Basic Math Examples

$\frac{2}{5} + \frac{3}{5} \cdot (\frac{5}{10} + \frac{10}{5})$

Step 1

Simplify each term.

Tap for more steps...

Step 1.1

Simplify each term.

Tap for more steps...

Step 1.1.1

Cancel the common factor of $5$ and $10$ .

Tap for more steps...

Step 1.1.1.1

Factor $5$ out of $5$ .

$\frac{2}{5} + \frac{3}{5} \cdot (\frac{5 (1)}{10} + \frac{10}{5})$

Step 1.1.1.2

Cancel the common factors.

Tap for more steps...

Step 1.1.1.2.1

Factor $5$ out of $10$ .

$\frac{2}{5} + \frac{3}{5} \cdot (\frac{5 \cdot 1}{5 \cdot 2} + \frac{10}{5})$

Step 1.1.1.2.2

Cancel the common factor.

$\frac{2}{5} + \frac{3}{5} \cdot (\frac{5 \cdot 1}{5 \cdot 2} + \frac{10}{5})$

Step 1.1.1.2.3

Rewrite the expression.

$\frac{2}{5} + \frac{3}{5} \cdot (\frac{1}{2} + \frac{10}{5})$

Step 1.1.2

Divide $10$ by $5$ .

$\frac{2}{5} + \frac{3}{5} \cdot (\frac{1}{2} + 2)$

Step 1.2

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

$\frac{2}{5} + \frac{3}{5} \cdot (\frac{1}{2} + 2 \cdot \frac{2}{2})$

Step 1.3

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

$\frac{2}{5} + \frac{3}{5} \cdot (\frac{1}{2} + \frac{2 \cdot 2}{2})$

Step 1.4

Combine the numerators over the common denominator.

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

Step 1.5

Simplify the numerator.

Tap for more steps...

Step 1.5.1

Multiply $2$ by $2$ .

$\frac{2}{5} + \frac{3}{5} \cdot \frac{1 + 4}{2}$

Step 1.5.2

Add $1$ and $4$ .

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

Step 1.6

Cancel the common factor of $5$ .

Tap for more steps...

Step 1.6.1

Cancel the common factor.

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

Step 1.6.2

Rewrite the expression.

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

Step 1.7

Combine $3$ and $\frac{1}{2}$ .

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

Step 2

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

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

Step 3

To write $\frac{3}{2}$ as a fraction with a common denominator, multiply by $\frac{5}{5}$ .

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

Step 4

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

Tap for more steps...

Step 4.1

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

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

Step 4.2

Multiply $5$ by $2$ .

$\frac{2 \cdot 2}{10} + \frac{3}{2} \cdot \frac{5}{5}$

Step 4.3

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

$\frac{2 \cdot 2}{10} + \frac{3 \cdot 5}{2 \cdot 5}$

Step 4.4

Multiply $2$ by $5$ .

$\frac{2 \cdot 2}{10} + \frac{3 \cdot 5}{10}$

Step 5

Combine the numerators over the common denominator.

$\frac{2 \cdot 2 + 3 \cdot 5}{10}$

Step 6

Simplify the numerator.

Tap for more steps...

Step 6.1

Multiply $2$ by $2$ .

$\frac{4 + 3 \cdot 5}{10}$

Step 6.2

Multiply $3$ by $5$ .

$\frac{4 + 15}{10}$

Step 6.3

Add $4$ and $15$ .

$\frac{19}{10}$

Step 7

The result can be shown in multiple forms.

Exact Form:

$\frac{19}{10}$

Decimal Form:

$1.9$

Mixed Number Form:

$1 \frac{9}{10}$