Basic Math Examples

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

Step 1

Find the common denominator.

Tap for more steps...

Step 1.1

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

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

Step 1.2

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

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

Step 1.3

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

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

Step 1.4

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

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

Step 1.5

Write $- (\frac{6}{4} + \frac{4}{6})$ as a fraction with denominator $1$ .

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

Step 1.6

Multiply $\frac{- (\frac{6}{4} + \frac{4}{6})}{1}$ by $\frac{6}{6}$ .

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

Step 1.7

Multiply $\frac{- (\frac{6}{4} + \frac{4}{6})}{1}$ by $\frac{6}{6}$ .

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

Step 1.8

Reorder the factors of $3 \cdot 2$ .

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

Step 1.9

Multiply $2$ by $3$ .

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

Step 1.10

Multiply $2$ by $3$ .

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

Step 2

Combine the numerators over the common denominator.

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

Step 3

Simplify each term.

Tap for more steps...

Step 3.1

Multiply $2$ by $2$ .

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

Step 3.2

Multiply $3$ by $3$ .

$\frac{4 + 9 - (\frac{6}{4} + \frac{4}{6}) \cdot 6}{6}$

Step 3.3

Simplify each term.

Tap for more steps...

Step 3.3.1

Cancel the common factor of $6$ and $4$ .

Tap for more steps...

Step 3.3.1.1

Factor $2$ out of $6$ .

$\frac{4 + 9 - (\frac{2 (3)}{4} + \frac{4}{6}) \cdot 6}{6}$

Step 3.3.1.2

Cancel the common factors.

Tap for more steps...

Step 3.3.1.2.1

Factor $2$ out of $4$ .

$\frac{4 + 9 - (\frac{2 \cdot 3}{2 \cdot 2} + \frac{4}{6}) \cdot 6}{6}$

Step 3.3.1.2.2

Cancel the common factor.

$\frac{4 + 9 - (\frac{2 \cdot 3}{2 \cdot 2} + \frac{4}{6}) \cdot 6}{6}$

Step 3.3.1.2.3

Rewrite the expression.

$\frac{4 + 9 - (\frac{3}{2} + \frac{4}{6}) \cdot 6}{6}$

Step 3.3.2

Cancel the common factor of $4$ and $6$ .

Tap for more steps...

Step 3.3.2.1

Factor $2$ out of $4$ .

$\frac{4 + 9 - (\frac{3}{2} + \frac{2 (2)}{6}) \cdot 6}{6}$

Step 3.3.2.2

Cancel the common factors.

Tap for more steps...

Step 3.3.2.2.1

Factor $2$ out of $6$ .

$\frac{4 + 9 - (\frac{3}{2} + \frac{2 \cdot 2}{2 \cdot 3}) \cdot 6}{6}$

Step 3.3.2.2.2

Cancel the common factor.

$\frac{4 + 9 - (\frac{3}{2} + \frac{2 \cdot 2}{2 \cdot 3}) \cdot 6}{6}$

Step 3.3.2.2.3

Rewrite the expression.

$\frac{4 + 9 - (\frac{3}{2} + \frac{2}{3}) \cdot 6}{6}$

Step 3.4

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

$\frac{4 + 9 - (\frac{3}{2} \cdot \frac{3}{3} + \frac{2}{3}) \cdot 6}{6}$

Step 3.5

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

$\frac{4 + 9 - (\frac{3}{2} \cdot \frac{3}{3} + \frac{2}{3} \cdot \frac{2}{2}) \cdot 6}{6}$

Step 3.6

Write each expression with a common denominator of $6$ , by multiplying each by an appropriate factor of $1$ .

Tap for more steps...

Step 3.6.1

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

$\frac{4 + 9 - (\frac{3 \cdot 3}{2 \cdot 3} + \frac{2}{3} \cdot \frac{2}{2}) \cdot 6}{6}$

Step 3.6.2

Multiply $2$ by $3$ .

$\frac{4 + 9 - (\frac{3 \cdot 3}{6} + \frac{2}{3} \cdot \frac{2}{2}) \cdot 6}{6}$

Step 3.6.3

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

$\frac{4 + 9 - (\frac{3 \cdot 3}{6} + \frac{2 \cdot 2}{3 \cdot 2}) \cdot 6}{6}$

Step 3.6.4

Multiply $3$ by $2$ .

$\frac{4 + 9 - (\frac{3 \cdot 3}{6} + \frac{2 \cdot 2}{6}) \cdot 6}{6}$

Step 3.7

Combine the numerators over the common denominator.

$\frac{4 + 9 - \frac{3 \cdot 3 + 2 \cdot 2}{6} \cdot 6}{6}$

Step 3.8

Simplify the numerator.

Tap for more steps...

Step 3.8.1

Multiply $3$ by $3$ .

$\frac{4 + 9 - \frac{9 + 2 \cdot 2}{6} \cdot 6}{6}$

Step 3.8.2

Multiply $2$ by $2$ .

$\frac{4 + 9 - \frac{9 + 4}{6} \cdot 6}{6}$

Step 3.8.3

Add $9$ and $4$ .

$\frac{4 + 9 - \frac{13}{6} \cdot 6}{6}$

Step 3.9

Cancel the common factor of $6$ .

Tap for more steps...

Step 3.9.1

Move the leading negative in $- \frac{13}{6}$ into the numerator.

$\frac{4 + 9 + \frac{- 13}{6} \cdot 6}{6}$

Step 3.9.2

Cancel the common factor.

$\frac{4 + 9 + \frac{- 13}{6} \cdot 6}{6}$

Step 3.9.3

Rewrite the expression.

$\frac{4 + 9 - 13}{6}$

Step 4

Simplify the expression.

Tap for more steps...

Step 4.1

Add $4$ and $9$ .

$\frac{13 - 13}{6}$

Step 4.2

Subtract $13$ from $13$ .

$\frac{0}{6}$

Step 4.3

Divide $0$ by $6$ .

$0$