Solve 2/3+(4/5-1/2)+3/4-(-2+frac{1}{3})*frac{4}{5}

$$\frac { 2 } { 3 } + ( \frac { 4 } { 5 } - \frac { 1 } { 2 } ) + \frac { 3 } { 4 } - ( - 2 + \frac { 1 } { 3 } ) \cdot \frac { 4 } { 5 }$$

Evaluate

$$\frac{61}{20}=3.05$$

Solution Steps

Least common multiple of 3 and 5 is 15. Convert \frac{2}{3} and \frac{4}{5} to fractions with denominator 15.

$$\frac{10}{15}+\frac{12}{15}-\frac{1}{2}+\frac{3}{4}-\left(-2+\frac{1}{3}\right)\times \frac{4}{5}$$

Since \frac{10}{15} and \frac{12}{15} have the same denominator, add them by adding their numerators.

$$\frac{10+12}{15}-\frac{1}{2}+\frac{3}{4}-\left(-2+\frac{1}{3}\right)\times \frac{4}{5}$$

Add 10 and 12 to get 22.

$$\frac{22}{15}-\frac{1}{2}+\frac{3}{4}-\left(-2+\frac{1}{3}\right)\times \frac{4}{5}$$

Least common multiple of 15 and 2 is 30. Convert \frac{22}{15} and \frac{1}{2} to fractions with denominator 30.

$$\frac{44}{30}-\frac{15}{30}+\frac{3}{4}-\left(-2+\frac{1}{3}\right)\times \frac{4}{5}$$

Since \frac{44}{30} and \frac{15}{30} have the same denominator, subtract them by subtracting their numerators.

$$\frac{44-15}{30}+\frac{3}{4}-\left(-2+\frac{1}{3}\right)\times \frac{4}{5}$$

Subtract 15 from 44 to get 29.

$$\frac{29}{30}+\frac{3}{4}-\left(-2+\frac{1}{3}\right)\times \frac{4}{5}$$

Least common multiple of 30 and 4 is 60. Convert \frac{29}{30} and \frac{3}{4} to fractions with denominator 60.

$$\frac{58}{60}+\frac{45}{60}-\left(-2+\frac{1}{3}\right)\times \frac{4}{5}$$

Since \frac{58}{60} and \frac{45}{60} have the same denominator, add them by adding their numerators.

$$\frac{58+45}{60}-\left(-2+\frac{1}{3}\right)\times \frac{4}{5}$$

Add 58 and 45 to get 103.

$$\frac{103}{60}-\left(-2+\frac{1}{3}\right)\times \frac{4}{5}$$

Convert -2 to fraction -\frac{6}{3}.

$$\frac{103}{60}-\left(-\frac{6}{3}+\frac{1}{3}\right)\times \frac{4}{5}$$

Since -\frac{6}{3} and \frac{1}{3} have the same denominator, add them by adding their numerators.

$$\frac{103}{60}-\frac{-6+1}{3}\times \frac{4}{5}$$

Add -6 and 1 to get -5.

$$\frac{103}{60}-\left(-\frac{5}{3}\times \frac{4}{5}\right)$$

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

$$\frac{103}{60}-\frac{-5\times 4}{3\times 5}$$

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

$$\frac{103}{60}-\frac{-20}{15}$$

Reduce the fraction \frac{-20}{15} to lowest terms by extracting and canceling out 5.

$$\frac{103}{60}-\left(-\frac{4}{3}\right)$$

The opposite of -\frac{4}{3} is \frac{4}{3}.

$$\frac{103}{60}+\frac{4}{3}$$

Least common multiple of 60 and 3 is 60. Convert \frac{103}{60} and \frac{4}{3} to fractions with denominator 60.

$$\frac{103}{60}+\frac{80}{60}$$

Since \frac{103}{60} and \frac{80}{60} have the same denominator, add them by adding their numerators.

$$\frac{103+80}{60}$$

Add 103 and 80 to get 183.

$$\frac{183}{60}$$

Reduce the fraction \frac{183}{60} to lowest terms by extracting and canceling out 3.

$$\frac{61}{20}$$

Factor

$$\frac{61}{2 ^ {2} \cdot 5} = 3\frac{1}{20} = 3.05$$