/5

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