Basic Math Examples

${(\frac{1}{2})}^{3} + \frac{1}{4} - (\frac{1}{15} - \frac{1}{20}) - \frac{2}{5} \cdot {(\frac{1}{4})}^{2}$

Step 1

Simplify each term.

Tap for more steps...

Step 1.1

Apply the product rule to $\frac{1}{2}$ .

$\frac{1^{3}}{2^{3}} + \frac{1}{4} - (\frac{1}{15} - \frac{1}{20}) - \frac{2}{5} \cdot {(\frac{1}{4})}^{2}$

Step 1.2

One to any power is one.

$\frac{1}{2^{3}} + \frac{1}{4} - (\frac{1}{15} - \frac{1}{20}) - \frac{2}{5} \cdot {(\frac{1}{4})}^{2}$

Step 1.3

Raise $2$ to the power of $3$ .

$\frac{1}{8} + \frac{1}{4} - (\frac{1}{15} - \frac{1}{20}) - \frac{2}{5} \cdot {(\frac{1}{4})}^{2}$

Step 1.4

To write $\frac{1}{15}$ as a fraction with a common denominator, multiply by $\frac{4}{4}$ .

$\frac{1}{8} + \frac{1}{4} - (\frac{1}{15} \cdot \frac{4}{4} - \frac{1}{20}) - \frac{2}{5} \cdot {(\frac{1}{4})}^{2}$

Step 1.5

To write $- \frac{1}{20}$ as a fraction with a common denominator, multiply by $\frac{3}{3}$ .

$\frac{1}{8} + \frac{1}{4} - (\frac{1}{15} \cdot \frac{4}{4} - \frac{1}{20} \cdot \frac{3}{3}) - \frac{2}{5} \cdot {(\frac{1}{4})}^{2}$

Step 1.6

Write each expression with a common denominator of $60$ , by multiplying each by an appropriate factor of $1$ .

Tap for more steps...

Step 1.6.1

Multiply $\frac{1}{15}$ by $\frac{4}{4}$ .

$\frac{1}{8} + \frac{1}{4} - (\frac{4}{15 \cdot 4} - \frac{1}{20} \cdot \frac{3}{3}) - \frac{2}{5} \cdot {(\frac{1}{4})}^{2}$

Step 1.6.2

Multiply $15$ by $4$ .

$\frac{1}{8} + \frac{1}{4} - (\frac{4}{60} - \frac{1}{20} \cdot \frac{3}{3}) - \frac{2}{5} \cdot {(\frac{1}{4})}^{2}$

Step 1.6.3

Multiply $\frac{1}{20}$ by $\frac{3}{3}$ .

$\frac{1}{8} + \frac{1}{4} - (\frac{4}{60} - \frac{3}{20 \cdot 3}) - \frac{2}{5} \cdot {(\frac{1}{4})}^{2}$

Step 1.6.4

Multiply $20$ by $3$ .

$\frac{1}{8} + \frac{1}{4} - (\frac{4}{60} - \frac{3}{60}) - \frac{2}{5} \cdot {(\frac{1}{4})}^{2}$

Step 1.7

Combine the numerators over the common denominator.

$\frac{1}{8} + \frac{1}{4} - \frac{4 - 3}{60} - \frac{2}{5} \cdot {(\frac{1}{4})}^{2}$

Step 1.8

Subtract $3$ from $4$ .

$\frac{1}{8} + \frac{1}{4} - \frac{1}{60} - \frac{2}{5} \cdot {(\frac{1}{4})}^{2}$

Step 1.9

Apply the product rule to $\frac{1}{4}$ .

$\frac{1}{8} + \frac{1}{4} - \frac{1}{60} - \frac{2}{5} \cdot \frac{1^{2}}{4^{2}}$

Step 1.10

One to any power is one.

$\frac{1}{8} + \frac{1}{4} - \frac{1}{60} - \frac{2}{5} \cdot \frac{1}{4^{2}}$

Step 1.11

Raise $4$ to the power of $2$ .

$\frac{1}{8} + \frac{1}{4} - \frac{1}{60} - \frac{2}{5} \cdot \frac{1}{16}$

Step 1.12

Cancel the common factor of $2$ .

Tap for more steps...

Step 1.12.1

Move the leading negative in $- \frac{2}{5}$ into the numerator.

$\frac{1}{8} + \frac{1}{4} - \frac{1}{60} + \frac{- 2}{5} \cdot \frac{1}{16}$

Step 1.12.2

Factor $2$ out of $- 2$ .

$\frac{1}{8} + \frac{1}{4} - \frac{1}{60} + \frac{2 (- 1)}{5} \cdot \frac{1}{16}$

Step 1.12.3

Factor $2$ out of $16$ .

$\frac{1}{8} + \frac{1}{4} - \frac{1}{60} + \frac{2 \cdot - 1}{5} \cdot \frac{1}{2 \cdot 8}$

Step 1.12.4

Cancel the common factor.

$\frac{1}{8} + \frac{1}{4} - \frac{1}{60} + \frac{2 \cdot - 1}{5} \cdot \frac{1}{2 \cdot 8}$

Step 1.12.5

Rewrite the expression.

