Solve 2-3/4*3/2+1/3div5*2-2*3/2+3*frac{1}{3}

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

Evaluate

$$-\frac{119}{120}\approx -0.991666667$$

Solution Steps

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

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

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

$$2-\frac{9}{8}+\frac{\frac{1}{3}}{5}\times 2-2\times \frac{3}{2}+3\times \frac{1}{3}$$

Convert 2 to fraction \frac{16}{8}.

$$\frac{16}{8}-\frac{9}{8}+\frac{\frac{1}{3}}{5}\times 2-2\times \frac{3}{2}+3\times \frac{1}{3}$$

Since \frac{16}{8} and \frac{9}{8} have the same denominator, subtract them by subtracting their numerators.

$$\frac{16-9}{8}+\frac{\frac{1}{3}}{5}\times 2-2\times \frac{3}{2}+3\times \frac{1}{3}$$

Subtract 9 from 16 to get 7.

$$\frac{7}{8}+\frac{\frac{1}{3}}{5}\times 2-2\times \frac{3}{2}+3\times \frac{1}{3}$$

Express \frac{\frac{1}{3}}{5} as a single fraction.

$$\frac{7}{8}+\frac{1}{3\times 5}\times 2-2\times \frac{3}{2}+3\times \frac{1}{3}$$

Multiply 3 and 5 to get 15.

$$\frac{7}{8}+\frac{1}{15}\times 2-2\times \frac{3}{2}+3\times \frac{1}{3}$$

Multiply \frac{1}{15} and 2 to get \frac{2}{15}.

$$\frac{7}{8}+\frac{2}{15}-2\times \frac{3}{2}+3\times \frac{1}{3}$$

Least common multiple of 8 and 15 is 120. Convert \frac{7}{8} and \frac{2}{15} to fractions with denominator 120.

$$\frac{105}{120}+\frac{16}{120}-2\times \frac{3}{2}+3\times \frac{1}{3}$$

Since \frac{105}{120} and \frac{16}{120} have the same denominator, add them by adding their numerators.

$$\frac{105+16}{120}-2\times \frac{3}{2}+3\times \frac{1}{3}$$

Add 105 and 16 to get 121.

$$\frac{121}{120}-2\times \frac{3}{2}+3\times \frac{1}{3}$$

Cancel out 2 and 2.

$$\frac{121}{120}-3+3\times \frac{1}{3}$$

Convert 3 to fraction \frac{360}{120}.

$$\frac{121}{120}-\frac{360}{120}+3\times \frac{1}{3}$$

Since \frac{121}{120} and \frac{360}{120} have the same denominator, subtract them by subtracting their numerators.

$$\frac{121-360}{120}+3\times \frac{1}{3}$$

Subtract 360 from 121 to get -239.

$$-\frac{239}{120}+3\times \frac{1}{3}$$

Cancel out 3 and 3.

$$-\frac{239}{120}+1$$

Convert 1 to fraction \frac{120}{120}.

$$-\frac{239}{120}+\frac{120}{120}$$

Since -\frac{239}{120} and \frac{120}{120} have the same denominator, add them by adding their numerators.

$$\frac{-239+120}{120}$$

Add -239 and 120 to get -119.

$$-\frac{119}{120}$$

Factor

$$-\frac{119}{120} = -0.9916666666666667$$