Basic Math Examples

$\frac{\frac{3}{4} + \frac{5}{6} \cdot \frac{3}{5}}{\frac{1}{2} - (\frac{2}{7} \cdot \frac{7}{5})}$

Step 1

Multiply the numerator and denominator of the fraction by $4$ .

Tap for more steps...

Step 1.1

Multiply $\frac{\frac{3}{4} + \frac{5}{6} \cdot \frac{3}{5}}{\frac{1}{2} - \frac{2}{7} \cdot \frac{7}{5}}$ by $\frac{4}{4}$ .

$\frac{4}{4} \cdot \frac{\frac{3}{4} + \frac{5}{6} \cdot \frac{3}{5}}{\frac{1}{2} - \frac{2}{7} \cdot \frac{7}{5}}$

Step 1.2

Combine.

$\frac{4 (\frac{3}{4} + \frac{5}{6} \cdot \frac{3}{5})}{4 (\frac{1}{2} - \frac{2}{7} \cdot \frac{7}{5})}$

Step 2

Apply the distributive property.

$\frac{4 (\frac{3}{4}) + 4 (\frac{5}{6} \cdot \frac{3}{5})}{4 (\frac{1}{2}) + 4 (- \frac{2}{7} \cdot \frac{7}{5})}$

Step 3

Simplify by cancelling.

Tap for more steps...

Step 3.1

Cancel the common factor of $4$ .

Tap for more steps...

Step 3.1.1

Cancel the common factor.

$\frac{4 (\frac{3}{4}) + 4 (\frac{5}{6} \cdot \frac{3}{5})}{4 (\frac{1}{2}) + 4 (- \frac{2}{7} \cdot \frac{7}{5})}$

Step 3.1.2

Rewrite the expression.

$\frac{3 + 4 (\frac{5}{6} \cdot \frac{3}{5})}{4 (\frac{1}{2}) + 4 (- \frac{2}{7} \cdot \frac{7}{5})}$

Step 3.2

Cancel the common factor of $2$ .

Tap for more steps...

Step 3.2.1

Factor $2$ out of $4$ .

$\frac{3 + 4 (\frac{5}{6} \cdot \frac{3}{5})}{2 (2) \frac{1}{2} + 4 (- \frac{2}{7} \cdot \frac{7}{5})}$

Step 3.2.2

Cancel the common factor.

$\frac{3 + 4 (\frac{5}{6} \cdot \frac{3}{5})}{2 \cdot 2 \frac{1}{2} + 4 (- \frac{2}{7} \cdot \frac{7}{5})}$

Step 3.2.3

Rewrite the expression.

$\frac{3 + 4 (\frac{5}{6} \cdot \frac{3}{5})}{2 + 4 (- \frac{2}{7} \cdot \frac{7}{5})}$

Step 4

Simplify the numerator.

Tap for more steps...

Step 4.1

Cancel the common factor of $2$ .

Tap for more steps...

Step 4.1.1

Factor $2$ out of $4$ .

$\frac{3 + 2 (2) \frac{5}{6} \cdot \frac{3}{5}}{2 + 4 (- \frac{2}{7} \cdot \frac{7}{5})}$

Step 4.1.2

Factor $2$ out of $6$ .

$\frac{3 + 2 \cdot 2 \frac{5}{2 \cdot 3} \cdot \frac{3}{5}}{2 + 4 (- \frac{2}{7} \cdot \frac{7}{5})}$

Step 4.1.3

Cancel the common factor.

$\frac{3 + 2 \cdot 2 \frac{5}{2 \cdot 3} \cdot \frac{3}{5}}{2 + 4 (- \frac{2}{7} \cdot \frac{7}{5})}$

Step 4.1.4

Rewrite the expression.

$\frac{3 + 2 (\frac{5}{3}) \cdot \frac{3}{5}}{2 + 4 (- \frac{2}{7} \cdot \frac{7}{5})}$

Step 4.2

Combine $2$ and $\frac{5}{3}$ .

$\frac{3 + \frac{2 \cdot 5}{3} \cdot \frac{3}{5}}{2 + 4 (- \frac{2}{7} \cdot \frac{7}{5})}$

Step 4.3

Multiply $2$ by $5$ .

