Solve 9*(1/9+3/4)-1:5/6*28/48

$$9 \cdot ( \frac { 1 } { 9 } + \frac { 3 } { 4 } ) - 1 : \frac { 5 } { 6 } \cdot \frac { 28 } { 48 }$$

Evaluate

$$\frac{141}{20}=7.05$$

Solution Steps

Least common multiple of 9 and 4 is 36. Convert \frac{1}{9} and \frac{3}{4} to fractions with denominator 36.

$$9\left(\frac{4}{36}+\frac{27}{36}\right)-\frac{1}{\frac{5}{6}}\times \frac{28}{48}$$

Since \frac{4}{36} and \frac{27}{36} have the same denominator, add them by adding their numerators.

$$9\times \frac{4+27}{36}-\frac{1}{\frac{5}{6}}\times \frac{28}{48}$$

Add 4 and 27 to get 31.

$$9\times \frac{31}{36}-\frac{1}{\frac{5}{6}}\times \frac{28}{48}$$

Express 9\times \frac{31}{36} as a single fraction.

$$\frac{9\times 31}{36}-\frac{1}{\frac{5}{6}}\times \frac{28}{48}$$

Multiply 9 and 31 to get 279.

$$\frac{279}{36}-\frac{1}{\frac{5}{6}}\times \frac{28}{48}$$

Reduce the fraction \frac{279}{36} to lowest terms by extracting and canceling out 9.

$$\frac{31}{4}-\frac{1}{\frac{5}{6}}\times \frac{28}{48}$$

Divide 1 by \frac{5}{6} by multiplying 1 by the reciprocal of \frac{5}{6}.

$$\frac{31}{4}-1\times \frac{6}{5}\times \frac{28}{48}$$

Multiply 1 and \frac{6}{5} to get \frac{6}{5}.

$$\frac{31}{4}-\frac{6}{5}\times \frac{28}{48}$$

Reduce the fraction \frac{28}{48} to lowest terms by extracting and canceling out 4.

$$\frac{31}{4}-\frac{6}{5}\times \frac{7}{12}$$

Multiply \frac{6}{5} times \frac{7}{12} by multiplying numerator times numerator and denominator times denominator.

$$\frac{31}{4}-\frac{6\times 7}{5\times 12}$$

Do the multiplications in the fraction \frac{6\times 7}{5\times 12}.

$$\frac{31}{4}-\frac{42}{60}$$

Reduce the fraction \frac{42}{60} to lowest terms by extracting and canceling out 6.

$$\frac{31}{4}-\frac{7}{10}$$

Least common multiple of 4 and 10 is 20. Convert \frac{31}{4} and \frac{7}{10} to fractions with denominator 20.

$$\frac{155}{20}-\frac{14}{20}$$

Since \frac{155}{20} and \frac{14}{20} have the same denominator, subtract them by subtracting their numerators.

$$\frac{155-14}{20}$$

Subtract 14 from 155 to get 141.

$$\frac{141}{20}$$

Factor

$$\frac{3 \cdot 47}{2 ^ {2} \cdot 5} = 7\frac{1}{20} = 7.05$$