Basic Math Examples

$\frac{2}{3} - \frac{1}{5} \div \frac{7}{2} - \frac{5}{6}$

Step 1

Find the common denominator.

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Step 1.1

Multiply $\frac{2}{3}$ by $\frac{\frac{2 \cdot 7}{2}}{\frac{2 \cdot 7}{2}}$ .

$\frac{2}{3} \cdot \frac{\frac{2 \cdot 7}{2}}{\frac{2 \cdot 7}{2}} - \frac{1}{5} \div \frac{7}{2} - \frac{5}{6}$

Step 1.2

Multiply $\frac{2}{3}$ by $\frac{\frac{2 \cdot 7}{2}}{\frac{2 \cdot 7}{2}}$ .

$\frac{2 \frac{2 \cdot 7}{2}}{3 \frac{2 \cdot 7}{2}} - \frac{1}{5} \div \frac{7}{2} - \frac{5}{6}$

Step 1.3

Multiply $\frac{1}{5} \div \frac{7}{2}$ by $\frac{6}{6}$ .

$\frac{2 \frac{2 \cdot 7}{2}}{3 \frac{2 \cdot 7}{2}} - (\frac{1}{5} \div \frac{7}{2} \cdot \frac{6}{6}) - \frac{5}{6}$

Step 1.4

Multiply $\frac{1}{5} \div \frac{7}{2}$ by $\frac{6}{6}$ .

$\frac{2 \frac{2 \cdot 7}{2}}{3 \frac{2 \cdot 7}{2}} - \frac{\frac{1}{5} \cdot 6}{\frac{7}{2} \cdot 6} - \frac{5}{6}$

Step 1.5

Multiply $\frac{5}{6}$ by $\frac{\frac{7}{2}}{\frac{7}{2}}$ .

$\frac{2 \frac{2 \cdot 7}{2}}{3 \frac{2 \cdot 7}{2}} - \frac{\frac{1}{5} \cdot 6}{\frac{7}{2} \cdot 6} - (\frac{5}{6} \cdot \frac{\frac{7}{2}}{\frac{7}{2}})$

Step 1.6

Multiply $\frac{5}{6}$ by $\frac{\frac{7}{2}}{\frac{7}{2}}$ .

$\frac{2 \frac{2 \cdot 7}{2}}{3 \frac{2 \cdot 7}{2}} - \frac{\frac{1}{5} \cdot 6}{\frac{7}{2} \cdot 6} - \frac{5 (\frac{7}{2})}{6 (\frac{7}{2})}$

Step 1.7

Multiply $2$ by $7$ .

$\frac{2 \frac{2 \cdot 7}{2}}{3 (\frac{14}{2})} - \frac{\frac{1}{5} \cdot 6}{\frac{7}{2} \cdot 6} - \frac{5 (\frac{7}{2})}{6 (\frac{7}{2})}$

Step 1.8

Combine $3$ and $\frac{14}{2}$ .

$\frac{2 \frac{2 \cdot 7}{2}}{\frac{3 \cdot 14}{2}} - \frac{\frac{1}{5} \cdot 6}{\frac{7}{2} \cdot 6} - \frac{5 (\frac{7}{2})}{6 (\frac{7}{2})}$

Step 1.9

Multiply $3$ by $14$ .

$\frac{2 \frac{2 \cdot 7}{2}}{\frac{42}{2}} - \frac{\frac{1}{5} \cdot 6}{\frac{7}{2} \cdot 6} - \frac{5 (\frac{7}{2})}{6 (\frac{7}{2})}$

Step 1.10

Reorder the factors of $\frac{7}{2} \cdot 6$ .

$\frac{2 \frac{2 \cdot 7}{2}}{\frac{42}{2}} - \frac{\frac{1}{5} \cdot 6}{6 (\frac{7}{2})} - \frac{5 (\frac{7}{2})}{6 (\frac{7}{2})}$

Step 1.11

Combine $6$ and $\frac{7}{2}$ .

