Basic Math Examples

$12 - (\frac{8}{5} + 3 \div \frac{2}{3})$

Step 1

Simplify each term.

Tap for more steps...

Step 1.1

Simplify each term.

Tap for more steps...

Step 1.1.1

To divide by a fraction, multiply by its reciprocal.

$12 - (\frac{8}{5} + 3 (\frac{3}{2}))$

Step 1.1.2

Multiply $3 (\frac{3}{2})$ .

Tap for more steps...

Step 1.1.2.1

Combine $3$ and $\frac{3}{2}$ .

$12 - (\frac{8}{5} + \frac{3 \cdot 3}{2})$

Step 1.1.2.2

Multiply $3$ by $3$ .

$12 - (\frac{8}{5} + \frac{9}{2})$

Step 1.2

To write $\frac{8}{5}$ as a fraction with a common denominator, multiply by $\frac{2}{2}$ .

$12 - (\frac{8}{5} \cdot \frac{2}{2} + \frac{9}{2})$

Step 1.3

To write $\frac{9}{2}$ as a fraction with a common denominator, multiply by $\frac{5}{5}$ .

$12 - (\frac{8}{5} \cdot \frac{2}{2} + \frac{9}{2} \cdot \frac{5}{5})$

Step 1.4

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

Tap for more steps...

Step 1.4.1

Multiply $\frac{8}{5}$ by $\frac{2}{2}$ .

$12 - (\frac{8 \cdot 2}{5 \cdot 2} + \frac{9}{2} \cdot \frac{5}{5})$

Step 1.4.2

Multiply $5$ by $2$ .

$12 - (\frac{8 \cdot 2}{10} + \frac{9}{2} \cdot \frac{5}{5})$

Step 1.4.3

Multiply $\frac{9}{2}$ by $\frac{5}{5}$ .

$12 - (\frac{8 \cdot 2}{10} + \frac{9 \cdot 5}{2 \cdot 5})$

Step 1.4.4

Multiply $2$ by $5$ .

$12 - (\frac{8 \cdot 2}{10} + \frac{9 \cdot 5}{10})$

Step 1.5

Combine the numerators over the common denominator.

$12 - \frac{8 \cdot 2 + 9 \cdot 5}{10}$

Step 1.6

Simplify the numerator.

Tap for more steps...

Step 1.6.1

Multiply $8$ by $2$ .

$12 - \frac{16 + 9 \cdot 5}{10}$

Step 1.6.2

Multiply $9$ by $5$ .

$12 - \frac{16 + 45}{10}$

Step 1.6.3

Add $16$ and $45$ .

$12 - \frac{61}{10}$

Step 2

To write $12$ as a fraction with a common denominator, multiply by $\frac{10}{10}$ .

$12 \cdot \frac{10}{10} - \frac{61}{10}$

Step 3

Combine $12$ and $\frac{10}{10}$ .

$\frac{12 \cdot 10}{10} - \frac{61}{10}$

Step 4

Combine the numerators over the common denominator.

$\frac{12 \cdot 10 - 61}{10}$

Step 5

Simplify the numerator.

Tap for more steps...

Step 5.1

Multiply $12$ by $10$ .

$\frac{120 - 61}{10}$

Step 5.2

Subtract $61$ from $120$ .

$\frac{59}{10}$

Step 6

The result can be shown in multiple forms.

Exact Form:

$\frac{59}{10}$

Decimal Form:

$5.9$

Mixed Number Form:

$5 \frac{9}{10}$