Basic Math Examples

$4 \frac{5}{6} - \frac{2}{3} - 1 \frac{8}{9} \div 1 \frac{7}{10}$

Step 1

Convert $4 \frac{5}{6}$ to an improper fraction.

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Step 1.1

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

$4 + \frac{5}{6} - \frac{2}{3} - 1 \frac{8}{9} \div 1 \frac{7}{10}$

Step 1.2

Add $4$ and $\frac{5}{6}$ .

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Step 1.2.1

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

$4 \cdot \frac{6}{6} + \frac{5}{6} - \frac{2}{3} - 1 \frac{8}{9} \div 1 \frac{7}{10}$

Step 1.2.2

Combine $4$ and $\frac{6}{6}$ .

$\frac{4 \cdot 6}{6} + \frac{5}{6} - \frac{2}{3} - 1 \frac{8}{9} \div 1 \frac{7}{10}$

Step 1.2.3

Combine the numerators over the common denominator.

$\frac{4 \cdot 6 + 5}{6} - \frac{2}{3} - 1 \frac{8}{9} \div 1 \frac{7}{10}$

Step 1.2.4

Simplify the numerator.

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Step 1.2.4.1

Multiply $4$ by $6$ .

$\frac{24 + 5}{6} - \frac{2}{3} - 1 \frac{8}{9} \div 1 \frac{7}{10}$

Step 1.2.4.2

Add $24$ and $5$ .

$\frac{29}{6} - \frac{2}{3} - 1 \frac{8}{9} \div 1 \frac{7}{10}$

Step 2

Convert $1 \frac{8}{9}$ to an improper fraction.

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Step 2.1

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

$\frac{29}{6} - \frac{2}{3} - (1 + \frac{8}{9}) \div 1 \frac{7}{10}$

Step 2.2

Add $1$ and $\frac{8}{9}$ .

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Step 2.2.1

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

$\frac{29}{6} - \frac{2}{3} - (\frac{9}{9} + \frac{8}{9}) \div 1 \frac{7}{10}$

Step 2.2.2

Combine the numerators over the common denominator.

$\frac{29}{6} - \frac{2}{3} - \frac{9 + 8}{9} \div 1 \frac{7}{10}$

Step 2.2.3

Add $9$ and $8$ .

$\frac{29}{6} - \frac{2}{3} - \frac{17}{9} \div 1 \frac{7}{10}$

Step 3

Convert $1 \frac{7}{10}$ to an improper fraction.

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Step 3.1

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

$\frac{29}{6} - \frac{2}{3} - \frac{17}{9} \div (1 + \frac{7}{10})$

Step 3.2

Add $1$ and $\frac{7}{10}$ .

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Step 3.2.1

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

$\frac{29}{6} - \frac{2}{3} - \frac{17}{9} \div (\frac{10}{10} + \frac{7}{10})$

Step 3.2.2

Combine the numerators over the common denominator.

$\frac{29}{6} - \frac{2}{3} - \frac{17}{9} \div \frac{10 + 7}{10}$

Step 3.2.3

Add $10$ and $7$ .

$\frac{29}{6} - \frac{2}{3} - \frac{17}{9} \div \frac{17}{10}$

Step 4

Find the common denominator.

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Step 4.1

Multiply $\frac{29}{6}$ by $\frac{\frac{17}{10}}{\frac{17}{10}}$ .

$\frac{29}{6} \cdot \frac{\frac{17}{10}}{\frac{17}{10}} - \frac{2}{3} - \frac{17}{9} \div \frac{17}{10}$

Step 4.2

Multiply $\frac{29}{6}$ by $\frac{\frac{17}{10}}{\frac{17}{10}}$ .

$\frac{29 (\frac{17}{10})}{6 (\frac{17}{10})} - \frac{2}{3} - \frac{17}{9} \div \frac{17}{10}$

Step 4.3

Multiply $\frac{2}{3}$ by $\frac{\frac{2 \cdot 17}{10}}{\frac{2 \cdot 17}{10}}$ .

