Basic Math Examples

$(\frac{3}{2} + \frac{1}{8}) - (\frac{1}{4} + \frac{1}{8})$

Step 1

Find the common denominator.

Tap for more steps...

Step 1.1

Multiply $\frac{3}{2}$ by $\frac{4}{4}$ .

$\frac{3}{2} \cdot \frac{4}{4} + \frac{1}{8} - (\frac{1}{4} + \frac{1}{8})$

Step 1.2

Multiply $\frac{3}{2}$ by $\frac{4}{4}$ .

$\frac{3 \cdot 4}{2 \cdot 4} + \frac{1}{8} - (\frac{1}{4} + \frac{1}{8})$

Step 1.3

Write $- (\frac{1}{4} + \frac{1}{8})$ as a fraction with denominator $1$ .

$\frac{3 \cdot 4}{2 \cdot 4} + \frac{1}{8} + \frac{- (\frac{1}{4} + \frac{1}{8})}{1}$

Step 1.4

Multiply $\frac{- (\frac{1}{4} + \frac{1}{8})}{1}$ by $\frac{8}{8}$ .

$\frac{3 \cdot 4}{2 \cdot 4} + \frac{1}{8} + \frac{- (\frac{1}{4} + \frac{1}{8})}{1} \cdot \frac{8}{8}$

Step 1.5

Multiply $\frac{- (\frac{1}{4} + \frac{1}{8})}{1}$ by $\frac{8}{8}$ .

$\frac{3 \cdot 4}{2 \cdot 4} + \frac{1}{8} + \frac{- (\frac{1}{4} + \frac{1}{8}) \cdot 8}{8}$

Step 1.6

Multiply $2$ by $4$ .

$\frac{3 \cdot 4}{8} + \frac{1}{8} + \frac{- (\frac{1}{4} + \frac{1}{8}) \cdot 8}{8}$

Step 2

Combine the numerators over the common denominator.

$\frac{3 \cdot 4 + 1 - (\frac{1}{4} + \frac{1}{8}) \cdot 8}{8}$

Step 3

Simplify each term.

Tap for more steps...

Step 3.1

Multiply $3$ by $4$ .

$\frac{12 + 1 - (\frac{1}{4} + \frac{1}{8}) \cdot 8}{8}$

Step 3.2

To write $\frac{1}{4}$ as a fraction with a common denominator, multiply by $\frac{2}{2}$ .

$\frac{12 + 1 - (\frac{1}{4} \cdot \frac{2}{2} + \frac{1}{8}) \cdot 8}{8}$

Step 3.3

Write each expression with a common denominator of $8$ , by multiplying each by an appropriate factor of $1$ .

Tap for more steps...

Step 3.3.1

Multiply $\frac{1}{4}$ by $\frac{2}{2}$ .

$\frac{12 + 1 - (\frac{2}{4 \cdot 2} + \frac{1}{8}) \cdot 8}{8}$

Step 3.3.2

Multiply $4$ by $2$ .

$\frac{12 + 1 - (\frac{2}{8} + \frac{1}{8}) \cdot 8}{8}$

Step 3.4

Combine the numerators over the common denominator.

$\frac{12 + 1 - \frac{2 + 1}{8} \cdot 8}{8}$

Step 3.5

Add $2$ and $1$ .

$\frac{12 + 1 - \frac{3}{8} \cdot 8}{8}$

Step 3.6

Cancel the common factor of $8$ .

Tap for more steps...

Step 3.6.1

Move the leading negative in $- \frac{3}{8}$ into the numerator.

$\frac{12 + 1 + \frac{- 3}{8} \cdot 8}{8}$

Step 3.6.2

Cancel the common factor.

$\frac{12 + 1 + \frac{- 3}{8} \cdot 8}{8}$

Step 3.6.3

Rewrite the expression.

$\frac{12 + 1 - 3}{8}$

Step 4

Reduce the expression by cancelling the common factors.

Tap for more steps...

Step 4.1

Add $12$ and $1$ .

$\frac{13 - 3}{8}$

Step 4.2

Subtract $3$ from $13$ .

$\frac{10}{8}$

Step 4.3

Cancel the common factor of $10$ and $8$ .

Tap for more steps...

Step 4.3.1

Factor $2$ out of $10$ .

$\frac{2 (5)}{8}$

Step 4.3.2

Cancel the common factors.

Tap for more steps...

Step 4.3.2.1

Factor $2$ out of $8$ .

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

Step 4.3.2.2

Cancel the common factor.

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

Step 4.3.2.3

Rewrite the expression.

$\frac{5}{4}$

Step 5

The result can be shown in multiple forms.

Exact Form:

$\frac{5}{4}$

Decimal Form:

$1.25$

Mixed Number Form:

$1 \frac{1}{4}$