Basic Math Examples

$\frac{\frac{4 - \frac{2}{3}}{8 - \frac{2}{3}}}{4 \cdot \frac{7}{6} - 2 \cdot \frac{7}{12}}$

Step 1

Cancel the common factor of $4 - \frac{2}{3}$ and $8 - \frac{2}{3}$ .

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Step 1.1

Factor $2$ out of $4$ .

$\frac{\frac{2 \cdot 2 - \frac{2}{3}}{8 - \frac{2}{3}}}{4 \cdot \frac{7}{6} - 2 \cdot \frac{7}{12}}$

Step 1.2

Factor $2$ out of $- \frac{2}{3}$ .

$\frac{\frac{2 \cdot 2 + 2 (- \frac{1}{3})}{8 - \frac{2}{3}}}{4 \cdot \frac{7}{6} - 2 \cdot \frac{7}{12}}$

Step 1.3

Factor $2$ out of $2 (2) + 2 (- \frac{1}{3})$ .

$\frac{\frac{2 (2 - \frac{1}{3})}{8 - \frac{2}{3}}}{4 \cdot \frac{7}{6} - 2 \cdot \frac{7}{12}}$

Step 1.4

Cancel the common factors.

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Step 1.4.1

Factor $2$ out of $8$ .

$\frac{\frac{2 (2 - \frac{1}{3})}{2 (4) - \frac{2}{3}}}{4 \cdot \frac{7}{6} - 2 \cdot \frac{7}{12}}$

Step 1.4.2

Factor $2$ out of $- \frac{2}{3}$ .

$\frac{\frac{2 (2 - \frac{1}{3})}{2 (4) + 2 (- \frac{1}{3})}}{4 \cdot \frac{7}{6} - 2 \cdot \frac{7}{12}}$

Step 1.4.3

Factor $2$ out of $2 (4) + 2 (- \frac{1}{3})$ .

$\frac{\frac{2 (2 - \frac{1}{3})}{2 (4 - \frac{1}{3})}}{4 \cdot \frac{7}{6} - 2 \cdot \frac{7}{12}}$

Step 1.4.4

Cancel the common factor.

$\frac{\frac{2 (2 - \frac{1}{3})}{2 (4 - \frac{1}{3})}}{4 \cdot \frac{7}{6} - 2 \cdot \frac{7}{12}}$

Step 1.4.5

Rewrite the expression.

$\frac{\frac{2 - \frac{1}{3}}{4 - \frac{1}{3}}}{4 \cdot \frac{7}{6} - 2 \cdot \frac{7}{12}}$

Step 2

Multiply the numerator by the reciprocal of the denominator.

$\frac{2 - \frac{1}{3}}{4 - \frac{1}{3}} \cdot \frac{1}{4 \cdot \frac{7}{6} - 2 \cdot \frac{7}{12}}$

Step 3

Multiply the numerator and denominator of the fraction by $3$ .

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Step 3.1

Multiply $\frac{2 - \frac{1}{3}}{4 - \frac{1}{3}}$ by $\frac{3}{3}$ .

$\frac{3}{3} \cdot \frac{2 - \frac{1}{3}}{4 - \frac{1}{3}} \frac{1}{4 \cdot \frac{7}{6} - 2 \cdot \frac{7}{12}}$

Step 3.2

Combine.

$\frac{3 (2 - \frac{1}{3})}{3 (4 - \frac{1}{3})} \cdot \frac{1}{4 \cdot \frac{7}{6} - 2 \cdot \frac{7}{12}}$

Step 4

Apply the distributive property.

$\frac{3 \cdot 2 + 3 (- \frac{1}{3})}{3 \cdot 4 + 3 (- \frac{1}{3})} \cdot \frac{1}{4 \cdot \frac{7}{6} - 2 \cdot \frac{7}{12}}$

Step 5

Simplify by cancelling.

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Step 5.1

Cancel the common factor of $3$ .

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Step 5.1.1

Move the leading negative in $- \frac{1}{3}$ into the numerator.

