Solve 7/12div(75%-5/12)-17/24quad5/3*(80%+frac{9}{14}divfrac{36}{35})

$$\frac { 7 } { 12 } \div ( 75 \% - \frac { 5 } { 12 } ) - \frac { 17 } { 24 } \quad \frac { 5 } { 3 } \times ( 80 \% + \frac { 9 } { 14 } \div \frac { 36 } { 35 } )$$

Evaluate

$$\frac{13}{192}\approx 0.067708333$$

Solution Steps

Reduce the fraction \frac{75}{100} to lowest terms by extracting and canceling out 25.

$$\frac{\frac{7}{12}}{\frac{3}{4}-\frac{5}{12}}-\frac{17}{24}\times \frac{5}{3}\left(\frac{80}{100}+\frac{\frac{9}{14}}{\frac{36}{35}}\right)$$

Least common multiple of 4 and 12 is 12. Convert \frac{3}{4} and \frac{5}{12} to fractions with denominator 12.

$$\frac{\frac{7}{12}}{\frac{9}{12}-\frac{5}{12}}-\frac{17}{24}\times \frac{5}{3}\left(\frac{80}{100}+\frac{\frac{9}{14}}{\frac{36}{35}}\right)$$

Since \frac{9}{12} and \frac{5}{12} have the same denominator, subtract them by subtracting their numerators.

$$\frac{\frac{7}{12}}{\frac{9-5}{12}}-\frac{17}{24}\times \frac{5}{3}\left(\frac{80}{100}+\frac{\frac{9}{14}}{\frac{36}{35}}\right)$$

Subtract 5 from 9 to get 4.

$$\frac{\frac{7}{12}}{\frac{4}{12}}-\frac{17}{24}\times \frac{5}{3}\left(\frac{80}{100}+\frac{\frac{9}{14}}{\frac{36}{35}}\right)$$

Reduce the fraction \frac{4}{12} to lowest terms by extracting and canceling out 4.

$$\frac{\frac{7}{12}}{\frac{1}{3}}-\frac{17}{24}\times \frac{5}{3}\left(\frac{80}{100}+\frac{\frac{9}{14}}{\frac{36}{35}}\right)$$

Divide \frac{7}{12} by \frac{1}{3} by multiplying \frac{7}{12} by the reciprocal of \frac{1}{3}.

$$\frac{7}{12}\times 3-\frac{17}{24}\times \frac{5}{3}\left(\frac{80}{100}+\frac{\frac{9}{14}}{\frac{36}{35}}\right)$$

Express \frac{7}{12}\times 3 as a single fraction.

$$\frac{7\times 3}{12}-\frac{17}{24}\times \frac{5}{3}\left(\frac{80}{100}+\frac{\frac{9}{14}}{\frac{36}{35}}\right)$$

Multiply 7 and 3 to get 21.

$$\frac{21}{12}-\frac{17}{24}\times \frac{5}{3}\left(\frac{80}{100}+\frac{\frac{9}{14}}{\frac{36}{35}}\right)$$

Reduce the fraction \frac{21}{12} to lowest terms by extracting and canceling out 3.

$$\frac{7}{4}-\frac{17}{24}\times \frac{5}{3}\left(\frac{80}{100}+\frac{\frac{9}{14}}{\frac{36}{35}}\right)$$

Multiply \frac{17}{24} times \frac{5}{3} by multiplying numerator times numerator and denominator times denominator.

$$\frac{7}{4}-\frac{17\times 5}{24\times 3}\left(\frac{80}{100}+\frac{\frac{9}{14}}{\frac{36}{35}}\right)$$

Do the multiplications in the fraction \frac{17\times 5}{24\times 3}.

$$\frac{7}{4}-\frac{85}{72}\left(\frac{80}{100}+\frac{\frac{9}{14}}{\frac{36}{35}}\right)$$

Reduce the fraction \frac{80}{100} to lowest terms by extracting and canceling out 20.

$$\frac{7}{4}-\frac{85}{72}\left(\frac{4}{5}+\frac{\frac{9}{14}}{\frac{36}{35}}\right)$$

Divide \frac{9}{14} by \frac{36}{35} by multiplying \frac{9}{14} by the reciprocal of \frac{36}{35}.

$$\frac{7}{4}-\frac{85}{72}\left(\frac{4}{5}+\frac{9}{14}\times \frac{35}{36}\right)$$

Multiply \frac{9}{14} times \frac{35}{36} by multiplying numerator times numerator and denominator times denominator.

$$\frac{7}{4}-\frac{85}{72}\left(\frac{4}{5}+\frac{9\times 35}{14\times 36}\right)$$

Do the multiplications in the fraction \frac{9\times 35}{14\times 36}.

$$\frac{7}{4}-\frac{85}{72}\left(\frac{4}{5}+\frac{315}{504}\right)$$

Reduce the fraction \frac{315}{504} to lowest terms by extracting and canceling out 63.

$$\frac{7}{4}-\frac{85}{72}\left(\frac{4}{5}+\frac{5}{8}\right)$$

Least common multiple of 5 and 8 is 40. Convert \frac{4}{5} and \frac{5}{8} to fractions with denominator 40.

$$\frac{7}{4}-\frac{85}{72}\left(\frac{32}{40}+\frac{25}{40}\right)$$

Since \frac{32}{40} and \frac{25}{40} have the same denominator, add them by adding their numerators.

$$\frac{7}{4}-\frac{85}{72}\times \frac{32+25}{40}$$

Add 32 and 25 to get 57.

$$\frac{7}{4}-\frac{85}{72}\times \frac{57}{40}$$

Multiply \frac{85}{72} times \frac{57}{40} by multiplying numerator times numerator and denominator times denominator.

$$\frac{7}{4}-\frac{85\times 57}{72\times 40}$$

Do the multiplications in the fraction \frac{85\times 57}{72\times 40}.

$$\frac{7}{4}-\frac{4845}{2880}$$

Reduce the fraction \frac{4845}{2880} to lowest terms by extracting and canceling out 15.

$$\frac{7}{4}-\frac{323}{192}$$

Least common multiple of 4 and 192 is 192. Convert \frac{7}{4} and \frac{323}{192} to fractions with denominator 192.

$$\frac{336}{192}-\frac{323}{192}$$

Since \frac{336}{192} and \frac{323}{192} have the same denominator, subtract them by subtracting their numerators.

$$\frac{336-323}{192}$$

Subtract 323 from 336 to get 13.

$$\frac{13}{192}$$

Factor

$$\frac{13}{2 ^ {6} \cdot 3} = 0.06770833333333333$$