Algebra Examples

$\frac{2}{3} \div 2^{4} + (\frac{3}{4} + \frac{1}{6}) \div \frac{1}{3}$

Step 1

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

$\frac{2}{3} \div 2^{4} + (\frac{3}{4} \cdot \frac{3}{3} + \frac{1}{6}) \div \frac{1}{3}$

Step 2

To write $\frac{1}{6}$ as a fraction with a common denominator, multiply by $\frac{2}{2}$ .

$\frac{2}{3} \div 2^{4} + (\frac{3}{4} \cdot \frac{3}{3} + \frac{1}{6} \cdot \frac{2}{2}) \div \frac{1}{3}$

Step 3

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

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Step 3.1

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

$\frac{2}{3} \div 2^{4} + (\frac{3 \cdot 3}{4 \cdot 3} + \frac{1}{6} \cdot \frac{2}{2}) \div \frac{1}{3}$

Step 3.2

Multiply $4$ by $3$ .

$\frac{2}{3} \div 2^{4} + (\frac{3 \cdot 3}{12} + \frac{1}{6} \cdot \frac{2}{2}) \div \frac{1}{3}$

Step 3.3

Multiply $\frac{1}{6}$ by $\frac{2}{2}$ .

$\frac{2}{3} \div 2^{4} + (\frac{3 \cdot 3}{12} + \frac{2}{6 \cdot 2}) \div \frac{1}{3}$

Step 3.4

Multiply $6$ by $2$ .

$\frac{2}{3} \div 2^{4} + (\frac{3 \cdot 3}{12} + \frac{2}{12}) \div \frac{1}{3}$

Step 4

Combine the numerators over the common denominator.

$\frac{2}{3} \div 2^{4} + \frac{3 \cdot 3 + 2}{12} \div \frac{1}{3}$

Step 5

Simplify the numerator.

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Step 5.1

Multiply $3$ by $3$ .

$\frac{2}{3} \div 2^{4} + \frac{9 + 2}{12} \div \frac{1}{3}$

Step 5.2

Add $9$ and $2$ .

$\frac{2}{3} \div 2^{4} + \frac{11}{12} \div \frac{1}{3}$

Step 6

Simplify each term.

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Step 6.1

Rewrite the division as a fraction.

$\frac{\frac{2}{3}}{2^{4}} + \frac{11}{12} \div \frac{1}{3}$

Step 6.2

Multiply the numerator by the reciprocal of the denominator.

$\frac{2}{3} \cdot \frac{1}{2^{4}} + \frac{11}{12} \div \frac{1}{3}$

Step 6.3

Combine.

$\frac{2 \cdot 1}{3 \cdot 2^{4}} + \frac{11}{12} \div \frac{1}{3}$

Step 6.4

Cancel the common factor of $2$ and $2^{4}$ .

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Step 6.4.1

Factor $2$ out of $2 \cdot 1$ .

$\frac{2 (1)}{3 \cdot 2^{4}} + \frac{11}{12} \div \frac{1}{3}$

Step 6.4.2

Cancel the common factors.

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Step 6.4.2.1

Factor $2$ out of $3 \cdot 2^{4}$ .

$\frac{2 (1)}{2 (3 \cdot 2^{3})} + \frac{11}{12} \div \frac{1}{3}$

Step 6.4.2.2

Cancel the common factor.

$\frac{2 \cdot 1}{2 (3 \cdot 2^{3})} + \frac{11}{12} \div \frac{1}{3}$

Step 6.4.2.3

Rewrite the expression.

$\frac{1}{3 \cdot 2^{3}} + \frac{11}{12} \div \frac{1}{3}$

Step 6.5

Raise $2$ to the power of $3$ .

$\frac{1}{3 \cdot 8} + \frac{11}{12} \div \frac{1}{3}$

Step 6.6

Multiply $3$ by $8$ .

$\frac{1}{24} + \frac{11}{12} \div \frac{1}{3}$

Step 6.7

To divide by a fraction, multiply by its reciprocal.

$\frac{1}{24} + \frac{11}{12} \cdot 3$

Step 6.8

Cancel the common factor of $3$ .

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Step 6.8.1

Factor $3$ out of $12$ .

$\frac{1}{24} + \frac{11}{3 (4)} \cdot 3$

Step 6.8.2

Cancel the common factor.

$\frac{1}{24} + \frac{11}{3 \cdot 4} \cdot 3$

Step 6.8.3

Rewrite the expression.

$\frac{1}{24} + \frac{11}{4}$

Step 7

To write $\frac{11}{4}$ as a fraction with a common denominator, multiply by $\frac{6}{6}$ .

$\frac{1}{24} + \frac{11}{4} \cdot \frac{6}{6}$

Step 8

Write each expression with a common denominator of $24$ , by multiplying each by an appropriate factor of $1$ .

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Step 8.1

Multiply $\frac{11}{4}$ by $\frac{6}{6}$ .

$\frac{1}{24} + \frac{11 \cdot 6}{4 \cdot 6}$

Step 8.2

Multiply $4$ by $6$ .

$\frac{1}{24} + \frac{11 \cdot 6}{24}$

Step 9

Combine the numerators over the common denominator.

$\frac{1 + 11 \cdot 6}{24}$

Step 10

Simplify the numerator.

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Step 10.1

Multiply $11$ by $6$ .

$\frac{1 + 66}{24}$

Step 10.2

Add $1$ and $66$ .

$\frac{67}{24}$

Step 11

The result can be shown in multiple forms.

Exact Form:

$\frac{67}{24}$

Decimal Form:

$2.791\overline{6}$

Mixed Number Form:

$2 \frac{19}{24}$