$\frac{29 (\frac{17}{10})}{6 (\frac{17}{10})} - (\frac{2}{3} \cdot \frac{\frac{2 \cdot 17}{10}}{\frac{2 \cdot 17}{10}}) - \frac{17}{9} \div \frac{17}{10}$

Step 4.4

Multiply $\frac{2}{3}$ by $\frac{\frac{2 \cdot 17}{10}}{\frac{2 \cdot 17}{10}}$ .

$\frac{29 (\frac{17}{10})}{6 (\frac{17}{10})} - \frac{2 \frac{2 \cdot 17}{10}}{3 \frac{2 \cdot 17}{10}} - \frac{17}{9} \div \frac{17}{10}$

Step 4.5

Multiply $\frac{17}{9} \div \frac{17}{10}$ by $\frac{6}{6}$ .

$\frac{29 (\frac{17}{10})}{6 (\frac{17}{10})} - \frac{2 \frac{2 \cdot 17}{10}}{3 \frac{2 \cdot 17}{10}} - (\frac{17}{9} \div \frac{17}{10} \cdot \frac{6}{6})$

Step 4.6

Multiply $\frac{17}{9} \div \frac{17}{10}$ by $\frac{6}{6}$ .

$\frac{29 (\frac{17}{10})}{6 (\frac{17}{10})} - \frac{2 \frac{2 \cdot 17}{10}}{3 \frac{2 \cdot 17}{10}} - \frac{\frac{17}{9} \cdot 6}{\frac{17}{10} \cdot 6}$

Step 4.7

Multiply $2$ by $17$ .

$\frac{29 (\frac{17}{10})}{6 (\frac{17}{10})} - \frac{2 \frac{2 \cdot 17}{10}}{3 (\frac{34}{10})} - \frac{\frac{17}{9} \cdot 6}{\frac{17}{10} \cdot 6}$

Step 4.8

Combine $3$ and $\frac{34}{10}$ .

$\frac{29 (\frac{17}{10})}{6 (\frac{17}{10})} - \frac{2 \frac{2 \cdot 17}{10}}{\frac{3 \cdot 34}{10}} - \frac{\frac{17}{9} \cdot 6}{\frac{17}{10} \cdot 6}$

Step 4.9

Multiply $3$ by $34$ .

$\frac{29 (\frac{17}{10})}{6 (\frac{17}{10})} - \frac{2 \frac{2 \cdot 17}{10}}{\frac{102}{10}} - \frac{\frac{17}{9} \cdot 6}{\frac{17}{10} \cdot 6}$

Step 4.10

Reorder the factors of $\frac{17}{10} \cdot 6$ .

$\frac{29 (\frac{17}{10})}{6 (\frac{17}{10})} - \frac{2 \frac{2 \cdot 17}{10}}{\frac{102}{10}} - \frac{\frac{17}{9} \cdot 6}{6 (\frac{17}{10})}$

Step 4.11

Combine $6$ and $\frac{17}{10}$ .

$\frac{29 (\frac{17}{10})}{6 (\frac{17}{10})} - \frac{2 \frac{2 \cdot 17}{10}}{\frac{102}{10}} - \frac{\frac{17}{9} \cdot 6}{\frac{6 \cdot 17}{10}}$

Step 4.12

Multiply $6$ by $17$ .

$\frac{29 (\frac{17}{10})}{6 (\frac{17}{10})} - \frac{2 \frac{2 \cdot 17}{10}}{\frac{102}{10}} - \frac{\frac{17}{9} \cdot 6}{\frac{102}{10}}$

Step 5

Combine the numerators over the common denominator.

$\frac{29 (\frac{17}{10})}{6 (\frac{17}{10})} + \frac{- 2 \frac{2 \cdot 17}{10} - \frac{17}{9} \cdot 6}{\frac{102}{10}}$

Step 6

Simplify each term.

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Step 6.1

Cancel the common factor of $2$ .

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Step 6.1.1

Factor $2$ out of $- 2$ .

