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

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

Evaluate

$$\frac{221}{90}\approx 2.455555556$$

Solution Steps

Least common multiple of 5 and 3 is 15. Convert \frac{1}{5} and \frac{2}{3} to fractions with denominator 15.

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

Since \frac{3}{15} and \frac{10}{15} have the same denominator, subtract them by subtracting their numerators.

$$\frac{3}{2}-\frac{4}{3}\times \frac{3-10}{15}+\frac{1}{3}$$

Subtract 10 from 3 to get -7.

$$\frac{3}{2}-\frac{4}{3}\left(-\frac{7}{15}\right)+\frac{1}{3}$$

Multiply \frac{4}{3} times -\frac{7}{15} by multiplying numerator times numerator and denominator times denominator.

$$\frac{3}{2}-\frac{4\left(-7\right)}{3\times 15}+\frac{1}{3}$$

Do the multiplications in the fraction \frac{4\left(-7\right)}{3\times 15}.

$$\frac{3}{2}-\frac{-28}{45}+\frac{1}{3}$$

Fraction \frac{-28}{45} can be rewritten as -\frac{28}{45} by extracting the negative sign.

$$\frac{3}{2}-\left(-\frac{28}{45}\right)+\frac{1}{3}$$

The opposite of -\frac{28}{45} is \frac{28}{45}.

$$\frac{3}{2}+\frac{28}{45}+\frac{1}{3}$$

Least common multiple of 2 and 45 is 90. Convert \frac{3}{2} and \frac{28}{45} to fractions with denominator 90.

$$\frac{135}{90}+\frac{56}{90}+\frac{1}{3}$$

Since \frac{135}{90} and \frac{56}{90} have the same denominator, add them by adding their numerators.

$$\frac{135+56}{90}+\frac{1}{3}$$

Add 135 and 56 to get 191.

$$\frac{191}{90}+\frac{1}{3}$$

Least common multiple of 90 and 3 is 90. Convert \frac{191}{90} and \frac{1}{3} to fractions with denominator 90.

$$\frac{191}{90}+\frac{30}{90}$$

Since \frac{191}{90} and \frac{30}{90} have the same denominator, add them by adding their numerators.

$$\frac{191+30}{90}$$

Add 191 and 30 to get 221.

$$\frac{221}{90}$$

Factor

$$\frac{13 \cdot 17}{2 \cdot 3 ^ {2} \cdot 5} = 2\frac{41}{90} = 2.4555555555555557$$