$\frac{1}{8} + \frac{1}{4} - \frac{1}{60} + \frac{- 1}{5} \cdot \frac{1}{8}$

Step 1.13

Multiply $\frac{- 1}{5}$ by $\frac{1}{8}$ .

$\frac{1}{8} + \frac{1}{4} - \frac{1}{60} + \frac{- 1}{5 \cdot 8}$

Step 1.14

Multiply $5$ by $8$ .

$\frac{1}{8} + \frac{1}{4} - \frac{1}{60} + \frac{- 1}{40}$

Step 1.15

Move the negative in front of the fraction.

$\frac{1}{8} + \frac{1}{4} - \frac{1}{60} - \frac{1}{40}$

Step 2

Find the common denominator.

Tap for more steps...

Step 2.1

Multiply $\frac{1}{8}$ by $\frac{15}{15}$ .

$\frac{1}{8} \cdot \frac{15}{15} + \frac{1}{4} - \frac{1}{60} - \frac{1}{40}$

Step 2.2

Multiply $\frac{1}{8}$ by $\frac{15}{15}$ .

$\frac{15}{8 \cdot 15} + \frac{1}{4} - \frac{1}{60} - \frac{1}{40}$

Step 2.3

Multiply $\frac{1}{4}$ by $\frac{30}{30}$ .

$\frac{15}{8 \cdot 15} + \frac{1}{4} \cdot \frac{30}{30} - \frac{1}{60} - \frac{1}{40}$

Step 2.4

Multiply $\frac{1}{4}$ by $\frac{30}{30}$ .

$\frac{15}{8 \cdot 15} + \frac{30}{4 \cdot 30} - \frac{1}{60} - \frac{1}{40}$

Step 2.5

Multiply $\frac{1}{60}$ by $\frac{2}{2}$ .

$\frac{15}{8 \cdot 15} + \frac{30}{4 \cdot 30} - (\frac{1}{60} \cdot \frac{2}{2}) - \frac{1}{40}$

Step 2.6

Multiply $\frac{1}{60}$ by $\frac{2}{2}$ .

$\frac{15}{8 \cdot 15} + \frac{30}{4 \cdot 30} - \frac{2}{60 \cdot 2} - \frac{1}{40}$

Step 2.7

Multiply $\frac{1}{40}$ by $\frac{3}{3}$ .

$\frac{15}{8 \cdot 15} + \frac{30}{4 \cdot 30} - \frac{2}{60 \cdot 2} - (\frac{1}{40} \cdot \frac{3}{3})$

Step 2.8

Multiply $\frac{1}{40}$ by $\frac{3}{3}$ .

$\frac{15}{8 \cdot 15} + \frac{30}{4 \cdot 30} - \frac{2}{60 \cdot 2} - \frac{3}{40 \cdot 3}$

Step 2.9

Multiply $8$ by $15$ .

$\frac{15}{120} + \frac{30}{4 \cdot 30} - \frac{2}{60 \cdot 2} - \frac{3}{40 \cdot 3}$

Step 2.10

Multiply $4$ by $30$ .

$\frac{15}{120} + \frac{30}{120} - \frac{2}{60 \cdot 2} - \frac{3}{40 \cdot 3}$

Step 2.11

Reorder the factors of $60 \cdot 2$ .

$\frac{15}{120} + \frac{30}{120} - \frac{2}{2 \cdot 60} - \frac{3}{40 \cdot 3}$

Step 2.12

Multiply $2$ by $60$ .

$\frac{15}{120} + \frac{30}{120} - \frac{2}{120} - \frac{3}{40 \cdot 3}$

Step 2.13

Reorder the factors of $40 \cdot 3$ .

$\frac{15}{120} + \frac{30}{120} - \frac{2}{120} - \frac{3}{3 \cdot 40}$

Step 2.14

Multiply $3$ by $40$ .

$\frac{15}{120} + \frac{30}{120} - \frac{2}{120} - \frac{3}{120}$

Step 3

Combine the numerators over the common denominator.

$\frac{15 + 30 - 2 - 3}{120}$

Step 4

Simplify by adding and subtracting.

Tap for more steps...

Step 4.1

Add $15$ and $30$ .

$\frac{45 - 2 - 3}{120}$

Step 4.2

Subtract $2$ from $45$ .

$\frac{43 - 3}{120}$

Step 4.3

Subtract $3$ from $43$ .

$\frac{40}{120}$

Step 5

Cancel the common factor of $40$ and $120$ .

Tap for more steps...

Step 5.1

Factor $40$ out of $40$ .

$\frac{40 (1)}{120}$

Step 5.2

Cancel the common factors.

Tap for more steps...

Step 5.2.1

Factor $40$ out of $120$ .

$\frac{40 \cdot 1}{40 \cdot 3}$

Step 5.2.2

Cancel the common factor.

$\frac{40 \cdot 1}{40 \cdot 3}$

Step 5.2.3

Rewrite the expression.

$\frac{1}{3}$

Step 6

The result can be shown in multiple forms.

Exact Form:

$\frac{1}{3}$

Decimal Form:

$0.\overline{3}$