Solve 2/3+1/4/frac{5{9}}+3/5:2=

$$\frac { \frac { 2 } { 3 } + \frac { 1 } { 4 } } { \frac { 5 } { 9 } } + \frac { 3 } { 5 } : 2 =$$

Evaluate

$$\frac{39}{20}=1.95$$

Solution Steps

Least common multiple of 3 and 4 is 12. Convert \frac{2}{3} and \frac{1}{4} to fractions with denominator 12.

$$\frac{\frac{8}{12}+\frac{3}{12}}{\frac{5}{9}}+\frac{\frac{3}{5}}{2}$$

Since \frac{8}{12} and \frac{3}{12} have the same denominator, add them by adding their numerators.

$$\frac{\frac{8+3}{12}}{\frac{5}{9}}+\frac{\frac{3}{5}}{2}$$

Add 8 and 3 to get 11.

$$\frac{\frac{11}{12}}{\frac{5}{9}}+\frac{\frac{3}{5}}{2}$$

Divide \frac{11}{12} by \frac{5}{9} by multiplying \frac{11}{12} by the reciprocal of \frac{5}{9}.

$$\frac{11}{12}\times \frac{9}{5}+\frac{\frac{3}{5}}{2}$$

Multiply \frac{11}{12} times \frac{9}{5} by multiplying numerator times numerator and denominator times denominator.

$$\frac{11\times 9}{12\times 5}+\frac{\frac{3}{5}}{2}$$

Do the multiplications in the fraction \frac{11\times 9}{12\times 5}.

$$\frac{99}{60}+\frac{\frac{3}{5}}{2}$$

Reduce the fraction \frac{99}{60} to lowest terms by extracting and canceling out 3.

$$\frac{33}{20}+\frac{\frac{3}{5}}{2}$$

Express \frac{\frac{3}{5}}{2} as a single fraction.

$$\frac{33}{20}+\frac{3}{5\times 2}$$

Multiply 5 and 2 to get 10.

$$\frac{33}{20}+\frac{3}{10}$$

Least common multiple of 20 and 10 is 20. Convert \frac{33}{20} and \frac{3}{10} to fractions with denominator 20.

$$\frac{33}{20}+\frac{6}{20}$$

Since \frac{33}{20} and \frac{6}{20} have the same denominator, add them by adding their numerators.

$$\frac{33+6}{20}$$

Add 33 and 6 to get 39.

$$\frac{39}{20}$$

Factor

$$\frac{3 \cdot 13}{2 ^ {2} \cdot 5} = 1\frac{19}{20} = 1.95$$