Basic Math Examples

$\frac{3}{8} - (- \frac{1}{6} - \frac{5}{2})$

Step 1

Simplify each term.

Tap for more steps...

Step 1.1

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

$\frac{3}{8} - (- \frac{1}{6} - \frac{5}{2} \cdot \frac{3}{3})$

Step 1.2

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

Tap for more steps...

Step 1.2.1

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

$\frac{3}{8} - (- \frac{1}{6} - \frac{5 \cdot 3}{2 \cdot 3})$

Step 1.2.2

Multiply $2$ by $3$ .

$\frac{3}{8} - (- \frac{1}{6} - \frac{5 \cdot 3}{6})$

Step 1.3

Combine the numerators over the common denominator.

$\frac{3}{8} - \frac{- 1 - 5 \cdot 3}{6}$

Step 1.4

Simplify the numerator.

Tap for more steps...

Step 1.4.1

Multiply $- 5$ by $3$ .

$\frac{3}{8} - \frac{- 1 - 15}{6}$

Step 1.4.2

Subtract $15$ from $- 1$ .

$\frac{3}{8} - \frac{- 16}{6}$

Step 1.5

Cancel the common factor of $- 16$ and $6$ .

Tap for more steps...

Step 1.5.1

Factor $2$ out of $- 16$ .

$\frac{3}{8} - \frac{2 (- 8)}{6}$

Step 1.5.2

Cancel the common factors.

Tap for more steps...

Step 1.5.2.1

Factor $2$ out of $6$ .

$\frac{3}{8} - \frac{2 \cdot - 8}{2 \cdot 3}$

Step 1.5.2.2

Cancel the common factor.

$\frac{3}{8} - \frac{2 \cdot - 8}{2 \cdot 3}$

Step 1.5.2.3

Rewrite the expression.

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

Step 1.6

Move the negative in front of the fraction.

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

Step 1.7

Multiply $- - \frac{8}{3}$ .

Tap for more steps...

Step 1.7.1

Multiply $- 1$ by $- 1$ .

$\frac{3}{8} + 1 (\frac{8}{3})$

Step 1.7.2

Multiply $\frac{8}{3}$ by $1$ .

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

Step 2

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

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

Step 3

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

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

Step 4

Write each expression with a common denominator of $24$ , by multiplying each by an appropriate factor of $1$ .

Tap for more steps...

Step 4.1

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

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

Step 4.2

Multiply $8$ by $3$ .

$\frac{3 \cdot 3}{24} + \frac{8}{3} \cdot \frac{8}{8}$

Step 4.3

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

$\frac{3 \cdot 3}{24} + \frac{8 \cdot 8}{3 \cdot 8}$

Step 4.4

Multiply $3$ by $8$ .

$\frac{3 \cdot 3}{24} + \frac{8 \cdot 8}{24}$

Step 5

Combine the numerators over the common denominator.

$\frac{3 \cdot 3 + 8 \cdot 8}{24}$

Step 6

Simplify the numerator.

Tap for more steps...

Step 6.1

Multiply $3$ by $3$ .

$\frac{9 + 8 \cdot 8}{24}$

Step 6.2

Multiply $8$ by $8$ .

$\frac{9 + 64}{24}$

Step 6.3

Add $9$ and $64$ .

$\frac{73}{24}$