Solve 3/5+1/3text{of}6/5-(1/5+frac{4}{3})

$$\frac { 3 } { 5 } + \frac { 1 } { 3 } \text { of } \frac { 6 } { 5 } - ( \frac { 1 } { 5 } + \frac { 4 } { 3 } )$$

Evaluate

$$-\frac{8}{15}\approx -0.533333333$$

Solution Steps

Multiply \frac{1}{3} times \frac{6}{5} by multiplying numerator times numerator and denominator times denominator.

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

Do the multiplications in the fraction \frac{1\times 6}{3\times 5}.

$$\frac{3}{5}+\frac{6}{15}-\left(\frac{1}{5}+\frac{4}{3}\right)$$

Reduce the fraction \frac{6}{15} to lowest terms by extracting and canceling out 3.

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

Since \frac{3}{5} and \frac{2}{5} have the same denominator, add them by adding their numerators.

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

Add 3 and 2 to get 5.

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

Divide 5 by 5 to get 1.

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

Least common multiple of 5 and 3 is 15. Convert \frac{1}{5} and \frac{4}{3} to fractions with denominator 15.

$$1-\left(\frac{3}{15}+\frac{20}{15}\right)$$

Since \frac{3}{15} and \frac{20}{15} have the same denominator, add them by adding their numerators.

$$1-\frac{3+20}{15}$$

Add 3 and 20 to get 23.

$$1-\frac{23}{15}$$

Convert 1 to fraction \frac{15}{15}.

$$\frac{15}{15}-\frac{23}{15}$$

Since \frac{15}{15} and \frac{23}{15} have the same denominator, subtract them by subtracting their numerators.

$$\frac{15-23}{15}$$

Subtract 23 from 15 to get -8.

$$-\frac{8}{15}$$

Factor

$$-\frac{8}{15} = -0.5333333333333333$$