Pre-Algebra Examples

${(\frac{6}{7})}^{2} - (\frac{1}{5} - \frac{1}{30}) \div \frac{7}{6}$

Step 1

Simplify each term.

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Step 1.1

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

$\frac{6^{2}}{7^{2}} - (\frac{1}{5} - \frac{1}{30}) \div \frac{7}{6}$

Step 1.2

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

$\frac{36}{7^{2}} - (\frac{1}{5} - \frac{1}{30}) \div \frac{7}{6}$

Step 1.3

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

$\frac{36}{49} - (\frac{1}{5} - \frac{1}{30}) \div \frac{7}{6}$

Step 1.4

To divide by a fraction, multiply by its reciprocal.

$\frac{36}{49} - ((\frac{1}{5} - \frac{1}{30}) \frac{6}{7})$

Step 1.5

To write $\frac{1}{5}$ as a fraction with a common denominator, multiply by $\frac{6}{6}$ .

$\frac{36}{49} - ((\frac{1}{5} \cdot \frac{6}{6} - \frac{1}{30}) \frac{6}{7})$

Step 1.6

Write each expression with a common denominator of $30$ , by multiplying each by an appropriate factor of $1$ .

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Step 1.6.1

Multiply $\frac{1}{5}$ by $\frac{6}{6}$ .

$\frac{36}{49} - ((\frac{6}{5 \cdot 6} - \frac{1}{30}) \frac{6}{7})$

Step 1.6.2

Multiply $5$ by $6$ .

$\frac{36}{49} - ((\frac{6}{30} - \frac{1}{30}) \frac{6}{7})$

Step 1.7

Combine the numerators over the common denominator.

$\frac{36}{49} - (\frac{6 - 1}{30} \cdot \frac{6}{7})$

Step 1.8

Subtract $1$ from $6$ .

$\frac{36}{49} - (\frac{5}{30} \cdot \frac{6}{7})$

Step 1.9

Cancel the common factor of $6$ .

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Step 1.9.1

Factor $6$ out of $30$ .

$\frac{36}{49} - (\frac{5}{6 (5)} \cdot \frac{6}{7})$

Step 1.9.2

Cancel the common factor.

$\frac{36}{49} - (\frac{5}{6 \cdot 5} \cdot \frac{6}{7})$

Step 1.9.3

Rewrite the expression.

$\frac{36}{49} - (\frac{5}{5} \cdot \frac{1}{7})$

Step 1.10

Multiply $\frac{5}{5}$ by $\frac{1}{7}$ .

$\frac{36}{49} - \frac{5}{5 \cdot 7}$

Step 1.11

Multiply $5$ by $7$ .

$\frac{36}{49} - \frac{5}{35}$

Step 1.12

Cancel the common factor of $5$ and $35$ .

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Step 1.12.1

Factor $5$ out of $5$ .

$\frac{36}{49} - \frac{5 (1)}{35}$

Step 1.12.2

Cancel the common factors.

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Step 1.12.2.1

Factor $5$ out of $35$ .

$\frac{36}{49} - \frac{5 \cdot 1}{5 \cdot 7}$

Step 1.12.2.2

Cancel the common factor.

$\frac{36}{49} - \frac{5 \cdot 1}{5 \cdot 7}$

Step 1.12.2.3

Rewrite the expression.

$\frac{36}{49} - \frac{1}{7}$

Step 2

To write $- \frac{1}{7}$ as a fraction with a common denominator, multiply by $\frac{7}{7}$ .

$\frac{36}{49} - \frac{1}{7} \cdot \frac{7}{7}$

Step 3

Write each expression with a common denominator of $49$ , by multiplying each by an appropriate factor of $1$ .

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Step 3.1

Multiply $\frac{1}{7}$ by $\frac{7}{7}$ .

$\frac{36}{49} - \frac{7}{7 \cdot 7}$

Step 3.2

Multiply $7$ by $7$ .

$\frac{36}{49} - \frac{7}{49}$

Step 4

Combine the numerators over the common denominator.

$\frac{36 - 7}{49}$

Step 5

Subtract $7$ from $36$ .

$\frac{29}{49}$

Step 6

The result can be shown in multiple forms.

Exact Form:

$\frac{29}{49}$

Decimal Form:

$0.59183673 \dots$