$\frac{2 \frac{2 \cdot 7}{2}}{\frac{42}{2}} - \frac{\frac{1}{5} \cdot 6}{\frac{6 \cdot 7}{2}} - \frac{5 (\frac{7}{2})}{6 (\frac{7}{2})}$

Step 1.12

Multiply $6$ by $7$ .

$\frac{2 \frac{2 \cdot 7}{2}}{\frac{42}{2}} - \frac{\frac{1}{5} \cdot 6}{\frac{42}{2}} - \frac{5 (\frac{7}{2})}{6 (\frac{7}{2})}$

Step 2

Combine the numerators over the common denominator.

$\frac{2 \frac{2 \cdot 7}{2} - \frac{1}{5} \cdot 6}{\frac{42}{2}} + \frac{- 5 (\frac{7}{2})}{6 (\frac{7}{2})}$

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

Cancel the common factor.

$\frac{2 \frac{2 \cdot 7}{2} - \frac{1}{5} \cdot 6}{\frac{42}{2}} + \frac{- 5 (\frac{7}{2})}{6 (\frac{7}{2})}$

Step 3.1.2

Rewrite the expression.

$\frac{2 \cdot 7 - \frac{1}{5} \cdot 6}{\frac{42}{2}} + \frac{- 5 (\frac{7}{2})}{6 (\frac{7}{2})}$

Step 3.2

Multiply $2$ by $7$ .

$\frac{14 - \frac{1}{5} \cdot 6}{\frac{42}{2}} + \frac{- 5 (\frac{7}{2})}{6 (\frac{7}{2})}$

Step 3.3

Multiply $- \frac{1}{5} \cdot 6$ .

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Step 3.3.1

Multiply $6$ by $- 1$ .

$\frac{14 - 6 (\frac{1}{5})}{\frac{42}{2}} + \frac{- 5 (\frac{7}{2})}{6 (\frac{7}{2})}$

Step 3.3.2

Combine $- 6$ and $\frac{1}{5}$ .

$\frac{14 + \frac{- 6}{5}}{\frac{42}{2}} + \frac{- 5 (\frac{7}{2})}{6 (\frac{7}{2})}$

Step 3.4

Move the negative in front of the fraction.

$\frac{14 - \frac{6}{5}}{\frac{42}{2}} + \frac{- 5 (\frac{7}{2})}{6 (\frac{7}{2})}$

Step 4

To write $14$ as a fraction with a common denominator, multiply by $\frac{5}{5}$ .

$\frac{14 \cdot \frac{5}{5} - \frac{6}{5}}{\frac{42}{2}} + \frac{- 5 (\frac{7}{2})}{6 (\frac{7}{2})}$

Step 5

Combine $14$ and $\frac{5}{5}$ .

$\frac{\frac{14 \cdot 5}{5} - \frac{6}{5}}{\frac{42}{2}} + \frac{- 5 (\frac{7}{2})}{6 (\frac{7}{2})}$

Step 6

Combine the numerators over the common denominator.

$\frac{\frac{14 \cdot 5 - 6}{5}}{\frac{42}{2}} + \frac{- 5 (\frac{7}{2})}{6 (\frac{7}{2})}$

Step 7

Simplify the numerator.

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Step 7.1

Multiply $14$ by $5$ .

$\frac{\frac{70 - 6}{5}}{\frac{42}{2}} + \frac{- 5 (\frac{7}{2})}{6 (\frac{7}{2})}$

Step 7.2

Subtract $6$ from $70$ .

$\frac{\frac{64}{5}}{\frac{42}{2}} + \frac{- 5 (\frac{7}{2})}{6 (\frac{7}{2})}$

Step 8

Simplify each term.

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Step 8.1

Cancel the common factor of $42$ and $2$ .

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Step 8.1.1

Factor $2$ out of $42$ .

$\frac{\frac{64}{5}}{\frac{2 \cdot 21}{2}} + \frac{- 5 (\frac{7}{2})}{6 (\frac{7}{2})}$

Step 8.1.2

Cancel the common factors.

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Step 8.1.2.1

Factor $2$ out of $2$ .

