Basic Math Examples

$\frac{1}{4} + (\frac{12}{5} + \frac{3}{2}) \cdot \frac{5}{2} + (\frac{73}{12} \div 6 - \frac{73}{72}) \div (\frac{61}{7} - \frac{131}{21}) - 11$

Step 1

To write $\frac{73}{12} \div 6$ as a fraction with a common denominator, multiply by $\frac{12}{12}$ .

$\frac{1}{4} + (\frac{12}{5} + \frac{3}{2}) \cdot \frac{5}{2} + (\frac{73}{12} \div 6 \cdot \frac{12}{12} - \frac{73}{72}) \div (\frac{61}{7} - \frac{131}{21}) - 11$

Step 2

Write each expression with a common denominator of $72$ , by multiplying each by an appropriate factor of $1$ .

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Step 2.1

Multiply $\frac{73}{12} \div 6$ by $\frac{12}{12}$ .

$\frac{1}{4} + (\frac{12}{5} + \frac{3}{2}) \cdot \frac{5}{2} + (\frac{\frac{73}{12} \cdot 12}{6 \cdot 12} - \frac{73}{72}) \div (\frac{61}{7} - \frac{131}{21}) - 11$

Step 2.2

Multiply $6$ by $12$ .

$\frac{1}{4} + (\frac{12}{5} + \frac{3}{2}) \cdot \frac{5}{2} + (\frac{\frac{73}{12} \cdot 12}{72} - \frac{73}{72}) \div (\frac{61}{7} - \frac{131}{21}) - 11$

Step 3

Combine the numerators over the common denominator.

$\frac{1}{4} + (\frac{12}{5} + \frac{3}{2}) \cdot \frac{5}{2} + \frac{\frac{73}{12} \cdot 12 - 73}{72} \div (\frac{61}{7} - \frac{131}{21}) - 11$

Step 4

Simplify the numerator.

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Step 4.1

Divide $73$ by $12$ .

$\frac{1}{4} + (\frac{12}{5} + \frac{3}{2}) \cdot \frac{5}{2} + \frac{6.08\overline{3} \cdot 12 - 73}{72} \div (\frac{61}{7} - \frac{131}{21}) - 11$

Step 4.2

Multiply $6.08\overline{3}$ by $12$ .

$\frac{1}{4} + (\frac{12}{5} + \frac{3}{2}) \cdot \frac{5}{2} + \frac{73 - 73}{72} \div (\frac{61}{7} - \frac{131}{21}) - 11$

Step 4.3

Subtract $73$ from $73$ .

$\frac{1}{4} + (\frac{12}{5} + \frac{3}{2}) \cdot \frac{5}{2} + \frac{0}{72} \div (\frac{61}{7} - \frac{131}{21}) - 11$

Step 5

Simplify each term.

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Step 5.1

To write $\frac{12}{5}$ as a fraction with a common denominator, multiply by $\frac{2}{2}$ .

$\frac{1}{4} + (\frac{12}{5} \cdot \frac{2}{2} + \frac{3}{2}) \cdot \frac{5}{2} + \frac{0}{72} \div (\frac{61}{7} - \frac{131}{21}) - 11$

Step 5.2

To write $\frac{3}{2}$ as a fraction with a common denominator, multiply by $\frac{5}{5}$ .

$\frac{1}{4} + (\frac{12}{5} \cdot \frac{2}{2} + \frac{3}{2} \cdot \frac{5}{5}) \cdot \frac{5}{2} + \frac{0}{72} \div (\frac{61}{7} - \frac{131}{21}) - 11$

Step 5.3

Write each expression with a common denominator of $10$ , by multiplying each by an appropriate factor of $1$ .

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Step 5.3.1

Multiply $\frac{12}{5}$ by $\frac{2}{2}$ .

$\frac{1}{4} + (\frac{12 \cdot 2}{5 \cdot 2} + \frac{3}{2} \cdot \frac{5}{5}) \cdot \frac{5}{2} + \frac{0}{72} \div (\frac{61}{7} - \frac{131}{21}) - 11$

Step 5.3.2

Multiply $5$ by $2$ .

$\frac{1}{4} + (\frac{12 \cdot 2}{10} + \frac{3}{2} \cdot \frac{5}{5}) \cdot \frac{5}{2} + \frac{0}{72} \div (\frac{61}{7} - \frac{131}{21}) - 11$

Step 5.3.3

Multiply $\frac{3}{2}$ by $\frac{5}{5}$ .

$\frac{1}{4} + (\frac{12 \cdot 2}{10} + \frac{3 \cdot 5}{2 \cdot 5}) \cdot \frac{5}{2} + \frac{0}{72} \div (\frac{61}{7} - \frac{131}{21}) - 11$

Step 5.3.4

Multiply $2$ by $5$ .

$\frac{1}{4} + (\frac{12 \cdot 2}{10} + \frac{3 \cdot 5}{10}) \cdot \frac{5}{2} + \frac{0}{72} \div (\frac{61}{7} - \frac{131}{21}) - 11$

Step 5.4

Combine the numerators over the common denominator.

$\frac{1}{4} + \frac{12 \cdot 2 + 3 \cdot 5}{10} \cdot \frac{5}{2} + \frac{0}{72} \div (\frac{61}{7} - \frac{131}{21}) - 11$

Step 5.5

Simplify the numerator.

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Step 5.5.1

Multiply $12$ by $2$ .

$\frac{1}{4} + \frac{24 + 3 \cdot 5}{10} \cdot \frac{5}{2} + \frac{0}{72} \div (\frac{61}{7} - \frac{131}{21}) - 11$

Step 5.5.2

Multiply $3$ by $5$ .

