Solve 14/5:2/3-1/3

$$1 \frac { 4 } { 5 } : \frac { 2 } { 3 } - \frac { 1 } { 3 }$$

Evaluate

$$\frac{71}{30}\approx 2.366666667$$

Solution Steps

Divide \frac{1\times 5+4}{5} by \frac{2}{3} by multiplying \frac{1\times 5+4}{5} by the reciprocal of \frac{2}{3}.

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

Multiply 1 and 5 to get 5.

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

Add 5 and 4 to get 9.

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

Multiply 9 and 3 to get 27.

$$\frac{27}{5\times 2}-\frac{1}{3}$$

Multiply 5 and 2 to get 10.

$$\frac{27}{10}-\frac{1}{3}$$

Least common multiple of 10 and 3 is 30. Convert \frac{27}{10} and \frac{1}{3} to fractions with denominator 30.

$$\frac{81}{30}-\frac{10}{30}$$

Since \frac{81}{30} and \frac{10}{30} have the same denominator, subtract them by subtracting their numerators.

$$\frac{81-10}{30}$$

Subtract 10 from 81 to get 71.

$$\frac{71}{30}$$

Factor

$$\frac{71}{2 \cdot 3 \cdot 5} = 2\frac{11}{30} = 2.3666666666666667$$