$\frac{3 \cdot 2 + 3 (\frac{- 1}{3})}{3 \cdot 4 + 3 (- \frac{1}{3})} \cdot \frac{1}{4 \cdot \frac{7}{6} - 2 \cdot \frac{7}{12}}$

Step 5.1.2

Cancel the common factor.

$\frac{3 \cdot 2 + 3 (\frac{- 1}{3})}{3 \cdot 4 + 3 (- \frac{1}{3})} \cdot \frac{1}{4 \cdot \frac{7}{6} - 2 \cdot \frac{7}{12}}$

Step 5.1.3

Rewrite the expression.

$\frac{3 \cdot 2 - 1}{3 \cdot 4 + 3 (- \frac{1}{3})} \cdot \frac{1}{4 \cdot \frac{7}{6} - 2 \cdot \frac{7}{12}}$

Step 5.2

Cancel the common factor of $3$ .

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Step 5.2.1

Move the leading negative in $- \frac{1}{3}$ into the numerator.

$\frac{3 \cdot 2 - 1}{3 \cdot 4 + 3 (\frac{- 1}{3})} \cdot \frac{1}{4 \cdot \frac{7}{6} - 2 \cdot \frac{7}{12}}$

Step 5.2.2

Cancel the common factor.

$\frac{3 \cdot 2 - 1}{3 \cdot 4 + 3 (\frac{- 1}{3})} \cdot \frac{1}{4 \cdot \frac{7}{6} - 2 \cdot \frac{7}{12}}$

Step 5.2.3

Rewrite the expression.

$\frac{3 \cdot 2 - 1}{3 \cdot 4 - 1} \cdot \frac{1}{4 \cdot \frac{7}{6} - 2 \cdot \frac{7}{12}}$

Step 6

Simplify the numerator.

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Step 6.1

Multiply $3$ by $2$ .

$\frac{6 - 1}{3 \cdot 4 - 1} \cdot \frac{1}{4 \cdot \frac{7}{6} - 2 \cdot \frac{7}{12}}$

Step 6.2

Subtract $1$ from $6$ .

$\frac{5}{3 \cdot 4 - 1} \cdot \frac{1}{4 \cdot \frac{7}{6} - 2 \cdot \frac{7}{12}}$

Step 7

Simplify the denominator.

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Step 7.1

Multiply $3$ by $4$ .

$\frac{5}{12 - 1} \cdot \frac{1}{4 \cdot \frac{7}{6} - 2 \cdot \frac{7}{12}}$

Step 7.2

Subtract $1$ from $12$ .

$\frac{5}{11} \cdot \frac{1}{4 \cdot \frac{7}{6} - 2 \cdot \frac{7}{12}}$

Step 8

Simplify the denominator.

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Step 8.1

Cancel the common factor of $2$ .

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Step 8.1.1

Factor $2$ out of $4$ .

$\frac{5}{11} \cdot \frac{1}{2 (2) \cdot \frac{7}{6} - 2 \cdot \frac{7}{12}}$

Step 8.1.2

Factor $2$ out of $6$ .

$\frac{5}{11} \cdot \frac{1}{2 \cdot 2 \cdot \frac{7}{2 \cdot 3} - 2 \cdot \frac{7}{12}}$

Step 8.1.3

Cancel the common factor.

$\frac{5}{11} \cdot \frac{1}{2 \cdot 2 \cdot \frac{7}{2 \cdot 3} - 2 \cdot \frac{7}{12}}$

Step 8.1.4

Rewrite the expression.

$\frac{5}{11} \cdot \frac{1}{2 \cdot \frac{7}{3} - 2 \cdot \frac{7}{12}}$

Step 8.2

Combine $2$ and $\frac{7}{3}$ .

$\frac{5}{11} \cdot \frac{1}{\frac{2 \cdot 7}{3} - 2 \cdot \frac{7}{12}}$

Step 8.3

Multiply $2$ by $7$ .

$\frac{5}{11} \cdot \frac{1}{\frac{14}{3} - 2 \cdot \frac{7}{12}}$

Step 8.4

Cancel the common factor of $2$ .

