Basic Math Examples

$\frac{11}{\frac{3 (6 \frac{5}{7})}{6}} \div 2$

Step 1

Convert $6 \frac{5}{7}$ to an improper fraction.

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Step 1.1

A mixed number is an addition of its whole and fractional parts.

$\frac{11}{\frac{3 (6 + \frac{5}{7})}{6}} \div 2$

Step 1.2

Add $6$ and $\frac{5}{7}$ .

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Step 1.2.1

To write $6$ as a fraction with a common denominator, multiply by $\frac{7}{7}$ .

$\frac{11}{\frac{3 (6 \cdot \frac{7}{7} + \frac{5}{7})}{6}} \div 2$

Step 1.2.2

Combine $6$ and $\frac{7}{7}$ .

$\frac{11}{\frac{3 (\frac{6 \cdot 7}{7} + \frac{5}{7})}{6}} \div 2$

Step 1.2.3

Combine the numerators over the common denominator.

$\frac{11}{\frac{3 \frac{6 \cdot 7 + 5}{7}}{6}} \div 2$

Step 1.2.4

Simplify the numerator.

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Step 1.2.4.1

Multiply $6$ by $7$ .

$\frac{11}{\frac{3 \frac{42 + 5}{7}}{6}} \div 2$

Step 1.2.4.2

Add $42$ and $5$ .

$\frac{11}{\frac{3 (\frac{47}{7})}{6}} \div 2$

Step 2

Rewrite the division as a fraction.

$\frac{\frac{11}{\frac{3 (\frac{47}{7})}{6}}}{2}$

Step 3

Cancel the common factors.

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Step 3.1

Factor $3$ out of $6$ .

$\frac{\frac{11}{\frac{3 (\frac{47}{7})}{3 \cdot 2}}}{2}$

Step 3.2

Cancel the common factor.

$\frac{\frac{11}{\frac{3 (\frac{47}{7})}{3 \cdot 2}}}{2}$

Step 3.3

Rewrite the expression.

$\frac{\frac{11}{\frac{\frac{47}{7}}{2}}}{2}$

Step 4

Multiply the numerator by the reciprocal of the denominator.

$\frac{11}{\frac{\frac{47}{7}}{2}} \cdot \frac{1}{2}$

Step 5

Multiply the numerator by the reciprocal of the denominator.

$11 \frac{2}{\frac{47}{7}} \frac{1}{2}$

Step 6

Multiply the numerator by the reciprocal of the denominator.

$11 (2 (\frac{7}{47})) \frac{1}{2}$

Step 7

Multiply $2 (\frac{7}{47})$ .

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Step 7.1

Combine $2$ and $\frac{7}{47}$ .

$11 \frac{2 \cdot 7}{47} \frac{1}{2}$

Step 7.2

Multiply $2$ by $7$ .

$11 (\frac{14}{47}) \frac{1}{2}$

Step 8

Multiply $11 (\frac{14}{47})$ .

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Step 8.1

Combine $11$ and $\frac{14}{47}$ .

$\frac{11 \cdot 14}{47} \cdot \frac{1}{2}$

Step 8.2

Multiply $11$ by $14$ .

$\frac{154}{47} \cdot \frac{1}{2}$

Step 9

Cancel the common factor of $2$ .

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Step 9.1

Factor $2$ out of $154$ .

$\frac{2 (77)}{47} \cdot \frac{1}{2}$

Step 9.2

Cancel the common factor.

$\frac{2 \cdot 77}{47} \cdot \frac{1}{2}$

Step 9.3

Rewrite the expression.

$\frac{77}{47}$

Step 10

The result can be shown in multiple forms.

Exact Form:

$\frac{77}{47}$

Decimal Form:

$1.63829787 \dots$

Mixed Number Form:

$1 \frac{30}{47}$