Basic Math Examples

$(4 + \frac{4}{11}) \div 2 \frac{5}{11}$

Step 1

Convert $2 \frac{5}{11}$ to an improper fraction.

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Step 1.1

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

$(4 + \frac{4}{11}) \div (2 + \frac{5}{11})$

Step 1.2

Add $2$ and $\frac{5}{11}$ .

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Step 1.2.1

To write $2$ as a fraction with a common denominator, multiply by $\frac{11}{11}$ .

$(4 + \frac{4}{11}) \div (2 \cdot \frac{11}{11} + \frac{5}{11})$

Step 1.2.2

Combine $2$ and $\frac{11}{11}$ .

$(4 + \frac{4}{11}) \div (\frac{2 \cdot 11}{11} + \frac{5}{11})$

Step 1.2.3

Combine the numerators over the common denominator.

$(4 + \frac{4}{11}) \div \frac{2 \cdot 11 + 5}{11}$

Step 1.2.4

Simplify the numerator.

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Step 1.2.4.1

Multiply $2$ by $11$ .

$(4 + \frac{4}{11}) \div \frac{22 + 5}{11}$

Step 1.2.4.2

Add $22$ and $5$ .

$(4 + \frac{4}{11}) \div \frac{27}{11}$

Step 2

To divide by a fraction, multiply by its reciprocal.

$(4 + \frac{4}{11}) \frac{11}{27}$

Step 3

To write $4$ as a fraction with a common denominator, multiply by $\frac{11}{11}$ .

$(4 \cdot \frac{11}{11} + \frac{4}{11}) \frac{11}{27}$

Step 4

Combine $4$ and $\frac{11}{11}$ .

$(\frac{4 \cdot 11}{11} + \frac{4}{11}) \frac{11}{27}$

Step 5

Combine the numerators over the common denominator.

$\frac{4 \cdot 11 + 4}{11} \cdot \frac{11}{27}$

Step 6

Simplify the numerator.

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Step 6.1

Multiply $4$ by $11$ .

$\frac{44 + 4}{11} \cdot \frac{11}{27}$

Step 6.2

Add $44$ and $4$ .

$\frac{48}{11} \cdot \frac{11}{27}$

Step 7

Cancel the common factor of $3$ .

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Step 7.1

Factor $3$ out of $48$ .

$\frac{3 (16)}{11} \cdot \frac{11}{27}$

Step 7.2

Factor $3$ out of $27$ .

$\frac{3 \cdot 16}{11} \cdot \frac{11}{3 \cdot 9}$

Step 7.3

Cancel the common factor.

$\frac{3 \cdot 16}{11} \cdot \frac{11}{3 \cdot 9}$

Step 7.4

Rewrite the expression.

$\frac{16}{11} \cdot \frac{11}{9}$

Step 8

Cancel the common factor of $11$ .

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Step 8.1

Cancel the common factor.

$\frac{16}{11} \cdot \frac{11}{9}$

Step 8.2

Rewrite the expression.

$16 (\frac{1}{9})$

Step 9

Combine $16$ and $\frac{1}{9}$ .

$\frac{16}{9}$

Step 10

The result can be shown in multiple forms.

Exact Form:

$\frac{16}{9}$

Decimal Form:

$1.\overline{7}$

Mixed Number Form:

$1 \frac{7}{9}$