Solve 860*(5/6-3/10+1/2)

$$860 \times ( \frac { 5 } { 6 } - \frac { 3 } { 10 } + \frac { 1 } { 2 } )$$

Evaluate

$$\frac{2666}{3}\approx 888.666666667$$

Solution Steps

Least common multiple of 6 and 10 is 30. Convert \frac{5}{6} and \frac{3}{10} to fractions with denominator 30.

$$860\left(\frac{25}{30}-\frac{9}{30}+\frac{1}{2}\right)$$

Since \frac{25}{30} and \frac{9}{30} have the same denominator, subtract them by subtracting their numerators.

$$860\left(\frac{25-9}{30}+\frac{1}{2}\right)$$

Subtract 9 from 25 to get 16.

$$860\left(\frac{16}{30}+\frac{1}{2}\right)$$

Reduce the fraction \frac{16}{30} to lowest terms by extracting and canceling out 2.

$$860\left(\frac{8}{15}+\frac{1}{2}\right)$$

Least common multiple of 15 and 2 is 30. Convert \frac{8}{15} and \frac{1}{2} to fractions with denominator 30.

$$860\left(\frac{16}{30}+\frac{15}{30}\right)$$

Since \frac{16}{30} and \frac{15}{30} have the same denominator, add them by adding their numerators.

$$860\times \frac{16+15}{30}$$

Add 16 and 15 to get 31.

$$860\times \frac{31}{30}$$

Express 860\times \frac{31}{30} as a single fraction.

$$\frac{860\times 31}{30}$$

Multiply 860 and 31 to get 26660.

$$\frac{26660}{30}$$

Reduce the fraction \frac{26660}{30} to lowest terms by extracting and canceling out 10.

$$\frac{2666}{3}$$

Factor

$$\frac{2 \cdot 31 \cdot 43}{3} = 888\frac{2}{3} = 888.6666666666666$$