Solve (151/2-23/8)-(55/6+63/4)

$$( 15 \frac { 1 } { 2 } - 2 \frac { 3 } { 8 } ) - ( 5 \frac { 5 } { 6 } + 6 \frac { 3 } { 4 } )$$

Evaluate

$$\frac{13}{24}\approx 0.541666667$$

Solution Steps

Multiply 15 and 2 to get 30.

$$\frac{30+1}{2}-\frac{2\times 8+3}{8}-\left(\frac{5\times 6+5}{6}+\frac{6\times 4+3}{4}\right)$$

Add 30 and 1 to get 31.

$$\frac{31}{2}-\frac{2\times 8+3}{8}-\left(\frac{5\times 6+5}{6}+\frac{6\times 4+3}{4}\right)$$

Multiply 2 and 8 to get 16.

$$\frac{31}{2}-\frac{16+3}{8}-\left(\frac{5\times 6+5}{6}+\frac{6\times 4+3}{4}\right)$$

Add 16 and 3 to get 19.

$$\frac{31}{2}-\frac{19}{8}-\left(\frac{5\times 6+5}{6}+\frac{6\times 4+3}{4}\right)$$

Least common multiple of 2 and 8 is 8. Convert \frac{31}{2} and \frac{19}{8} to fractions with denominator 8.

$$\frac{124}{8}-\frac{19}{8}-\left(\frac{5\times 6+5}{6}+\frac{6\times 4+3}{4}\right)$$

Since \frac{124}{8} and \frac{19}{8} have the same denominator, subtract them by subtracting their numerators.

$$\frac{124-19}{8}-\left(\frac{5\times 6+5}{6}+\frac{6\times 4+3}{4}\right)$$

Subtract 19 from 124 to get 105.

$$\frac{105}{8}-\left(\frac{5\times 6+5}{6}+\frac{6\times 4+3}{4}\right)$$

Multiply 5 and 6 to get 30.

$$\frac{105}{8}-\left(\frac{30+5}{6}+\frac{6\times 4+3}{4}\right)$$

Add 30 and 5 to get 35.

$$\frac{105}{8}-\left(\frac{35}{6}+\frac{6\times 4+3}{4}\right)$$

Multiply 6 and 4 to get 24.

$$\frac{105}{8}-\left(\frac{35}{6}+\frac{24+3}{4}\right)$$

Add 24 and 3 to get 27.

$$\frac{105}{8}-\left(\frac{35}{6}+\frac{27}{4}\right)$$

Least common multiple of 6 and 4 is 12. Convert \frac{35}{6} and \frac{27}{4} to fractions with denominator 12.

$$\frac{105}{8}-\left(\frac{70}{12}+\frac{81}{12}\right)$$

Since \frac{70}{12} and \frac{81}{12} have the same denominator, add them by adding their numerators.

$$\frac{105}{8}-\frac{70+81}{12}$$

Add 70 and 81 to get 151.

$$\frac{105}{8}-\frac{151}{12}$$

Least common multiple of 8 and 12 is 24. Convert \frac{105}{8} and \frac{151}{12} to fractions with denominator 24.

$$\frac{315}{24}-\frac{302}{24}$$

Since \frac{315}{24} and \frac{302}{24} have the same denominator, subtract them by subtracting their numerators.

$$\frac{315-302}{24}$$

Subtract 302 from 315 to get 13.

$$\frac{13}{24}$$

Factor

$$\frac{13}{2 ^ {3} \cdot 3} = 0.5416666666666666$$