$\frac{3 + \frac{10}{3} \cdot \frac{3}{5}}{2 + 4 (- \frac{2}{7} \cdot \frac{7}{5})}$

Step 4.4

Cancel the common factor of $5$ .

Tap for more steps...

Step 4.4.1

Factor $5$ out of $10$ .

$\frac{3 + \frac{5 (2)}{3} \cdot \frac{3}{5}}{2 + 4 (- \frac{2}{7} \cdot \frac{7}{5})}$

Step 4.4.2

Cancel the common factor.

$\frac{3 + \frac{5 \cdot 2}{3} \cdot \frac{3}{5}}{2 + 4 (- \frac{2}{7} \cdot \frac{7}{5})}$

Step 4.4.3

Rewrite the expression.

$\frac{3 + \frac{2}{3} \cdot 3}{2 + 4 (- \frac{2}{7} \cdot \frac{7}{5})}$

Step 4.5

Cancel the common factor of $3$ .

Tap for more steps...

Step 4.5.1

Cancel the common factor.

$\frac{3 + \frac{2}{3} \cdot 3}{2 + 4 (- \frac{2}{7} \cdot \frac{7}{5})}$

Step 4.5.2

Rewrite the expression.

$\frac{3 + 2}{2 + 4 (- \frac{2}{7} \cdot \frac{7}{5})}$

Step 4.6

Add $3$ and $2$ .

$\frac{5}{2 + 4 (- \frac{2}{7} \cdot \frac{7}{5})}$

Step 5

Simplify the denominator.

Tap for more steps...

Step 5.1

Cancel the common factor of $7$ .

Tap for more steps...

Step 5.1.1

Move the leading negative in $- \frac{2}{7}$ into the numerator.

$\frac{5}{2 + 4 (\frac{- 2}{7} \cdot \frac{7}{5})}$

Step 5.1.2

Cancel the common factor.

$\frac{5}{2 + 4 (\frac{- 2}{7} \cdot \frac{7}{5})}$

Step 5.1.3

Rewrite the expression.

$\frac{5}{2 + 4 (- 2 \cdot \frac{1}{5})}$

Step 5.2

Combine $- 2$ and $\frac{1}{5}$ .

$\frac{5}{2 + 4 (\frac{- 2}{5})}$

Step 5.3

Move the negative in front of the fraction.

$\frac{5}{2 + 4 (- \frac{2}{5})}$

Step 5.4

Multiply $4 (- \frac{2}{5})$ .

Tap for more steps...

Step 5.4.1

Multiply $- 1$ by $4$ .

$\frac{5}{2 - 4 (\frac{2}{5})}$

Step 5.4.2

Combine $- 4$ and $\frac{2}{5}$ .

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

Step 5.4.3

Multiply $- 4$ by $2$ .

$\frac{5}{2 + \frac{- 8}{5}}$

Step 5.5

Move the negative in front of the fraction.

$\frac{5}{2 - \frac{8}{5}}$

Step 5.6

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

$\frac{5}{2 \cdot \frac{5}{5} - \frac{8}{5}}$

Step 5.7

Combine $2$ and $\frac{5}{5}$ .

$\frac{5}{\frac{2 \cdot 5}{5} - \frac{8}{5}}$

Step 5.8

Combine the numerators over the common denominator.

$\frac{5}{\frac{2 \cdot 5 - 8}{5}}$

Step 5.9

Simplify the numerator.

Tap for more steps...

Step 5.9.1

Multiply $2$ by $5$ .

$\frac{5}{\frac{10 - 8}{5}}$

Step 5.9.2

Subtract $8$ from $10$ .

$\frac{5}{\frac{2}{5}}$

Step 6

Multiply the numerator by the reciprocal of the denominator.

$5 (\frac{5}{2})$

Step 7

Multiply $5 (\frac{5}{2})$ .

Tap for more steps...

Step 7.1

Combine $5$ and $\frac{5}{2}$ .

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

Step 7.2

Multiply $5$ by $5$ .

$\frac{25}{2}$

Step 8

The result can be shown in multiple forms.

Exact Form:

$\frac{25}{2}$

Decimal Form:

$12.5$

Mixed Number Form:

$12 \frac{1}{2}$