Basic Math Examples

${(- \frac{7}{6})}^{2} - 3 (\frac{1}{12} - \frac{1}{3})$

Step 1

Simplify each term.

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Step 1.1

Use the power rule ${(a b)}^{n} = a^{n} b^{n}$ to distribute the exponent.

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Step 1.1.1

Apply the product rule to $- \frac{7}{6}$ .

${(- 1)}^{2} {(\frac{7}{6})}^{2} - 3 (\frac{1}{12} - \frac{1}{3})$

Step 1.1.2

Apply the product rule to $\frac{7}{6}$ .

${(- 1)}^{2} \frac{7^{2}}{6^{2}} - 3 (\frac{1}{12} - \frac{1}{3})$

Step 1.2

Raise $- 1$ to the power of $2$ .

$1 \frac{7^{2}}{6^{2}} - 3 (\frac{1}{12} - \frac{1}{3})$

Step 1.3

Multiply $\frac{7^{2}}{6^{2}}$ by $1$ .

$\frac{7^{2}}{6^{2}} - 3 (\frac{1}{12} - \frac{1}{3})$

Step 1.4

Raise $7$ to the power of $2$ .

$\frac{49}{6^{2}} - 3 (\frac{1}{12} - \frac{1}{3})$

Step 1.5

Raise $6$ to the power of $2$ .

$\frac{49}{36} - 3 (\frac{1}{12} - \frac{1}{3})$

Step 1.6

To write $- \frac{1}{3}$ as a fraction with a common denominator, multiply by $\frac{4}{4}$ .

$\frac{49}{36} - 3 (\frac{1}{12} - \frac{1}{3} \cdot \frac{4}{4})$

Step 1.7

Write each expression with a common denominator of $12$ , by multiplying each by an appropriate factor of $1$ .

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Step 1.7.1

Multiply $\frac{1}{3}$ by $\frac{4}{4}$ .

$\frac{49}{36} - 3 (\frac{1}{12} - \frac{4}{3 \cdot 4})$

Step 1.7.2

Multiply $3$ by $4$ .

$\frac{49}{36} - 3 (\frac{1}{12} - \frac{4}{12})$

Step 1.8

Combine the numerators over the common denominator.

$\frac{49}{36} - 3 \frac{1 - 4}{12}$

Step 1.9

Subtract $4$ from $1$ .

$\frac{49}{36} - 3 (\frac{- 3}{12})$

Step 1.10

Cancel the common factor of $3$ .

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Step 1.10.1

Factor $3$ out of $- 3$ .

$\frac{49}{36} + 3 (- 1) \frac{- 3}{12}$

Step 1.10.2

Factor $3$ out of $12$ .

$\frac{49}{36} + 3 \cdot - 1 \frac{- 3}{3 \cdot 4}$

Step 1.10.3

Cancel the common factor.

$\frac{49}{36} + 3 \cdot - 1 \frac{- 3}{3 \cdot 4}$

Step 1.10.4

Rewrite the expression.

$\frac{49}{36} - 1 (\frac{- 3}{4})$

Step 1.11

Move the negative in front of the fraction.

$\frac{49}{36} - 1 (- \frac{3}{4})$

Step 1.12

Multiply $- 1 (- \frac{3}{4})$ .

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Step 1.12.1

Multiply $- 1$ by $- 1$ .

$\frac{49}{36} + 1 (\frac{3}{4})$

Step 1.12.2

Multiply $\frac{3}{4}$ by $1$ .

$\frac{49}{36} + \frac{3}{4}$

Step 2

To write $\frac{3}{4}$ as a fraction with a common denominator, multiply by $\frac{9}{9}$ .

$\frac{49}{36} + \frac{3}{4} \cdot \frac{9}{9}$

Step 3

Write each expression with a common denominator of $36$ , by multiplying each by an appropriate factor of $1$ .

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Step 3.1

Multiply $\frac{3}{4}$ by $\frac{9}{9}$ .

$\frac{49}{36} + \frac{3 \cdot 9}{4 \cdot 9}$

Step 3.2

Multiply $4$ by $9$ .

$\frac{49}{36} + \frac{3 \cdot 9}{36}$

Step 4

Combine the numerators over the common denominator.

$\frac{49 + 3 \cdot 9}{36}$

Step 5

Simplify the numerator.

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Step 5.1

Multiply $3$ by $9$ .

$\frac{49 + 27}{36}$

Step 5.2

Add $49$ and $27$ .

$\frac{76}{36}$

Step 6

Cancel the common factor of $76$ and $36$ .

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Step 6.1

Factor $4$ out of $76$ .

$\frac{4 (19)}{36}$

Step 6.2

Cancel the common factors.

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Step 6.2.1

Factor $4$ out of $36$ .

$\frac{4 \cdot 19}{4 \cdot 9}$

Step 6.2.2

Cancel the common factor.

$\frac{4 \cdot 19}{4 \cdot 9}$

Step 6.2.3

Rewrite the expression.

$\frac{19}{9}$

Step 7

The result can be shown in multiple forms.

Exact Form:

$\frac{19}{9}$

Decimal Form:

$2.\overline{1}$

Mixed Number Form:

$2 \frac{1}{9}$