Basic Math Examples

$\frac{2}{3} - \frac{11}{12} \div \frac{1}{10} + \frac{12}{5}$

Step 1

Find the common denominator.

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Step 1.1

Multiply $\frac{2}{3}$ by $\frac{\frac{5}{10}}{\frac{5}{10}}$ .

$\frac{2}{3} \cdot \frac{\frac{5}{10}}{\frac{5}{10}} - \frac{11}{12} \div \frac{1}{10} + \frac{12}{5}$

Step 1.2

Multiply $\frac{2}{3}$ by $\frac{\frac{5}{10}}{\frac{5}{10}}$ .

$\frac{2 (\frac{5}{10})}{3 (\frac{5}{10})} - \frac{11}{12} \div \frac{1}{10} + \frac{12}{5}$

Step 1.3

Multiply $\frac{11}{12} \div \frac{1}{10}$ by $\frac{15}{15}$ .

$\frac{2 (\frac{5}{10})}{3 (\frac{5}{10})} - (\frac{11}{12} \div \frac{1}{10} \cdot \frac{15}{15}) + \frac{12}{5}$

Step 1.4

Multiply $\frac{11}{12} \div \frac{1}{10}$ by $\frac{15}{15}$ .

$\frac{2 (\frac{5}{10})}{3 (\frac{5}{10})} - \frac{\frac{11}{12} \cdot 15}{\frac{1}{10} \cdot 15} + \frac{12}{5}$

Step 1.5

Multiply $\frac{12}{5}$ by $\frac{\frac{3}{10}}{\frac{3}{10}}$ .

$\frac{2 (\frac{5}{10})}{3 (\frac{5}{10})} - \frac{\frac{11}{12} \cdot 15}{\frac{1}{10} \cdot 15} + \frac{12}{5} \cdot \frac{\frac{3}{10}}{\frac{3}{10}}$

Step 1.6

Multiply $\frac{12}{5}$ by $\frac{\frac{3}{10}}{\frac{3}{10}}$ .

$\frac{2 (\frac{5}{10})}{3 (\frac{5}{10})} - \frac{\frac{11}{12} \cdot 15}{\frac{1}{10} \cdot 15} + \frac{12 (\frac{3}{10})}{5 (\frac{3}{10})}$

Step 1.7

Combine $3$ and $\frac{5}{10}$ .

$\frac{2 (\frac{5}{10})}{\frac{3 \cdot 5}{10}} - \frac{\frac{11}{12} \cdot 15}{\frac{1}{10} \cdot 15} + \frac{12 (\frac{3}{10})}{5 (\frac{3}{10})}$

Step 1.8

Multiply $3$ by $5$ .

$\frac{2 (\frac{5}{10})}{\frac{15}{10}} - \frac{\frac{11}{12} \cdot 15}{\frac{1}{10} \cdot 15} + \frac{12 (\frac{3}{10})}{5 (\frac{3}{10})}$

Step 1.9

Reorder the factors of $\frac{1}{10} \cdot 15$ .

$\frac{2 (\frac{5}{10})}{\frac{15}{10}} - \frac{\frac{11}{12} \cdot 15}{15 (\frac{1}{10})} + \frac{12 (\frac{3}{10})}{5 (\frac{3}{10})}$

Step 1.10

Combine $15$ and $\frac{1}{10}$ .

$\frac{2 (\frac{5}{10})}{\frac{15}{10}} - \frac{\frac{11}{12} \cdot 15}{\frac{15}{10}} + \frac{12 (\frac{3}{10})}{5 (\frac{3}{10})}$

Step 1.11

Combine $5$ and $\frac{3}{10}$ .

$\frac{2 (\frac{5}{10})}{\frac{15}{10}} - \frac{\frac{11}{12} \cdot 15}{\frac{15}{10}} + \frac{12 (\frac{3}{10})}{\frac{5 \cdot 3}{10}}$

Step 1.12

Multiply $5$ by $3$ .

$\frac{2 (\frac{5}{10})}{\frac{15}{10}} - \frac{\frac{11}{12} \cdot 15}{\frac{15}{10}} + \frac{12 (\frac{3}{10})}{\frac{15}{10}}$

Step 2

Combine the numerators over the common denominator.

$\frac{2 (\frac{5}{10}) - \frac{11}{12} \cdot 15 + 12 (\frac{3}{10})}{\frac{15}{10}}$

Step 3

Simplify each term.

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Step 3.1

Cancel the common factor of $2$ .

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Step 3.1.1

Factor $2$ out of $10$ .

