Pre-Algebra Examples

$2 \frac{2}{3} - \frac{4}{5}$

Step 1

Convert $2 \frac{2}{3}$ to an improper fraction.

Tap for more steps...

Step 1.1

A mixed number is an addition of its whole and fractional parts.

$2 + \frac{2}{3} - \frac{4}{5}$

Step 1.2

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

Tap for more steps...

Step 1.2.1

To write $2$ as a fraction with a common denominator, multiply by $\frac{3}{3}$ .

$2 \cdot \frac{3}{3} + \frac{2}{3} - \frac{4}{5}$

Step 1.2.2

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

$\frac{2 \cdot 3}{3} + \frac{2}{3} - \frac{4}{5}$

Step 1.2.3

Combine the numerators over the common denominator.

$\frac{2 \cdot 3 + 2}{3} - \frac{4}{5}$

Step 1.2.4

Simplify the numerator.

Tap for more steps...

Step 1.2.4.1

Multiply $2$ by $3$ .

$\frac{6 + 2}{3} - \frac{4}{5}$

Step 1.2.4.2

Add $6$ and $2$ .

$\frac{8}{3} - \frac{4}{5}$

Step 2

To write $\frac{8}{3}$ as a fraction with a common denominator, multiply by $\frac{5}{5}$ .

$\frac{8}{3} \cdot \frac{5}{5} - \frac{4}{5}$

Step 3

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

$\frac{8}{3} \cdot \frac{5}{5} - \frac{4}{5} \cdot \frac{3}{3}$

Step 4

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

Tap for more steps...

Step 4.1

Multiply $\frac{8}{3}$ by $\frac{5}{5}$ .

$\frac{8 \cdot 5}{3 \cdot 5} - \frac{4}{5} \cdot \frac{3}{3}$

Step 4.2

Multiply $3$ by $5$ .

$\frac{8 \cdot 5}{15} - \frac{4}{5} \cdot \frac{3}{3}$

Step 4.3

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

$\frac{8 \cdot 5}{15} - \frac{4 \cdot 3}{5 \cdot 3}$

Step 4.4

Multiply $5$ by $3$ .

$\frac{8 \cdot 5}{15} - \frac{4 \cdot 3}{15}$

Step 5

Combine the numerators over the common denominator.

$\frac{8 \cdot 5 - 4 \cdot 3}{15}$

Step 6

Simplify the numerator.

Tap for more steps...

Step 6.1

Multiply $8$ by $5$ .

$\frac{40 - 4 \cdot 3}{15}$

Step 6.2

Multiply $- 4$ by $3$ .

$\frac{40 - 12}{15}$

Step 6.3

Subtract $12$ from $40$ .

$\frac{28}{15}$

Step 7

The result can be shown in multiple forms.

Exact Form:

$\frac{28}{15}$

Decimal Form:

$1.8\overline{6}$

Mixed Number Form:

$1 \frac{13}{15}$