$\frac{1}{4} + \frac{24 + 15}{10} \cdot \frac{5}{2} + \frac{0}{72} \div (\frac{61}{7} - \frac{131}{21}) - 11$

Step 5.5.3

Add $24$ and $15$ .

$\frac{1}{4} + \frac{39}{10} \cdot \frac{5}{2} + \frac{0}{72} \div (\frac{61}{7} - \frac{131}{21}) - 11$

Step 5.6

Cancel the common factor of $5$ .

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Step 5.6.1

Factor $5$ out of $10$ .

$\frac{1}{4} + \frac{39}{5 (2)} \cdot \frac{5}{2} + \frac{0}{72} \div (\frac{61}{7} - \frac{131}{21}) - 11$

Step 5.6.2

Cancel the common factor.

$\frac{1}{4} + \frac{39}{5 \cdot 2} \cdot \frac{5}{2} + \frac{0}{72} \div (\frac{61}{7} - \frac{131}{21}) - 11$

Step 5.6.3

Rewrite the expression.

$\frac{1}{4} + \frac{39}{2} \cdot \frac{1}{2} + \frac{0}{72} \div (\frac{61}{7} - \frac{131}{21}) - 11$

Step 5.7

Multiply $\frac{39}{2}$ by $\frac{1}{2}$ .

$\frac{1}{4} + \frac{39}{2 \cdot 2} + \frac{0}{72} \div (\frac{61}{7} - \frac{131}{21}) - 11$

Step 5.8

Multiply $2$ by $2$ .

$\frac{1}{4} + \frac{39}{4} + \frac{0}{72} \div (\frac{61}{7} - \frac{131}{21}) - 11$

Step 5.9

Rewrite the division as a fraction.

$\frac{1}{4} + \frac{39}{4} + \frac{\frac{0}{72}}{\frac{61}{7} - \frac{131}{21}} - 11$

Step 5.10

Cancel the common factor of $0$ and $72$ .

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Step 5.10.1

Factor $72$ out of $0$ .

$\frac{1}{4} + \frac{39}{4} + \frac{\frac{72 \cdot 0}{72}}{\frac{61}{7} - \frac{131}{21}} - 11$

Step 5.10.2

Cancel the common factors.

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Step 5.10.2.1

Factor $72$ out of $72$ .

$\frac{1}{4} + \frac{39}{4} + \frac{\frac{72 \cdot 0}{72 (1)}}{\frac{61}{7} - \frac{131}{21}} - 11$

Step 5.10.2.2

Cancel the common factor.

$\frac{1}{4} + \frac{39}{4} + \frac{\frac{72 \cdot 0}{72 \cdot 1}}{\frac{61}{7} - \frac{131}{21}} - 11$

Step 5.10.2.3

Rewrite the expression.

$\frac{1}{4} + \frac{39}{4} + \frac{\frac{0}{1}}{\frac{61}{7} - \frac{131}{21}} - 11$

Step 5.10.2.4

Divide $0$ by $1$ .

$\frac{1}{4} + \frac{39}{4} + \frac{0}{\frac{61}{7} - \frac{131}{21}} - 11$

Step 5.11

Simplify the denominator.

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Step 5.11.1

To write $\frac{61}{7}$ as a fraction with a common denominator, multiply by $\frac{3}{3}$ .

$\frac{1}{4} + \frac{39}{4} + \frac{0}{\frac{61}{7} \cdot \frac{3}{3} - \frac{131}{21}} - 11$

Step 5.11.2

Write each expression with a common denominator of $21$ , by multiplying each by an appropriate factor of $1$ .

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Step 5.11.2.1

Multiply $\frac{61}{7}$ by $\frac{3}{3}$ .

$\frac{1}{4} + \frac{39}{4} + \frac{0}{\frac{61 \cdot 3}{7 \cdot 3} - \frac{131}{21}} - 11$

Step 5.11.2.2

Multiply $7$ by $3$ .

$\frac{1}{4} + \frac{39}{4} + \frac{0}{\frac{61 \cdot 3}{21} - \frac{131}{21}} - 11$

Step 5.11.3

Combine the numerators over the common denominator.

$\frac{1}{4} + \frac{39}{4} + \frac{0}{\frac{61 \cdot 3 - 131}{21}} - 11$

Step 5.11.4

Simplify the numerator.

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Step 5.11.4.1

Multiply $61$ by $3$ .

$\frac{1}{4} + \frac{39}{4} + \frac{0}{\frac{183 - 131}{21}} - 11$

Step 5.11.4.2

Subtract $131$ from $183$ .

$\frac{1}{4} + \frac{39}{4} + \frac{0}{\frac{52}{21}} - 11$

Step 5.12

Multiply the numerator by the reciprocal of the denominator.

$\frac{1}{4} + \frac{39}{4} + 0 (\frac{21}{52}) - 11$

Step 5.13

Multiply $0$ by $\frac{21}{52}$ .

$\frac{1}{4} + \frac{39}{4} + 0 - 11$

Step 6

Combine fractions.

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Step 6.1

Combine the numerators over the common denominator.

$- 11 + \frac{1 + 39}{4}$

Step 6.2

Simplify the expression.

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Step 6.2.1

Add $1$ and $39$ .

$- 11 + \frac{40}{4}$

Step 6.2.2

Divide $40$ by $4$ .

$- 11 + 10$

Step 6.2.3

Add $- 11$ and $10$ .

$- 1$