$\frac{2 \frac{5}{2 (5)} - \frac{11}{12} \cdot 15 + 12 (\frac{3}{10})}{\frac{15}{10}}$

Step 3.1.2

Cancel the common factor.

$\frac{2 \frac{5}{2 \cdot 5} - \frac{11}{12} \cdot 15 + 12 (\frac{3}{10})}{\frac{15}{10}}$

Step 3.1.3

Rewrite the expression.

$\frac{\frac{5}{5} - \frac{11}{12} \cdot 15 + 12 (\frac{3}{10})}{\frac{15}{10}}$

Step 3.2

Divide $5$ by $5$ .

$\frac{1 - \frac{11}{12} \cdot 15 + 12 (\frac{3}{10})}{\frac{15}{10}}$

Step 3.3

Cancel the common factor of $3$ .

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Step 3.3.1

Move the leading negative in $- \frac{11}{12}$ into the numerator.

$\frac{1 + \frac{- 11}{12} \cdot 15 + 12 (\frac{3}{10})}{\frac{15}{10}}$

Step 3.3.2

Factor $3$ out of $12$ .

$\frac{1 + \frac{- 11}{3 (4)} \cdot 15 + 12 (\frac{3}{10})}{\frac{15}{10}}$

Step 3.3.3

Factor $3$ out of $15$ .

$\frac{1 + \frac{- 11}{3 \cdot 4} \cdot (3 \cdot 5) + 12 (\frac{3}{10})}{\frac{15}{10}}$

Step 3.3.4

Cancel the common factor.

$\frac{1 + \frac{- 11}{3 \cdot 4} \cdot (3 \cdot 5) + 12 (\frac{3}{10})}{\frac{15}{10}}$

Step 3.3.5

Rewrite the expression.

$\frac{1 + \frac{- 11}{4} \cdot 5 + 12 (\frac{3}{10})}{\frac{15}{10}}$

Step 3.4

Combine $\frac{- 11}{4}$ and $5$ .

$\frac{1 + \frac{- 11 \cdot 5}{4} + 12 (\frac{3}{10})}{\frac{15}{10}}$

Step 3.5

Multiply $- 11$ by $5$ .

$\frac{1 + \frac{- 55}{4} + 12 (\frac{3}{10})}{\frac{15}{10}}$

Step 3.6

Move the negative in front of the fraction.

$\frac{1 - \frac{55}{4} + 12 (\frac{3}{10})}{\frac{15}{10}}$

Step 3.7

Cancel the common factor of $2$ .

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Step 3.7.1

Factor $2$ out of $12$ .

$\frac{1 - \frac{55}{4} + 2 (6) \frac{3}{10}}{\frac{15}{10}}$

Step 3.7.2

Factor $2$ out of $10$ .

$\frac{1 - \frac{55}{4} + 2 \cdot 6 \frac{3}{2 \cdot 5}}{\frac{15}{10}}$

Step 3.7.3

Cancel the common factor.

$\frac{1 - \frac{55}{4} + 2 \cdot 6 \frac{3}{2 \cdot 5}}{\frac{15}{10}}$

Step 3.7.4

Rewrite the expression.

$\frac{1 - \frac{55}{4} + 6 (\frac{3}{5})}{\frac{15}{10}}$

Step 3.8

Combine $6$ and $\frac{3}{5}$ .

$\frac{1 - \frac{55}{4} + \frac{6 \cdot 3}{5}}{\frac{15}{10}}$

Step 3.9

Multiply $6$ by $3$ .

$\frac{1 - \frac{55}{4} + \frac{18}{5}}{\frac{15}{10}}$

Step 4

Find the common denominator.

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Step 4.1

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

$\frac{\frac{1}{1} - \frac{55}{4} + \frac{18}{5}}{\frac{15}{10}}$

Step 4.2

Multiply $\frac{1}{1}$ by $\frac{20}{20}$ .

$\frac{\frac{1}{1} \cdot \frac{20}{20} - \frac{55}{4} + \frac{18}{5}}{\frac{15}{10}}$

Step 4.3

Multiply $\frac{1}{1}$ by $\frac{20}{20}$ .

$\frac{\frac{20}{20} - \frac{55}{4} + \frac{18}{5}}{\frac{15}{10}}$

Step 4.4

Multiply $\frac{55}{4}$ by $\frac{5}{5}$ .

$\frac{\frac{20}{20} - (\frac{55}{4} \cdot \frac{5}{5}) + \frac{18}{5}}{\frac{15}{10}}$

Step 4.5

Multiply $\frac{55}{4}$ by $\frac{5}{5}$ .

