Basic Math Examples

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

Step 1

Combine the numerators over the common denominator.

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

Step 2

Simplify by adding numbers.

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Step 2.1

Add $2$ and $2$ .

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

Step 2.2

Add $4$ and $4$ .

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

Step 3

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

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

Step 4

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

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

Step 5

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

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Step 5.1

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

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

Step 5.2

Multiply $3$ by $5$ .

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

Step 5.3

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

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

Step 5.4

Multiply $5$ by $3$ .

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

Step 6

Combine the numerators over the common denominator.

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

Step 7

Simplify the numerator.

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Step 7.1

Multiply $4$ by $5$ .

$\frac{20 + 8 \cdot 3}{15}$

Step 7.2

Multiply $8$ by $3$ .

$\frac{20 + 24}{15}$

Step 7.3

Add $20$ and $24$ .

$\frac{44}{15}$

Step 8

The result can be shown in multiple forms.

Exact Form:

$\frac{44}{15}$

Decimal Form:

$2.9\overline{3}$

Mixed Number Form:

$2 \frac{14}{15}$