Algebra Examples

$\frac{1}{3} \div \frac{3}{7} - \frac{3}{5} \cdot \frac{1}{2}$

Step 1

Simplify each term.

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Step 1.1

To divide by a fraction, multiply by its reciprocal.

$\frac{1}{3} \cdot \frac{7}{3} - \frac{3}{5} \cdot \frac{1}{2}$

Step 1.2

Multiply $\frac{1}{3} \cdot \frac{7}{3}$ .

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Step 1.2.1

Multiply $\frac{1}{3}$ by $\frac{7}{3}$ .

$\frac{7}{3 \cdot 3} - \frac{3}{5} \cdot \frac{1}{2}$

Step 1.2.2

Multiply $3$ by $3$ .

$\frac{7}{9} - \frac{3}{5} \cdot \frac{1}{2}$

Step 1.3

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

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Step 1.3.1

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

$\frac{7}{9} - \frac{3}{2 \cdot 5}$

Step 1.3.2

Multiply $2$ by $5$ .

$\frac{7}{9} - \frac{3}{10}$

Step 2

To write $\frac{7}{9}$ as a fraction with a common denominator, multiply by $\frac{10}{10}$ .

$\frac{7}{9} \cdot \frac{10}{10} - \frac{3}{10}$

Step 3

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

$\frac{7}{9} \cdot \frac{10}{10} - \frac{3}{10} \cdot \frac{9}{9}$

Step 4

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

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Step 4.1

Multiply $\frac{7}{9}$ by $\frac{10}{10}$ .

$\frac{7 \cdot 10}{9 \cdot 10} - \frac{3}{10} \cdot \frac{9}{9}$

Step 4.2

Multiply $9$ by $10$ .

$\frac{7 \cdot 10}{90} - \frac{3}{10} \cdot \frac{9}{9}$

Step 4.3

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

$\frac{7 \cdot 10}{90} - \frac{3 \cdot 9}{10 \cdot 9}$

Step 4.4

Multiply $10$ by $9$ .

$\frac{7 \cdot 10}{90} - \frac{3 \cdot 9}{90}$

Step 5

Combine the numerators over the common denominator.

$\frac{7 \cdot 10 - 3 \cdot 9}{90}$

Step 6

Simplify the numerator.

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Step 6.1

Multiply $7$ by $10$ .

$\frac{70 - 3 \cdot 9}{90}$

Step 6.2

Multiply $- 3$ by $9$ .

$\frac{70 - 27}{90}$

Step 6.3

Subtract $27$ from $70$ .

$\frac{43}{90}$

Step 7

The result can be shown in multiple forms.

Exact Form:

$\frac{43}{90}$

Decimal Form:

$0.4\overline{7}$