Solve 1/2+3*4/9-5/2*(-1/2)^3+2:frac{4}{3}=

$$\frac { 1 } { 2 } + 3 \cdot \frac { 4 } { 9 } - \frac { 5 } { 2 } \cdot ( - \frac { 1 } { 2 } ) ^ { 3 } + 2 : \frac { 4 } { 3 } =$$

Evaluate

$$\frac{175}{48}\approx 3.645833333$$

Solution Steps

Express 3\times \frac{4}{9} as a single fraction.

$$\frac{1}{2}+\frac{3\times 4}{9}-\frac{5}{2}\left(-\frac{1}{2}\right)^{3}+\frac{2}{\frac{4}{3}}$$

Multiply 3 and 4 to get 12.

$$\frac{1}{2}+\frac{12}{9}-\frac{5}{2}\left(-\frac{1}{2}\right)^{3}+\frac{2}{\frac{4}{3}}$$

Reduce the fraction \frac{12}{9} to lowest terms by extracting and canceling out 3.

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

Least common multiple of 2 and 3 is 6. Convert \frac{1}{2} and \frac{4}{3} to fractions with denominator 6.

$$\frac{3}{6}+\frac{8}{6}-\frac{5}{2}\left(-\frac{1}{2}\right)^{3}+\frac{2}{\frac{4}{3}}$$

Since \frac{3}{6} and \frac{8}{6} have the same denominator, add them by adding their numerators.

$$\frac{3+8}{6}-\frac{5}{2}\left(-\frac{1}{2}\right)^{3}+\frac{2}{\frac{4}{3}}$$

Add 3 and 8 to get 11.

$$\frac{11}{6}-\frac{5}{2}\left(-\frac{1}{2}\right)^{3}+\frac{2}{\frac{4}{3}}$$

Calculate -\frac{1}{2} to the power of 3 and get -\frac{1}{8}.

$$\frac{11}{6}-\frac{5}{2}\left(-\frac{1}{8}\right)+\frac{2}{\frac{4}{3}}$$

Multiply \frac{5}{2} times -\frac{1}{8} by multiplying numerator times numerator and denominator times denominator.

$$\frac{11}{6}-\frac{5\left(-1\right)}{2\times 8}+\frac{2}{\frac{4}{3}}$$

Do the multiplications in the fraction \frac{5\left(-1\right)}{2\times 8}.

$$\frac{11}{6}-\frac{-5}{16}+\frac{2}{\frac{4}{3}}$$

Fraction \frac{-5}{16} can be rewritten as -\frac{5}{16} by extracting the negative sign.

$$\frac{11}{6}-\left(-\frac{5}{16}\right)+\frac{2}{\frac{4}{3}}$$

The opposite of -\frac{5}{16} is \frac{5}{16}.

$$\frac{11}{6}+\frac{5}{16}+\frac{2}{\frac{4}{3}}$$

Least common multiple of 6 and 16 is 48. Convert \frac{11}{6} and \frac{5}{16} to fractions with denominator 48.

$$\frac{88}{48}+\frac{15}{48}+\frac{2}{\frac{4}{3}}$$

Since \frac{88}{48} and \frac{15}{48} have the same denominator, add them by adding their numerators.

$$\frac{88+15}{48}+\frac{2}{\frac{4}{3}}$$

Add 88 and 15 to get 103.

$$\frac{103}{48}+\frac{2}{\frac{4}{3}}$$

Divide 2 by \frac{4}{3} by multiplying 2 by the reciprocal of \frac{4}{3}.

$$\frac{103}{48}+2\times \frac{3}{4}$$

Express 2\times \frac{3}{4} as a single fraction.

$$\frac{103}{48}+\frac{2\times 3}{4}$$

Multiply 2 and 3 to get 6.

$$\frac{103}{48}+\frac{6}{4}$$

Reduce the fraction \frac{6}{4} to lowest terms by extracting and canceling out 2.

$$\frac{103}{48}+\frac{3}{2}$$

Least common multiple of 48 and 2 is 48. Convert \frac{103}{48} and \frac{3}{2} to fractions with denominator 48.

$$\frac{103}{48}+\frac{72}{48}$$

Since \frac{103}{48} and \frac{72}{48} have the same denominator, add them by adding their numerators.

$$\frac{103+72}{48}$$

Add 103 and 72 to get 175.

$$\frac{175}{48}$$

Factor

$$\frac{5 ^ {2} \cdot 7}{2 ^ {4} \cdot 3} = 3\frac{31}{48} = 3.6458333333333335$$