$\frac{29 (\frac{17}{10})}{6 (\frac{17}{10})} + \frac{2 (- 1) \frac{2 \cdot 17}{10} - \frac{17}{9} \cdot 6}{\frac{102}{10}}$

Step 6.1.2

Factor $2$ out of $10$ .

$\frac{29 (\frac{17}{10})}{6 (\frac{17}{10})} + \frac{2 \cdot - 1 \frac{2 \cdot 17}{2 \cdot 5} - \frac{17}{9} \cdot 6}{\frac{102}{10}}$

Step 6.1.3

Cancel the common factor.

$\frac{29 (\frac{17}{10})}{6 (\frac{17}{10})} + \frac{2 \cdot - 1 \frac{2 \cdot 17}{2 \cdot 5} - \frac{17}{9} \cdot 6}{\frac{102}{10}}$

Step 6.1.4

Rewrite the expression.

$\frac{29 (\frac{17}{10})}{6 (\frac{17}{10})} + \frac{- \frac{2 \cdot 17}{5} - \frac{17}{9} \cdot 6}{\frac{102}{10}}$

Step 6.2

Multiply $2$ by $17$ .

$\frac{29 (\frac{17}{10})}{6 (\frac{17}{10})} + \frac{- \frac{34}{5} - \frac{17}{9} \cdot 6}{\frac{102}{10}}$

Step 6.3

Cancel the common factor of $3$ .

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Step 6.3.1

Move the leading negative in $- \frac{17}{9}$ into the numerator.

$\frac{29 (\frac{17}{10})}{6 (\frac{17}{10})} + \frac{- \frac{34}{5} + \frac{- 17}{9} \cdot 6}{\frac{102}{10}}$

Step 6.3.2

Factor $3$ out of $9$ .

$\frac{29 (\frac{17}{10})}{6 (\frac{17}{10})} + \frac{- \frac{34}{5} + \frac{- 17}{3 (3)} \cdot 6}{\frac{102}{10}}$

Step 6.3.3

Factor $3$ out of $6$ .

$\frac{29 (\frac{17}{10})}{6 (\frac{17}{10})} + \frac{- \frac{34}{5} + \frac{- 17}{3 \cdot 3} \cdot (3 \cdot 2)}{\frac{102}{10}}$

Step 6.3.4

Cancel the common factor.

$\frac{29 (\frac{17}{10})}{6 (\frac{17}{10})} + \frac{- \frac{34}{5} + \frac{- 17}{3 \cdot 3} \cdot (3 \cdot 2)}{\frac{102}{10}}$

Step 6.3.5

Rewrite the expression.

$\frac{29 (\frac{17}{10})}{6 (\frac{17}{10})} + \frac{- \frac{34}{5} + \frac{- 17}{3} \cdot 2}{\frac{102}{10}}$

Step 6.4

Combine $\frac{- 17}{3}$ and $2$ .

$\frac{29 (\frac{17}{10})}{6 (\frac{17}{10})} + \frac{- \frac{34}{5} + \frac{- 17 \cdot 2}{3}}{\frac{102}{10}}$

Step 6.5

Multiply $- 17$ by $2$ .

$\frac{29 (\frac{17}{10})}{6 (\frac{17}{10})} + \frac{- \frac{34}{5} + \frac{- 34}{3}}{\frac{102}{10}}$

Step 6.6

Move the negative in front of the fraction.

$\frac{29 (\frac{17}{10})}{6 (\frac{17}{10})} + \frac{- \frac{34}{5} - \frac{34}{3}}{\frac{102}{10}}$

Step 7

To write $- \frac{34}{5}$ as a fraction with a common denominator, multiply by $\frac{3}{3}$ .

$\frac{29 (\frac{17}{10})}{6 (\frac{17}{10})} + \frac{- \frac{34}{5} \cdot \frac{3}{3} - \frac{34}{3}}{\frac{102}{10}}$

Step 8

To write $- \frac{34}{3}$ as a fraction with a common denominator, multiply by $\frac{5}{5}$ .

