Algebra Examples

$1 \frac{2}{3} \div (11 \cdot 1 \frac{2}{11} - 8)$

Step 1

Convert $1 \frac{2}{3}$ to an improper fraction.

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Step 1.1

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

$(1 + \frac{2}{3}) \div (11 \cdot 1 \frac{2}{11} - 8)$

Step 1.2

Add $1$ and $\frac{2}{3}$ .

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Step 1.2.1

Write $1$ as a fraction with a common denominator.

$(\frac{3}{3} + \frac{2}{3}) \div (11 \cdot 1 \frac{2}{11} - 8)$

Step 1.2.2

Combine the numerators over the common denominator.

$\frac{3 + 2}{3} \div (11 \cdot 1 \frac{2}{11} - 8)$

Step 1.2.3

Add $3$ and $2$ .

$\frac{5}{3} \div (11 \cdot 1 \frac{2}{11} - 8)$

Step 2

Convert $1 \frac{2}{11}$ to an improper fraction.

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Step 2.1

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

$\frac{5}{3} \div (11 \cdot (1 + \frac{2}{11}) - 8)$

Step 2.2

Add $1$ and $\frac{2}{11}$ .

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Step 2.2.1

Write $1$ as a fraction with a common denominator.

$\frac{5}{3} \div (11 \cdot (\frac{11}{11} + \frac{2}{11}) - 8)$

Step 2.2.2

Combine the numerators over the common denominator.

$\frac{5}{3} \div (11 \cdot \frac{11 + 2}{11} - 8)$

Step 2.2.3

Add $11$ and $2$ .

$\frac{5}{3} \div (11 \cdot \frac{13}{11} - 8)$

Step 3

Rewrite the division as a fraction.

$\frac{\frac{5}{3}}{11 \cdot \frac{13}{11} - 8}$

Step 4

Multiply the numerator by the reciprocal of the denominator.

$\frac{5}{3} \cdot \frac{1}{11 \cdot \frac{13}{11} - 8}$

Step 5

Simplify the denominator.

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Step 5.1

Cancel the common factor of $11$ .

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Step 5.1.1

Cancel the common factor.

$\frac{5}{3} \cdot \frac{1}{11 \cdot \frac{13}{11} - 8}$

Step 5.1.2

Rewrite the expression.

$\frac{5}{3} \cdot \frac{1}{13 - 8}$

Step 5.2

Subtract $8$ from $13$ .

$\frac{5}{3} \cdot \frac{1}{5}$

Step 6

Cancel the common factor of $5$ .

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Step 6.1

Cancel the common factor.

$\frac{5}{3} \cdot \frac{1}{5}$

Step 6.2

Rewrite the expression.

$\frac{1}{3}$

Step 7

The result can be shown in multiple forms.

Exact Form:

$\frac{1}{3}$

Decimal Form:

$0.\overline{3}$