$\frac{\frac{20}{20} - \frac{55 \cdot 5}{4 \cdot 5} + \frac{18}{5}}{\frac{15}{10}}$

Step 4.6

Multiply $\frac{18}{5}$ by $\frac{4}{4}$ .

$\frac{\frac{20}{20} - \frac{55 \cdot 5}{4 \cdot 5} + \frac{18}{5} \cdot \frac{4}{4}}{\frac{15}{10}}$

Step 4.7

Multiply $\frac{18}{5}$ by $\frac{4}{4}$ .

$\frac{\frac{20}{20} - \frac{55 \cdot 5}{4 \cdot 5} + \frac{18 \cdot 4}{5 \cdot 4}}{\frac{15}{10}}$

Step 4.8

Multiply $4$ by $5$ .

$\frac{\frac{20}{20} - \frac{55 \cdot 5}{20} + \frac{18 \cdot 4}{5 \cdot 4}}{\frac{15}{10}}$

Step 4.9

Reorder the factors of $5 \cdot 4$ .

$\frac{\frac{20}{20} - \frac{55 \cdot 5}{20} + \frac{18 \cdot 4}{4 \cdot 5}}{\frac{15}{10}}$

Step 4.10

Multiply $4$ by $5$ .

$\frac{\frac{20}{20} - \frac{55 \cdot 5}{20} + \frac{18 \cdot 4}{20}}{\frac{15}{10}}$

Step 5

Combine the numerators over the common denominator.

$\frac{\frac{20 - 55 \cdot 5 + 18 \cdot 4}{20}}{\frac{15}{10}}$

Step 6

Simplify each term.

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Step 6.1

Multiply $- 55$ by $5$ .

$\frac{\frac{20 - 275 + 18 \cdot 4}{20}}{\frac{15}{10}}$

Step 6.2

Multiply $18$ by $4$ .

$\frac{\frac{20 - 275 + 72}{20}}{\frac{15}{10}}$

Step 7

Reduce the expression by cancelling the common factors.

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Step 7.1

Subtract $275$ from $20$ .

$\frac{\frac{- 255 + 72}{20}}{\frac{15}{10}}$

Step 7.2

Simplify the expression.

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Step 7.2.1

Add $- 255$ and $72$ .

$\frac{\frac{- 183}{20}}{\frac{15}{10}}$

Step 7.2.2

Move the negative in front of the fraction.

$\frac{- \frac{183}{20}}{\frac{15}{10}}$

Step 7.3

Cancel the common factor of $15$ and $10$ .

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Step 7.3.1

Factor $5$ out of $15$ .

$\frac{- \frac{183}{20}}{\frac{5 (3)}{10}}$

Step 7.3.2

Cancel the common factors.

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Step 7.3.2.1

Factor $5$ out of $10$ .

$\frac{- \frac{183}{20}}{\frac{5 \cdot 3}{5 \cdot 2}}$

Step 7.3.2.2

Cancel the common factor.

$\frac{- \frac{183}{20}}{\frac{5 \cdot 3}{5 \cdot 2}}$

Step 7.3.2.3

Rewrite the expression.

$\frac{- \frac{183}{20}}{\frac{3}{2}}$

Step 8

Multiply the numerator by the reciprocal of the denominator.

$- \frac{183}{20} \cdot \frac{2}{3}$

Step 9

Cancel the common factor of $3$ .

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Step 9.1

Move the leading negative in $- \frac{183}{20}$ into the numerator.

$\frac{- 183}{20} \cdot \frac{2}{3}$

Step 9.2

Factor $3$ out of $- 183$ .

$\frac{3 (- 61)}{20} \cdot \frac{2}{3}$

Step 9.3

Cancel the common factor.

$\frac{3 \cdot - 61}{20} \cdot \frac{2}{3}$

Step 9.4

Rewrite the expression.

$\frac{- 61}{20} \cdot 2$

Step 10

Cancel the common factor of $2$ .

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Step 10.1

Factor $2$ out of $20$ .

$\frac{- 61}{2 (10)} \cdot 2$

Step 10.2

Cancel the common factor.

$\frac{- 61}{2 \cdot 10} \cdot 2$

Step 10.3

Rewrite the expression.

$\frac{- 61}{10}$

Step 11

Move the negative in front of the fraction.

$- \frac{61}{10}$

Step 12

The result can be shown in multiple forms.

Exact Form:

$- \frac{61}{10}$

Decimal Form:

$- 6.1$

Mixed Number Form:

$- 6 \frac{1}{10}$