Basic Math Examples

$\frac{15}{14} \cdot (- \frac{2}{3}) \div (\frac{1}{4} - \frac{2}{3}) \div \sqrt{\frac{64}{4}}$

Step 1

Rewrite the division as a fraction.

$\frac{\frac{15}{14} \cdot (- \frac{2}{3}) \div (\frac{1}{4} - \frac{2}{3})}{\sqrt{\frac{64}{4}}}$

Step 2

Cancel the common factor of $64$ and $4$ .

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Step 2.1

Factor $4$ out of $64$ .

$\frac{\frac{15}{14} \cdot (- \frac{2}{3}) \div (\frac{1}{4} - \frac{2}{3})}{\sqrt{\frac{4 \cdot 16}{4}}}$

Step 2.2

Cancel the common factors.

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Step 2.2.1

Factor $4$ out of $4$ .

$\frac{\frac{15}{14} \cdot (- \frac{2}{3}) \div (\frac{1}{4} - \frac{2}{3})}{\sqrt{\frac{4 \cdot 16}{4 (1)}}}$

Step 2.2.2

Cancel the common factor.

$\frac{\frac{15}{14} \cdot (- \frac{2}{3}) \div (\frac{1}{4} - \frac{2}{3})}{\sqrt{\frac{4 \cdot 16}{4 \cdot 1}}}$

Step 2.2.3

Rewrite the expression.

$\frac{\frac{15}{14} \cdot (- \frac{2}{3}) \div (\frac{1}{4} - \frac{2}{3})}{\sqrt{\frac{16}{1}}}$

Step 2.2.4

Divide $16$ by $1$ .

$\frac{\frac{15}{14} \cdot (- \frac{2}{3}) \div (\frac{1}{4} - \frac{2}{3})}{\sqrt{16}}$

Step 3

Multiply the numerator by the reciprocal of the denominator.

$\frac{15}{14} \cdot - 1 \frac{2}{3} \div (\frac{1}{4} - \frac{2}{3}) \cdot \frac{1}{\sqrt{16}}$

Step 4

Rewrite the division as a fraction.

$\frac{\frac{15}{14} \cdot - 1 \frac{2}{3}}{\frac{1}{4} - \frac{2}{3}} \cdot \frac{1}{\sqrt{16}}$

Step 5

Simplify the numerator.

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Step 5.1

Combine $\frac{15}{14}$ and $- 1$ .

$\frac{\frac{15 \cdot - 1}{14} \cdot \frac{2}{3}}{\frac{1}{4} - \frac{2}{3}} \cdot \frac{1}{\sqrt{16}}$

Step 5.2

Multiply $\frac{15 \cdot - 1}{14}$ by $\frac{2}{3}$ .

$\frac{\frac{15 \cdot - 1 \cdot 2}{14 \cdot 3}}{\frac{1}{4} - \frac{2}{3}} \cdot \frac{1}{\sqrt{16}}$

Step 6

Simplify the denominator.

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Step 6.1

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

$\frac{\frac{15 \cdot - 1 \cdot 2}{14 \cdot 3}}{\frac{1}{4} \cdot \frac{3}{3} - \frac{2}{3}} \cdot \frac{1}{\sqrt{16}}$

Step 6.2

To write $- \frac{2}{3}$ as a fraction with a common denominator, multiply by $\frac{4}{4}$ .

$\frac{\frac{15 \cdot - 1 \cdot 2}{14 \cdot 3}}{\frac{1}{4} \cdot \frac{3}{3} - \frac{2}{3} \cdot \frac{4}{4}} \cdot \frac{1}{\sqrt{16}}$

Step 6.3

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

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Step 6.3.1

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

$\frac{\frac{15 \cdot - 1 \cdot 2}{14 \cdot 3}}{\frac{3}{4 \cdot 3} - \frac{2}{3} \cdot \frac{4}{4}} \cdot \frac{1}{\sqrt{16}}$

Step 6.3.2

Multiply $4$ by $3$ .

$\frac{\frac{15 \cdot - 1 \cdot 2}{14 \cdot 3}}{\frac{3}{12} - \frac{2}{3} \cdot \frac{4}{4}} \cdot \frac{1}{\sqrt{16}}$

Step 6.3.3

Multiply $\frac{2}{3}$ by $\frac{4}{4}$ .

$\frac{\frac{15 \cdot - 1 \cdot 2}{14 \cdot 3}}{\frac{3}{12} - \frac{2 \cdot 4}{3 \cdot 4}} \cdot \frac{1}{\sqrt{16}}$

Step 6.3.4

Multiply $3$ by $4$ .

