What is ([\frac{-5)/(8\times (9/(7-(\frac{-8){5))})}]}{((-9)/(11))} ?

The solution to ([\frac{-5)/(8\times (9/(7-(\frac{-8){5))})}]}{((-9)/(11))} is 473/648

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Popular >

simplify ([\frac{-5)/(8\times (9/(7-(\frac{-8){5))})}]}{((-9)/(11))}

Solution

simplify

\frac{\frac{- 5}{8 \cdot ( \frac{9}{7 - ( \frac{- 8}{5} )} )}}{( \frac{- 9}{11} )}

Solution

\frac{473}{648}

Decimal Notation

0.72993 \dots

Solution steps

\frac{\frac{- 5}{8 ( \frac{9}{7 - ( \frac{- 8}{5} )} )}}{\frac{- 9}{11}}

8 (\frac{9}{7 - ( \frac{- 8}{5} )}) = 8 \cdot \frac{9}{7 - \frac{- 8}{5}}

8 (\frac{9}{7 - ( \frac{- 8}{5} )})

Apply rule:

- (a) = - a

- (\frac{- 8}{5}) = - \frac{- 8}{5}

= 8 (\frac{9}{7 - \frac{- 8}{5}})

Apply rule:

(a) = a

(\frac{9}{7 - \frac{- 8}{5}}) = \frac{9}{7 - \frac{- 8}{5}}

= 8 \cdot \frac{9}{7 - \frac{- 8}{5}}

= \frac{\frac{- 5}{8 \cdot \frac{9}{7 - \frac{- 8}{5}}}}{\frac{- 9}{11}}

Apply the fraction rule:

\frac{\frac{a}{b}}{\frac{c}{d}} = \frac{a \cdot d}{b \cdot c}

= \frac{- 5 \cdot 11}{8 \cdot \frac{9}{7 - \frac{- 8}{5}} ( - 9 )}

Apply the fraction rule:

\frac{- a}{b} = - \frac{a}{b}

= - \frac{5 \cdot 11}{8 \cdot \frac{9}{7 - \frac{- 8}{5}} ( - 9 )}

Apply the fraction rule:

- \frac{- a}{b} = \frac{a}{b}

- \frac{- 8}{5} = \frac{8}{5}

= - \frac{5 \cdot 11}{8 \cdot \frac{9}{7 + \frac{8}{5}} ( - 9 )}

Multiply the numbers:

5 \cdot 11 = 55

= - \frac{55}{8 \cdot \frac{9}{7 + \frac{8}{5}} ( - 9 )}

8 \cdot \frac{9}{7 + \frac{8}{5}} (- 9) = - \frac{3240}{43}

8 \cdot \frac{9}{7 + \frac{8}{5}} (- 9)

\frac{9}{7 + \frac{8}{5}} = \frac{9 \cdot 5}{43}

\frac{9}{7 + \frac{8}{5}}

7 + \frac{8}{5} = \frac{43}{5}

7 + \frac{8}{5}

Convert

7

to fraction

: \frac{35}{5}

7

Apply the fraction rule:

a = \frac{ab}{b}

= \frac{7 \cdot 5}{5}

Multiply the numbers:

7 \cdot 5 = 35

= \frac{35}{5}

= \frac{35}{5} + \frac{8}{5}

\frac{35}{5} + \frac{8}{5} = \frac{43}{5}

\frac{35}{5} + \frac{8}{5}

Apply the fraction rule:

\frac{a}{c} + \frac{b}{c} = \frac{a + b}{c}

= \frac{35 + 8}{5}

Add the numbers:

35 + 8 = 43

= \frac{43}{5}

= \frac{43}{5}

= \frac{9}{\frac{43}{5}}

Apply the fraction rule:

\frac{a}{\frac{b}{c}} = \frac{a \cdot c}{b}

= \frac{9 \cdot 5}{43}

= 8 \cdot \frac{9 \cdot 5}{43} (- 9)

8 \cdot \frac{9 \cdot 5}{43} (- 9) = \frac{360}{43} (- 9)

8 \cdot \frac{9 \cdot 5}{43} (- 9)

Convert element to fraction:

8 = \frac{8}{1}

= \frac{8}{1} \cdot \frac{9 \cdot 5}{43} (- 9)

Apply the fraction rule:

\frac{a}{b} \cdot \frac{c}{d} = \frac{a \cdot c}{b \cdot d}

\frac{8}{1} \cdot \frac{9 \cdot 5}{43} = \frac{8 \cdot 9 \cdot 5}{1 \cdot 43}

= \frac{8 \cdot 9 \cdot 5}{1 \cdot 43} (- 9)

Multiply the numbers:

8 \cdot 9 \cdot 5 = 360

= \frac{360}{1 \cdot 43} (- 9)

Multiply the numbers:

1 \cdot 43 = 43

= \frac{360}{43} (- 9)

= \frac{360}{43} (- 9)

Apply rule:

a (- b) = - ab

\frac{360}{43} (- 9) = - \frac{360}{43} \cdot 9

= - \frac{360}{43} \cdot 9

- \frac{360}{43} \cdot 9 = - \frac{3240}{43}

- \frac{360}{43} \cdot 9

Convert element to fraction:

9 = \frac{9}{1}

= - \frac{360}{43} \cdot \frac{9}{1}

Apply the fraction rule:

\frac{a}{b} \cdot \frac{c}{d} = \frac{a \cdot c}{b \cdot d}

\frac{360}{43} \cdot \frac{9}{1} = \frac{360 \cdot 9}{43 \cdot 1}

= - \frac{360 \cdot 9}{43 \cdot 1}

Multiply the numbers:

360 \cdot 9 = 3240

= - \frac{3240}{43 \cdot 1}

Multiply the numbers:

43 \cdot 1 = 43

= - \frac{3240}{43}

= - \frac{3240}{43}

= - \frac{55}{- \frac{3240}{43}}

Apply the fraction rule:

\frac{a}{- b} = - \frac{a}{b}

\frac{55}{- \frac{3240}{43}} = - \frac{55}{\frac{3240}{43}}

= - (- \frac{55}{\frac{3240}{43}})

Apply rule:

- (- a) = a

- (- \frac{55}{\frac{3240}{43}}) = \frac{55}{\frac{3240}{43}}

= \frac{55}{\frac{3240}{43}}

Apply the fraction rule:

\frac{a}{\frac{b}{c}} = \frac{a \cdot c}{b}

= \frac{55 \cdot 43}{3240}

Cancel

\frac{55 \cdot 43}{3240} : \frac{473}{648}

\frac{55 \cdot 43}{3240}

Factor the number:

55 = 5 \cdot 11

= \frac{5 \cdot 11 \cdot 43}{3240}

Factor the number:

3240 = 5 \cdot 648

= \frac{5 \cdot 11 \cdot 43}{5 \cdot 648}

Cancel the common factor:

5

= \frac{11 \cdot 43}{648}

Multiply the numbers:

11 \cdot 43 = 473

= \frac{473}{648}

= \frac{473}{648}

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Frequently Asked Questions (FAQ)

What is ([\frac{-5)/(8\times (9/(7-(\frac{-8){5))})}]}{((-9)/(11))} ?
The solution to ([\frac{-5)/(8\times (9/(7-(\frac{-8){5))})}]}{((-9)/(11))} is 473/648