Basic Math Examples

$\frac{1}{5} \cdot {(\frac{6}{12})}^{2} - \frac{3}{4}$

Step 1

Simplify each term.

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Step 1.1

Cancel the common factor of $6$ and $12$ .

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Step 1.1.1

Factor $6$ out of $6$ .

$\frac{1}{5} \cdot {(\frac{6 (1)}{12})}^{2} - \frac{3}{4}$

Step 1.1.2

Cancel the common factors.

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Step 1.1.2.1

Factor $6$ out of $12$ .

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

Step 1.1.2.2

Cancel the common factor.

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

Step 1.1.2.3

Rewrite the expression.

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

Step 1.2

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

$\frac{1}{5} \cdot \frac{1^{2}}{2^{2}} - \frac{3}{4}$

Step 1.3

Combine.

$\frac{1 \cdot 1^{2}}{5 \cdot 2^{2}} - \frac{3}{4}$

Step 1.4

Multiply $1$ by $1^{2}$ by adding the exponents.

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Step 1.4.1

Multiply $1$ by $1^{2}$ .

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Step 1.4.1.1

Raise $1$ to the power of $1$ .

$\frac{1^{1} \cdot 1^{2}}{5 \cdot 2^{2}} - \frac{3}{4}$

Step 1.4.1.2

Use the power rule $a^{m} a^{n} = a^{m + n}$ to combine exponents.

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

Step 1.4.2

Add $1$ and $2$ .

$\frac{1^{3}}{5 \cdot 2^{2}} - \frac{3}{4}$

Step 1.5

One to any power is one.

$\frac{1}{5 \cdot 2^{2}} - \frac{3}{4}$

Step 1.6

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

$\frac{1}{5 \cdot 4} - \frac{3}{4}$

Step 1.7

Multiply $5$ by $4$ .

$\frac{1}{20} - \frac{3}{4}$

Step 2

To write $- \frac{3}{4}$ as a fraction with a common denominator, multiply by $\frac{5}{5}$ .

$\frac{1}{20} - \frac{3}{4} \cdot \frac{5}{5}$

Step 3

Write each expression with a common denominator of $20$ , by multiplying each by an appropriate factor of $1$ .

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Step 3.1

Multiply $\frac{3}{4}$ by $\frac{5}{5}$ .

$\frac{1}{20} - \frac{3 \cdot 5}{4 \cdot 5}$

Step 3.2

Multiply $4$ by $5$ .

$\frac{1}{20} - \frac{3 \cdot 5}{20}$

Step 4

Combine the numerators over the common denominator.

$\frac{1 - 3 \cdot 5}{20}$

Step 5

Simplify the numerator.

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Step 5.1

Multiply $- 3$ by $5$ .

$\frac{1 - 15}{20}$

Step 5.2

Subtract $15$ from $1$ .

$\frac{- 14}{20}$

Step 6

Cancel the common factor of $- 14$ and $20$ .

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Step 6.1

Factor $2$ out of $- 14$ .

$\frac{2 (- 7)}{20}$

Step 6.2

Cancel the common factors.

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Step 6.2.1

Factor $2$ out of $20$ .

$\frac{2 \cdot - 7}{2 \cdot 10}$

Step 6.2.2

Cancel the common factor.

$\frac{2 \cdot - 7}{2 \cdot 10}$

Step 6.2.3

Rewrite the expression.

$\frac{- 7}{10}$

Step 7

Move the negative in front of the fraction.

$- \frac{7}{10}$

Step 8

The result can be shown in multiple forms.

Exact Form:

$- \frac{7}{10}$

Decimal Form:

$- 0.7$