Evaluate (6/35+(4/9-3/55))÷(15/35+(10/9-3/22))

$(\frac{6}{35} + (\frac{4}{9} - \frac{3}{55})) \div (\frac{15}{35} + (\frac{10}{9} - \frac{3}{22}))$

Remove parentheses.

$\frac{\frac{6}{35} + \frac{4}{9} - \frac{3}{55}}{\frac{15}{35} + \frac{10}{9} - \frac{3}{22}}$

Cancel the common factor of $15$ and $35$ .

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Factor $5$ out of $15$ .

$\frac{\frac{6}{35} + \frac{4}{9} - \frac{3}{55}}{\frac{5 (3)}{35} + \frac{10}{9} - \frac{3}{22}}$

Cancel the common factors.

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Factor $5$ out of $35$ .

$\frac{\frac{6}{35} + \frac{4}{9} - \frac{3}{55}}{\frac{5 \cdot 3}{5 \cdot 7} + \frac{10}{9} - \frac{3}{22}}$

Cancel the common factor.

$\frac{\frac{6}{35} + \frac{4}{9} - \frac{3}{55}}{\frac{5 \cdot 3}{5 \cdot 7} + \frac{10}{9} - \frac{3}{22}}$

Rewrite the expression.

$\frac{\frac{6}{35} + \frac{4}{9} - \frac{3}{55}}{\frac{3}{7} + \frac{10}{9} - \frac{3}{22}}$

Multiply the numerator and denominator of the complex fraction by $6930$ .

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Multiply $\frac{\frac{6}{35} + \frac{4}{9} - \frac{3}{55}}{\frac{3}{7} + \frac{10}{9} - \frac{3}{22}}$ by $\frac{6930}{6930}$ .

$\frac{6930}{6930} \cdot \frac{\frac{6}{35} + \frac{4}{9} - \frac{3}{55}}{\frac{3}{7} + \frac{10}{9} - \frac{3}{22}}$

Combine.

$\frac{6930 (\frac{6}{35} + \frac{4}{9} - \frac{3}{55})}{6930 (\frac{3}{7} + \frac{10}{9} - \frac{3}{22})}$

Apply the distributive property.

$\frac{6930 (\frac{6}{35}) + 6930 (\frac{4}{9}) + 6930 (- \frac{3}{55})}{6930 (\frac{3}{7}) + 6930 (\frac{10}{9}) + 6930 (- \frac{3}{22})}$

Simplify by cancelling.

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Cancel the common factor of $35$ .

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Factor $35$ out of $6930$ .

$\frac{35 (198) \frac{6}{35} + 6930 (\frac{4}{9}) + 6930 (- \frac{3}{55})}{6930 (\frac{3}{7}) + 6930 (\frac{10}{9}) + 6930 (- \frac{3}{22})}$

Cancel the common factor.

$\frac{35 \cdot 198 \frac{6}{35} + 6930 (\frac{4}{9}) + 6930 (- \frac{3}{55})}{6930 (\frac{3}{7}) + 6930 (\frac{10}{9}) + 6930 (- \frac{3}{22})}$

Rewrite the expression.

$\frac{198 \cdot 6 + 6930 (\frac{4}{9}) + 6930 (- \frac{3}{55})}{6930 (\frac{3}{7}) + 6930 (\frac{10}{9}) + 6930 (- \frac{3}{22})}$

Multiply $198$ by $6$ .

$\frac{1188 + 6930 (\frac{4}{9}) + 6930 (- \frac{3}{55})}{6930 (\frac{3}{7}) + 6930 (\frac{10}{9}) + 6930 (- \frac{3}{22})}$

Cancel the common factor of $9$ .

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Factor $9$ out of $6930$ .

$\frac{1188 + 9 (770) \frac{4}{9} + 6930 (- \frac{3}{55})}{6930 (\frac{3}{7}) + 6930 (\frac{10}{9}) + 6930 (- \frac{3}{22})}$

Cancel the common factor.

$\frac{1188 + 9 \cdot 770 \frac{4}{9} + 6930 (- \frac{3}{55})}{6930 (\frac{3}{7}) + 6930 (\frac{10}{9}) + 6930 (- \frac{3}{22})}$

Rewrite the expression.

$\frac{1188 + 770 \cdot 4 + 6930 (- \frac{3}{55})}{6930 (\frac{3}{7}) + 6930 (\frac{10}{9}) + 6930 (- \frac{3}{22})}$

Multiply $770$ by $4$ .

$\frac{1188 + 3080 + 6930 (- \frac{3}{55})}{6930 (\frac{3}{7}) + 6930 (\frac{10}{9}) + 6930 (- \frac{3}{22})}$

Cancel the common factor of $55$ .

