Solve 1/3*5/2-7(1/4-2/3)-frac{4}{5}:3

$$\frac { 1 } { 3 } \cdot \frac { 5 } { 2 } - 7 ( \frac { 1 } { 4 } - \frac { 2 } { 3 } ) - \frac { 4 } { 5 } : 3$$

Evaluate

$$\frac{209}{60}\approx 3.483333333$$

Solution Steps

Multiply \frac{1}{3} times \frac{5}{2} by multiplying numerator times numerator and denominator times denominator.

$$\frac{1\times 5}{3\times 2}-7\left(\frac{1}{4}-\frac{2}{3}\right)-\frac{\frac{4}{5}}{3}$$

Do the multiplications in the fraction \frac{1\times 5}{3\times 2}.

$$\frac{5}{6}-7\left(\frac{1}{4}-\frac{2}{3}\right)-\frac{\frac{4}{5}}{3}$$

Least common multiple of 4 and 3 is 12. Convert \frac{1}{4} and \frac{2}{3} to fractions with denominator 12.

$$\frac{5}{6}-7\left(\frac{3}{12}-\frac{8}{12}\right)-\frac{\frac{4}{5}}{3}$$

Since \frac{3}{12} and \frac{8}{12} have the same denominator, subtract them by subtracting their numerators.

$$\frac{5}{6}-7\times \frac{3-8}{12}-\frac{\frac{4}{5}}{3}$$

Subtract 8 from 3 to get -5.

$$\frac{5}{6}-7\left(-\frac{5}{12}\right)-\frac{\frac{4}{5}}{3}$$

Express 7\left(-\frac{5}{12}\right) as a single fraction.

$$\frac{5}{6}-\frac{7\left(-5\right)}{12}-\frac{\frac{4}{5}}{3}$$

Multiply 7 and -5 to get -35.

$$\frac{5}{6}-\frac{-35}{12}-\frac{\frac{4}{5}}{3}$$

Fraction \frac{-35}{12} can be rewritten as -\frac{35}{12} by extracting the negative sign.

$$\frac{5}{6}-\left(-\frac{35}{12}\right)-\frac{\frac{4}{5}}{3}$$

The opposite of -\frac{35}{12} is \frac{35}{12}.

$$\frac{5}{6}+\frac{35}{12}-\frac{\frac{4}{5}}{3}$$

Least common multiple of 6 and 12 is 12. Convert \frac{5}{6} and \frac{35}{12} to fractions with denominator 12.

$$\frac{10}{12}+\frac{35}{12}-\frac{\frac{4}{5}}{3}$$

Since \frac{10}{12} and \frac{35}{12} have the same denominator, add them by adding their numerators.

$$\frac{10+35}{12}-\frac{\frac{4}{5}}{3}$$

Add 10 and 35 to get 45.

$$\frac{45}{12}-\frac{\frac{4}{5}}{3}$$

Reduce the fraction \frac{45}{12} to lowest terms by extracting and canceling out 3.

$$\frac{15}{4}-\frac{\frac{4}{5}}{3}$$

Express \frac{\frac{4}{5}}{3} as a single fraction.

$$\frac{15}{4}-\frac{4}{5\times 3}$$

Multiply 5 and 3 to get 15.

$$\frac{15}{4}-\frac{4}{15}$$

Least common multiple of 4 and 15 is 60. Convert \frac{15}{4} and \frac{4}{15} to fractions with denominator 60.

$$\frac{225}{60}-\frac{16}{60}$$

Since \frac{225}{60} and \frac{16}{60} have the same denominator, subtract them by subtracting their numerators.

$$\frac{225-16}{60}$$

Subtract 16 from 225 to get 209.

$$\frac{209}{60}$$

Factor

$$\frac{11 \cdot 19}{2 ^ {2} \cdot 3 \cdot 5} = 3\frac{29}{60} = 3.4833333333333334$$