$\frac{29 (\frac{17}{10})}{6 (\frac{17}{10})} + \frac{- \frac{34}{5} \cdot \frac{3}{3} - \frac{34}{3} \cdot \frac{5}{5}}{\frac{102}{10}}$

Step 9

Write each expression with a common denominator of $15$ , by multiplying each by an appropriate factor of $1$ .

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Step 9.1

Multiply $\frac{34}{5}$ by $\frac{3}{3}$ .

$\frac{29 (\frac{17}{10})}{6 (\frac{17}{10})} + \frac{- \frac{34 \cdot 3}{5 \cdot 3} - \frac{34}{3} \cdot \frac{5}{5}}{\frac{102}{10}}$

Step 9.2

Multiply $5$ by $3$ .

$\frac{29 (\frac{17}{10})}{6 (\frac{17}{10})} + \frac{- \frac{34 \cdot 3}{15} - \frac{34}{3} \cdot \frac{5}{5}}{\frac{102}{10}}$

Step 9.3

Multiply $\frac{34}{3}$ by $\frac{5}{5}$ .

$\frac{29 (\frac{17}{10})}{6 (\frac{17}{10})} + \frac{- \frac{34 \cdot 3}{15} - \frac{34 \cdot 5}{3 \cdot 5}}{\frac{102}{10}}$

Step 9.4

Multiply $3$ by $5$ .

$\frac{29 (\frac{17}{10})}{6 (\frac{17}{10})} + \frac{- \frac{34 \cdot 3}{15} - \frac{34 \cdot 5}{15}}{\frac{102}{10}}$

Step 10

Combine the numerators over the common denominator.

$\frac{29 (\frac{17}{10})}{6 (\frac{17}{10})} + \frac{\frac{- 34 \cdot 3 - 34 \cdot 5}{15}}{\frac{102}{10}}$

Step 11

Simplify the numerator.

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Step 11.1

Multiply $- 34$ by $3$ .

$\frac{29 (\frac{17}{10})}{6 (\frac{17}{10})} + \frac{\frac{- 102 - 34 \cdot 5}{15}}{\frac{102}{10}}$

Step 11.2

Multiply $- 34$ by $5$ .

$\frac{29 (\frac{17}{10})}{6 (\frac{17}{10})} + \frac{\frac{- 102 - 170}{15}}{\frac{102}{10}}$

Step 11.3

Subtract $170$ from $- 102$ .

$\frac{29 (\frac{17}{10})}{6 (\frac{17}{10})} + \frac{\frac{- 272}{15}}{\frac{102}{10}}$

Step 12

Move the negative in front of the fraction.

$\frac{29 (\frac{17}{10})}{6 (\frac{17}{10})} + \frac{- \frac{272}{15}}{\frac{102}{10}}$

Step 13

Simplify each term.

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Step 13.1

Cancel the common factor of $\frac{17}{10}$ .

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Step 13.1.1

Cancel the common factor.

$\frac{29 (\frac{17}{10})}{6 (\frac{17}{10})} + \frac{- \frac{272}{15}}{\frac{102}{10}}$

Step 13.1.2

Rewrite the expression.

$\frac{29}{6} + \frac{- \frac{272}{15}}{\frac{102}{10}}$

Step 13.2

Cancel the common factor of $102$ and $10$ .

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Step 13.2.1

Factor $2$ out of $102$ .

$\frac{29}{6} + \frac{- \frac{272}{15}}{\frac{2 (51)}{10}}$

Step 13.2.2

Cancel the common factors.

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Step 13.2.2.1

Factor $2$ out of $10$ .

$\frac{29}{6} + \frac{- \frac{272}{15}}{\frac{2 \cdot 51}{2 \cdot 5}}$

Step 13.2.2.2

Cancel the common factor.

$\frac{29}{6} + \frac{- \frac{272}{15}}{\frac{2 \cdot 51}{2 \cdot 5}}$

Step 13.2.2.3

Rewrite the expression.