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Move the leading negative in $- \frac{3}{55}$ into the numerator.

$\frac{1188 + 3080 + 6930 (\frac{- 3}{55})}{6930 (\frac{3}{7}) + 6930 (\frac{10}{9}) + 6930 (- \frac{3}{22})}$

Factor $55$ out of $6930$ .

$\frac{1188 + 3080 + 55 (126) \frac{- 3}{55}}{6930 (\frac{3}{7}) + 6930 (\frac{10}{9}) + 6930 (- \frac{3}{22})}$

Cancel the common factor.

$\frac{1188 + 3080 + 55 \cdot 126 \frac{- 3}{55}}{6930 (\frac{3}{7}) + 6930 (\frac{10}{9}) + 6930 (- \frac{3}{22})}$

Rewrite the expression.

$\frac{1188 + 3080 + 126 \cdot - 3}{6930 (\frac{3}{7}) + 6930 (\frac{10}{9}) + 6930 (- \frac{3}{22})}$

Multiply $126$ by $- 3$ .

$\frac{1188 + 3080 - 378}{6930 (\frac{3}{7}) + 6930 (\frac{10}{9}) + 6930 (- \frac{3}{22})}$

Cancel the common factor of $7$ .

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Factor $7$ out of $6930$ .

$\frac{1188 + 3080 - 378}{7 (990) \frac{3}{7} + 6930 (\frac{10}{9}) + 6930 (- \frac{3}{22})}$

Cancel the common factor.

$\frac{1188 + 3080 - 378}{7 \cdot 990 \frac{3}{7} + 6930 (\frac{10}{9}) + 6930 (- \frac{3}{22})}$

Rewrite the expression.

$\frac{1188 + 3080 - 378}{990 \cdot 3 + 6930 (\frac{10}{9}) + 6930 (- \frac{3}{22})}$

Multiply $990$ by $3$ .

$\frac{1188 + 3080 - 378}{2970 + 6930 (\frac{10}{9}) + 6930 (- \frac{3}{22})}$

Cancel the common factor of $9$ .

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Factor $9$ out of $6930$ .

$\frac{1188 + 3080 - 378}{2970 + 9 (770) \frac{10}{9} + 6930 (- \frac{3}{22})}$

Cancel the common factor.

$\frac{1188 + 3080 - 378}{2970 + 9 \cdot 770 \frac{10}{9} + 6930 (- \frac{3}{22})}$

Rewrite the expression.

$\frac{1188 + 3080 - 378}{2970 + 770 \cdot 10 + 6930 (- \frac{3}{22})}$

Multiply $770$ by $10$ .

$\frac{1188 + 3080 - 378}{2970 + 7700 + 6930 (- \frac{3}{22})}$

Cancel the common factor of $22$ .

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Move the leading negative in $- \frac{3}{22}$ into the numerator.

$\frac{1188 + 3080 - 378}{2970 + 7700 + 6930 (\frac{- 3}{22})}$

Factor $22$ out of $6930$ .

$\frac{1188 + 3080 - 378}{2970 + 7700 + 22 (315) \frac{- 3}{22}}$

Cancel the common factor.

$\frac{1188 + 3080 - 378}{2970 + 7700 + 22 \cdot 315 \frac{- 3}{22}}$

Rewrite the expression.

$\frac{1188 + 3080 - 378}{2970 + 7700 + 315 \cdot - 3}$

Multiply $315$ by $- 3$ .

$\frac{1188 + 3080 - 378}{2970 + 7700 - 945}$

Simplify the numerator.

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Add $1188$ and $3080$ .

$\frac{4268 - 378}{2970 + 7700 - 945}$

Subtract $378$ from $4268$ .

$\frac{3890}{2970 + 7700 - 945}$

Simplify the denominator.

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Add $2970$ and $7700$ .

$\frac{3890}{10670 - 945}$

Subtract $945$ from $10670$ .

$\frac{3890}{9725}$

Cancel the common factor of $3890$ and $9725$ .

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Factor $1945$ out of $3890$ .

$\frac{1945 (2)}{9725}$

Cancel the common factors.

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Factor $1945$ out of $9725$ .

$\frac{1945 \cdot 2}{1945 \cdot 5}$

Cancel the common factor.

$\frac{1945 \cdot 2}{1945 \cdot 5}$

Rewrite the expression.

$\frac{2}{5}$

The result can be shown in multiple forms.

Exact Form:

$\frac{2}{5}$

Decimal Form:

$0.4$

Evaluate (6/35+(4/9-3/55))÷(15/35+(10/9-3/22))

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