$\frac{\frac{15 \cdot - 1 \cdot 2}{14 \cdot 3}}{\frac{3}{12} - \frac{2 \cdot 4}{12}} \cdot \frac{1}{\sqrt{16}}$

Step 6.4

Combine the numerators over the common denominator.

$\frac{\frac{15 \cdot - 1 \cdot 2}{14 \cdot 3}}{\frac{3 - 2 \cdot 4}{12}} \cdot \frac{1}{\sqrt{16}}$

Step 6.5

Simplify the numerator.

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Step 6.5.1

Multiply $- 2$ by $4$ .

$\frac{\frac{15 \cdot - 1 \cdot 2}{14 \cdot 3}}{\frac{3 - 8}{12}} \cdot \frac{1}{\sqrt{16}}$

Step 6.5.2

Subtract $8$ from $3$ .

$\frac{\frac{15 \cdot - 1 \cdot 2}{14 \cdot 3}}{\frac{- 5}{12}} \cdot \frac{1}{\sqrt{16}}$

Step 6.6

Move the negative in front of the fraction.

$\frac{\frac{15 \cdot - 1 \cdot 2}{14 \cdot 3}}{- \frac{5}{12}} \cdot \frac{1}{\sqrt{16}}$

Step 7

Simplify the numerator.

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Step 7.1

Multiply $15$ by $- 1$ .

$\frac{\frac{- 15 \cdot 2}{14 \cdot 3}}{- \frac{5}{12}} \cdot \frac{1}{\sqrt{16}}$

Step 7.2

Multiply $- 15$ by $2$ .

$\frac{\frac{- 30}{14 \cdot 3}}{- \frac{5}{12}} \cdot \frac{1}{\sqrt{16}}$

Step 8

Multiply $14$ by $3$ .

$\frac{\frac{- 30}{42}}{- \frac{5}{12}} \cdot \frac{1}{\sqrt{16}}$

Step 9

Reduce the expression by cancelling the common factors.

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Step 9.1

Cancel the common factor of $- 30$ and $42$ .

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Step 9.1.1

Factor $6$ out of $- 30$ .

$\frac{\frac{6 (- 5)}{42}}{- \frac{5}{12}} \cdot \frac{1}{\sqrt{16}}$

Step 9.1.2

Cancel the common factors.

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Step 9.1.2.1

Factor $6$ out of $42$ .

$\frac{\frac{6 \cdot - 5}{6 \cdot 7}}{- \frac{5}{12}} \cdot \frac{1}{\sqrt{16}}$

Step 9.1.2.2

Cancel the common factor.

$\frac{\frac{6 \cdot - 5}{6 \cdot 7}}{- \frac{5}{12}} \cdot \frac{1}{\sqrt{16}}$

Step 9.1.2.3

Rewrite the expression.

$\frac{\frac{- 5}{7}}{- \frac{5}{12}} \cdot \frac{1}{\sqrt{16}}$

Step 9.2

Move the negative in front of the fraction.

$\frac{- \frac{5}{7}}{- \frac{5}{12}} \cdot \frac{1}{\sqrt{16}}$

Step 10

Dividing two negative values results in a positive value.

$\frac{\frac{5}{7}}{\frac{5}{12}} \cdot \frac{1}{\sqrt{16}}$

Step 11

Multiply the numerator by the reciprocal of the denominator.

$\frac{5}{7} \cdot \frac{12}{5} \frac{1}{\sqrt{16}}$

Step 12

Simplify terms.

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Step 12.1

Cancel the common factor of $5$ .

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Step 12.1.1

Cancel the common factor.

$\frac{5}{7} \cdot \frac{12}{5} \frac{1}{\sqrt{16}}$

Step 12.1.2

Rewrite the expression.

$\frac{1}{7} \cdot 12 \frac{1}{\sqrt{16}}$

Step 12.2

Combine $\frac{1}{7}$ and $12$ .

$\frac{12}{7} \cdot \frac{1}{\sqrt{16}}$

Step 13

Simplify the denominator.

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Step 13.1

Rewrite $16$ as $4^{2}$ .

$\frac{12}{7} \cdot \frac{1}{\sqrt{4^{2}}}$

Step 13.2

Pull terms out from under the radical, assuming positive real numbers.

$\frac{12}{7} \cdot \frac{1}{4}$

Step 14

Cancel the common factor of $4$ .

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Step 14.1

Factor $4$ out of $12$ .

$\frac{4 (3)}{7} \cdot \frac{1}{4}$

Step 14.2

Cancel the common factor.

$\frac{4 \cdot 3}{7} \cdot \frac{1}{4}$

Step 14.3

Rewrite the expression.

$\frac{3}{7}$

Step 15

The result can be shown in multiple forms.

Exact Form:

$\frac{3}{7}$

Decimal Form:

$0.\overline{428571}$