$\frac{29}{6} + \frac{- \frac{272}{15}}{\frac{51}{5}}$

Step 13.3

Multiply the numerator by the reciprocal of the denominator.

$\frac{29}{6} - \frac{272}{15} \cdot \frac{5}{51}$

Step 13.4

Cancel the common factor of $17$ .

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Step 13.4.1

Move the leading negative in $- \frac{272}{15}$ into the numerator.

$\frac{29}{6} + \frac{- 272}{15} \cdot \frac{5}{51}$

Step 13.4.2

Factor $17$ out of $- 272$ .

$\frac{29}{6} + \frac{17 (- 16)}{15} \cdot \frac{5}{51}$

Step 13.4.3

Factor $17$ out of $51$ .

$\frac{29}{6} + \frac{17 \cdot - 16}{15} \cdot \frac{5}{17 \cdot 3}$

Step 13.4.4

Cancel the common factor.

$\frac{29}{6} + \frac{17 \cdot - 16}{15} \cdot \frac{5}{17 \cdot 3}$

Step 13.4.5

Rewrite the expression.

$\frac{29}{6} + \frac{- 16}{15} \cdot \frac{5}{3}$

Step 13.5

Cancel the common factor of $5$ .

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Step 13.5.1

Factor $5$ out of $15$ .

$\frac{29}{6} + \frac{- 16}{5 (3)} \cdot \frac{5}{3}$

Step 13.5.2

Cancel the common factor.

$\frac{29}{6} + \frac{- 16}{5 \cdot 3} \cdot \frac{5}{3}$

Step 13.5.3

Rewrite the expression.

$\frac{29}{6} + \frac{- 16}{3} \cdot \frac{1}{3}$

Step 13.6

Multiply $\frac{- 16}{3}$ by $\frac{1}{3}$ .

$\frac{29}{6} + \frac{- 16}{3 \cdot 3}$

Step 13.7

Multiply $3$ by $3$ .

$\frac{29}{6} + \frac{- 16}{9}$

Step 13.8

Move the negative in front of the fraction.

$\frac{29}{6} - \frac{16}{9}$

Step 14

To write $\frac{29}{6}$ as a fraction with a common denominator, multiply by $\frac{3}{3}$ .

$\frac{29}{6} \cdot \frac{3}{3} - \frac{16}{9}$

Step 15

To write $- \frac{16}{9}$ as a fraction with a common denominator, multiply by $\frac{2}{2}$ .

$\frac{29}{6} \cdot \frac{3}{3} - \frac{16}{9} \cdot \frac{2}{2}$

Step 16

Write each expression with a common denominator of $18$ , by multiplying each by an appropriate factor of $1$ .

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Step 16.1

Multiply $\frac{29}{6}$ by $\frac{3}{3}$ .

$\frac{29 \cdot 3}{6 \cdot 3} - \frac{16}{9} \cdot \frac{2}{2}$

Step 16.2

Multiply $6$ by $3$ .

$\frac{29 \cdot 3}{18} - \frac{16}{9} \cdot \frac{2}{2}$

Step 16.3

Multiply $\frac{16}{9}$ by $\frac{2}{2}$ .

$\frac{29 \cdot 3}{18} - \frac{16 \cdot 2}{9 \cdot 2}$

Step 16.4

Multiply $9$ by $2$ .

$\frac{29 \cdot 3}{18} - \frac{16 \cdot 2}{18}$

Step 17

Combine the numerators over the common denominator.

$\frac{29 \cdot 3 - 16 \cdot 2}{18}$

Step 18

Simplify the numerator.

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Step 18.1

Multiply $29$ by $3$ .

$\frac{87 - 16 \cdot 2}{18}$

Step 18.2

Multiply $- 16$ by $2$ .

$\frac{87 - 32}{18}$

Step 18.3

Subtract $32$ from $87$ .

$\frac{55}{18}$

Step 19

The result can be shown in multiple forms.

Exact Form:

$\frac{55}{18}$

Decimal Form:

$3.0\overline{5}$

Mixed Number Form:

$3 \frac{1}{18}$