Solve 5/2*3/4*1/2+3/2+frac{1}{2}divfrac{3}{2}[frac{2}{3}-frac{1}{2}*frac{2}{3}]

$$\frac { 5 } { 2 } \times \frac { 3 } { 4 } \times \frac { 1 } { 2 } + \frac { 3 } { 2 } + \frac { 1 } { 2 } \div \frac { 3 } { 2 } [ \frac { 2 } { 3 } - \frac { 1 } { 2 } \times \frac { 2 } { 3 } ]$$

Evaluate

$$\frac{367}{144}\approx 2.548611111$$

Solution Steps

Multiply \frac{5}{2} times \frac{3}{4} by multiplying numerator times numerator and denominator times denominator.

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

Do the multiplications in the fraction \frac{5\times 3}{2\times 4}.

$$\frac{15}{8}\times \frac{1}{2}+\frac{3}{2}+\frac{\frac{1}{2}}{\frac{3}{2}}\left(\frac{2}{3}-\frac{1}{2}\times \frac{2}{3}\right)$$

Multiply \frac{15}{8} times \frac{1}{2} by multiplying numerator times numerator and denominator times denominator.

$$\frac{15\times 1}{8\times 2}+\frac{3}{2}+\frac{\frac{1}{2}}{\frac{3}{2}}\left(\frac{2}{3}-\frac{1}{2}\times \frac{2}{3}\right)$$

Do the multiplications in the fraction \frac{15\times 1}{8\times 2}.

$$\frac{15}{16}+\frac{3}{2}+\frac{\frac{1}{2}}{\frac{3}{2}}\left(\frac{2}{3}-\frac{1}{2}\times \frac{2}{3}\right)$$

Least common multiple of 16 and 2 is 16. Convert \frac{15}{16} and \frac{3}{2} to fractions with denominator 16.

$$\frac{15}{16}+\frac{24}{16}+\frac{\frac{1}{2}}{\frac{3}{2}}\left(\frac{2}{3}-\frac{1}{2}\times \frac{2}{3}\right)$$

Since \frac{15}{16} and \frac{24}{16} have the same denominator, add them by adding their numerators.

$$\frac{15+24}{16}+\frac{\frac{1}{2}}{\frac{3}{2}}\left(\frac{2}{3}-\frac{1}{2}\times \frac{2}{3}\right)$$

Add 15 and 24 to get 39.

$$\frac{39}{16}+\frac{\frac{1}{2}}{\frac{3}{2}}\left(\frac{2}{3}-\frac{1}{2}\times \frac{2}{3}\right)$$

Divide \frac{1}{2} by \frac{3}{2} by multiplying \frac{1}{2} by the reciprocal of \frac{3}{2}.

$$\frac{39}{16}+\frac{1}{2}\times \frac{2}{3}\left(\frac{2}{3}-\frac{1}{2}\times \frac{2}{3}\right)$$

Multiply \frac{1}{2} times \frac{2}{3} by multiplying numerator times numerator and denominator times denominator.

$$\frac{39}{16}+\frac{1\times 2}{2\times 3}\left(\frac{2}{3}-\frac{1}{2}\times \frac{2}{3}\right)$$

Cancel out 2 in both numerator and denominator.

$$\frac{39}{16}+\frac{1}{3}\left(\frac{2}{3}-\frac{1}{2}\times \frac{2}{3}\right)$$

Multiply \frac{1}{2} times \frac{2}{3} by multiplying numerator times numerator and denominator times denominator.

$$\frac{39}{16}+\frac{1}{3}\left(\frac{2}{3}-\frac{1\times 2}{2\times 3}\right)$$

Cancel out 2 in both numerator and denominator.

$$\frac{39}{16}+\frac{1}{3}\left(\frac{2}{3}-\frac{1}{3}\right)$$

Since \frac{2}{3} and \frac{1}{3} have the same denominator, subtract them by subtracting their numerators.

$$\frac{39}{16}+\frac{1}{3}\times \frac{2-1}{3}$$

Subtract 1 from 2 to get 1.

$$\frac{39}{16}+\frac{1}{3}\times \frac{1}{3}$$

Multiply \frac{1}{3} times \frac{1}{3} by multiplying numerator times numerator and denominator times denominator.

$$\frac{39}{16}+\frac{1\times 1}{3\times 3}$$

Do the multiplications in the fraction \frac{1\times 1}{3\times 3}.

$$\frac{39}{16}+\frac{1}{9}$$

Least common multiple of 16 and 9 is 144. Convert \frac{39}{16} and \frac{1}{9} to fractions with denominator 144.

$$\frac{351}{144}+\frac{16}{144}$$

Since \frac{351}{144} and \frac{16}{144} have the same denominator, add them by adding their numerators.

$$\frac{351+16}{144}$$

Add 351 and 16 to get 367.

$$\frac{367}{144}$$

Factor

$$\frac{367}{2 ^ {4} \cdot 3 ^ {2}} = 2\frac{79}{144} = 2.548611111111111$$