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Step 8.4.1

Factor $2$ out of $- 2$ .

$\frac{5}{11} \cdot \frac{1}{\frac{14}{3} + 2 (- 1) \cdot \frac{7}{12}}$

Step 8.4.2

Factor $2$ out of $12$ .

$\frac{5}{11} \cdot \frac{1}{\frac{14}{3} + 2 \cdot - 1 \cdot \frac{7}{2 \cdot 6}}$

Step 8.4.3

Cancel the common factor.

$\frac{5}{11} \cdot \frac{1}{\frac{14}{3} + 2 \cdot - 1 \cdot \frac{7}{2 \cdot 6}}$

Step 8.4.4

Rewrite the expression.

$\frac{5}{11} \cdot \frac{1}{\frac{14}{3} - 1 \cdot \frac{7}{6}}$

Step 8.5

Rewrite $- 1 (\frac{7}{6})$ as $- (\frac{7}{6})$ .

$\frac{5}{11} \cdot \frac{1}{\frac{14}{3} - (\frac{7}{6})}$

Step 8.6

To write $\frac{14}{3}$ as a fraction with a common denominator, multiply by $\frac{2}{2}$ .

$\frac{5}{11} \cdot \frac{1}{\frac{14}{3} \cdot \frac{2}{2} - \frac{7}{6}}$

Step 8.7

Write each expression with a common denominator of $6$ , by multiplying each by an appropriate factor of $1$ .

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Step 8.7.1

Multiply $\frac{14}{3}$ by $\frac{2}{2}$ .

$\frac{5}{11} \cdot \frac{1}{\frac{14 \cdot 2}{3 \cdot 2} - \frac{7}{6}}$

Step 8.7.2

Multiply $3$ by $2$ .

$\frac{5}{11} \cdot \frac{1}{\frac{14 \cdot 2}{6} - \frac{7}{6}}$

Step 8.8

Combine the numerators over the common denominator.

$\frac{5}{11} \cdot \frac{1}{\frac{14 \cdot 2 - 7}{6}}$

Step 8.9

Simplify the numerator.

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Step 8.9.1

Multiply $14$ by $2$ .

$\frac{5}{11} \cdot \frac{1}{\frac{28 - 7}{6}}$

Step 8.9.2

Subtract $7$ from $28$ .

$\frac{5}{11} \cdot \frac{1}{\frac{21}{6}}$

Step 8.10

Cancel the common factor of $21$ and $6$ .

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Step 8.10.1

Factor $3$ out of $21$ .

$\frac{5}{11} \cdot \frac{1}{\frac{3 (7)}{6}}$

Step 8.10.2

Cancel the common factors.

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Step 8.10.2.1

Factor $3$ out of $6$ .

$\frac{5}{11} \cdot \frac{1}{\frac{3 \cdot 7}{3 \cdot 2}}$

Step 8.10.2.2

Cancel the common factor.

$\frac{5}{11} \cdot \frac{1}{\frac{3 \cdot 7}{3 \cdot 2}}$

Step 8.10.2.3

Rewrite the expression.

$\frac{5}{11} \cdot \frac{1}{\frac{7}{2}}$

Step 9

Multiply the numerator by the reciprocal of the denominator.

$\frac{5}{11} (1 (\frac{2}{7}))$

Step 10

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

$\frac{5}{11} \cdot \frac{2}{7}$

Step 11

Multiply $\frac{5}{11} \cdot \frac{2}{7}$ .

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Step 11.1

Multiply $\frac{5}{11}$ by $\frac{2}{7}$ .

$\frac{5 \cdot 2}{11 \cdot 7}$

Step 11.2

Multiply $5$ by $2$ .

$\frac{10}{11 \cdot 7}$

Step 11.3

Multiply $11$ by $7$ .

$\frac{10}{77}$

Step 12

The result can be shown in multiple forms.

Exact Form:

$\frac{10}{77}$

Decimal Form:

$0.\overline{129870}$