Solve 3/frac{4{5}}-3/4/frac{5{6}}+frac{3/4}{6}

$$\frac { 3 } { \frac { 4 } { 5 } } - \frac { \frac { 3 } { 4 } } { \frac { 5 } { 6 } } + \frac { \frac { 3 } { 4 } } { 6 }$$

Evaluate

$$\frac{119}{40}=2.975$$

Solution Steps

Divide 3 by \frac{4}{5} by multiplying 3 by the reciprocal of \frac{4}{5}.

$$3\times \frac{5}{4}-\frac{\frac{3}{4}}{\frac{5}{6}}+\frac{\frac{3}{4}}{6}$$

Express 3\times \frac{5}{4} as a single fraction.

$$\frac{3\times 5}{4}-\frac{\frac{3}{4}}{\frac{5}{6}}+\frac{\frac{3}{4}}{6}$$

Multiply 3 and 5 to get 15.

$$\frac{15}{4}-\frac{\frac{3}{4}}{\frac{5}{6}}+\frac{\frac{3}{4}}{6}$$

Divide \frac{3}{4} by \frac{5}{6} by multiplying \frac{3}{4} by the reciprocal of \frac{5}{6}.

$$\frac{15}{4}-\frac{3}{4}\times \frac{6}{5}+\frac{\frac{3}{4}}{6}$$

Multiply \frac{3}{4} times \frac{6}{5} by multiplying numerator times numerator and denominator times denominator.

$$\frac{15}{4}-\frac{3\times 6}{4\times 5}+\frac{\frac{3}{4}}{6}$$

Do the multiplications in the fraction \frac{3\times 6}{4\times 5}.

$$\frac{15}{4}-\frac{18}{20}+\frac{\frac{3}{4}}{6}$$

Reduce the fraction \frac{18}{20} to lowest terms by extracting and canceling out 2.

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

Least common multiple of 4 and 10 is 20. Convert \frac{15}{4} and \frac{9}{10} to fractions with denominator 20.

$$\frac{75}{20}-\frac{18}{20}+\frac{\frac{3}{4}}{6}$$

Since \frac{75}{20} and \frac{18}{20} have the same denominator, subtract them by subtracting their numerators.

$$\frac{75-18}{20}+\frac{\frac{3}{4}}{6}$$

Subtract 18 from 75 to get 57.

$$\frac{57}{20}+\frac{\frac{3}{4}}{6}$$

Express \frac{\frac{3}{4}}{6} as a single fraction.

$$\frac{57}{20}+\frac{3}{4\times 6}$$

Multiply 4 and 6 to get 24.

$$\frac{57}{20}+\frac{3}{24}$$

Reduce the fraction \frac{3}{24} to lowest terms by extracting and canceling out 3.

$$\frac{57}{20}+\frac{1}{8}$$

Least common multiple of 20 and 8 is 40. Convert \frac{57}{20} and \frac{1}{8} to fractions with denominator 40.

$$\frac{114}{40}+\frac{5}{40}$$

Since \frac{114}{40} and \frac{5}{40} have the same denominator, add them by adding their numerators.

$$\frac{114+5}{40}$$

Add 114 and 5 to get 119.

$$\frac{119}{40}$$

Factor

$$\frac{7 \cdot 17}{2 ^ {3} \cdot 5} = 2\frac{39}{40} = 2.975$$