$\frac{\frac{64}{5}}{\frac{2 \cdot 21}{2 (1)}} + \frac{- 5 (\frac{7}{2})}{6 (\frac{7}{2})}$

Step 8.1.2.2

Cancel the common factor.

$\frac{\frac{64}{5}}{\frac{2 \cdot 21}{2 \cdot 1}} + \frac{- 5 (\frac{7}{2})}{6 (\frac{7}{2})}$

Step 8.1.2.3

Rewrite the expression.

$\frac{\frac{64}{5}}{\frac{21}{1}} + \frac{- 5 (\frac{7}{2})}{6 (\frac{7}{2})}$

Step 8.1.2.4

Divide $21$ by $1$ .

$\frac{\frac{64}{5}}{21} + \frac{- 5 (\frac{7}{2})}{6 (\frac{7}{2})}$

Step 8.2

Multiply the numerator by the reciprocal of the denominator.

$\frac{64}{5} \cdot \frac{1}{21} + \frac{- 5 (\frac{7}{2})}{6 (\frac{7}{2})}$

Step 8.3

Multiply $\frac{64}{5} \cdot \frac{1}{21}$ .

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Step 8.3.1

Multiply $\frac{64}{5}$ by $\frac{1}{21}$ .

$\frac{64}{5 \cdot 21} + \frac{- 5 (\frac{7}{2})}{6 (\frac{7}{2})}$

Step 8.3.2

Multiply $5$ by $21$ .

$\frac{64}{105} + \frac{- 5 (\frac{7}{2})}{6 (\frac{7}{2})}$

Step 8.4

Cancel the common factor of $\frac{7}{2}$ .

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Step 8.4.1

Cancel the common factor.

$\frac{64}{105} + \frac{- 5 (\frac{7}{2})}{6 (\frac{7}{2})}$

Step 8.4.2

Rewrite the expression.

$\frac{64}{105} + \frac{- 5}{6}$

Step 8.5

Move the negative in front of the fraction.

$\frac{64}{105} - \frac{5}{6}$

Step 9

To write $\frac{64}{105}$ as a fraction with a common denominator, multiply by $\frac{2}{2}$ .

$\frac{64}{105} \cdot \frac{2}{2} - \frac{5}{6}$

Step 10

To write $- \frac{5}{6}$ as a fraction with a common denominator, multiply by $\frac{35}{35}$ .

$\frac{64}{105} \cdot \frac{2}{2} - \frac{5}{6} \cdot \frac{35}{35}$

Step 11

Write each expression with a common denominator of $210$ , by multiplying each by an appropriate factor of $1$ .

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Step 11.1

Multiply $\frac{64}{105}$ by $\frac{2}{2}$ .

$\frac{64 \cdot 2}{105 \cdot 2} - \frac{5}{6} \cdot \frac{35}{35}$

Step 11.2

Multiply $105$ by $2$ .

$\frac{64 \cdot 2}{210} - \frac{5}{6} \cdot \frac{35}{35}$

Step 11.3

Multiply $\frac{5}{6}$ by $\frac{35}{35}$ .

$\frac{64 \cdot 2}{210} - \frac{5 \cdot 35}{6 \cdot 35}$

Step 11.4

Multiply $6$ by $35$ .

$\frac{64 \cdot 2}{210} - \frac{5 \cdot 35}{210}$

Step 12

Combine the numerators over the common denominator.

$\frac{64 \cdot 2 - 5 \cdot 35}{210}$

Step 13

Simplify the numerator.

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Step 13.1

Multiply $64$ by $2$ .

$\frac{128 - 5 \cdot 35}{210}$

Step 13.2

Multiply $- 5$ by $35$ .

$\frac{128 - 175}{210}$

Step 13.3

Subtract $175$ from $128$ .

$\frac{- 47}{210}$

Step 14

Move the negative in front of the fraction.

$- \frac{47}{210}$

Step 15

The result can be shown in multiple forms.

Exact Form:

$- \frac{47}{210}$

Decimal Form:

$- 0.2\overline{238095}$