Solve (153/8-82/3)+(475/6-325/12)-(12frac{1}{2}-5frac{3}{4})

$$( 15 \frac { 3 } { 8 } - 8 \frac { 2 } { 3 } ) + ( 47 \frac { 5 } { 6 } - 32 \frac { 5 } { 12 } ) - ( 12 \frac { 1 } { 2 } - 5 \frac { 3 } { 4 } )$$

Evaluate

$$\frac{123}{8}=15.375$$

Solution Steps

Multiply 15 and 8 to get 120.

$$\frac{120+3}{8}-\frac{8\times 3+2}{3}+\frac{47\times 6+5}{6}-\frac{32\times 12+5}{12}-\left(\frac{12\times 2+1}{2}-\frac{5\times 4+3}{4}\right)$$

Add 120 and 3 to get 123.

$$\frac{123}{8}-\frac{8\times 3+2}{3}+\frac{47\times 6+5}{6}-\frac{32\times 12+5}{12}-\left(\frac{12\times 2+1}{2}-\frac{5\times 4+3}{4}\right)$$

Multiply 8 and 3 to get 24.

$$\frac{123}{8}-\frac{24+2}{3}+\frac{47\times 6+5}{6}-\frac{32\times 12+5}{12}-\left(\frac{12\times 2+1}{2}-\frac{5\times 4+3}{4}\right)$$

Add 24 and 2 to get 26.

$$\frac{123}{8}-\frac{26}{3}+\frac{47\times 6+5}{6}-\frac{32\times 12+5}{12}-\left(\frac{12\times 2+1}{2}-\frac{5\times 4+3}{4}\right)$$

Least common multiple of 8 and 3 is 24. Convert \frac{123}{8} and \frac{26}{3} to fractions with denominator 24.

$$\frac{369}{24}-\frac{208}{24}+\frac{47\times 6+5}{6}-\frac{32\times 12+5}{12}-\left(\frac{12\times 2+1}{2}-\frac{5\times 4+3}{4}\right)$$

Since \frac{369}{24} and \frac{208}{24} have the same denominator, subtract them by subtracting their numerators.

$$\frac{369-208}{24}+\frac{47\times 6+5}{6}-\frac{32\times 12+5}{12}-\left(\frac{12\times 2+1}{2}-\frac{5\times 4+3}{4}\right)$$

Subtract 208 from 369 to get 161.

$$\frac{161}{24}+\frac{47\times 6+5}{6}-\frac{32\times 12+5}{12}-\left(\frac{12\times 2+1}{2}-\frac{5\times 4+3}{4}\right)$$

Multiply 47 and 6 to get 282.

$$\frac{161}{24}+\frac{282+5}{6}-\frac{32\times 12+5}{12}-\left(\frac{12\times 2+1}{2}-\frac{5\times 4+3}{4}\right)$$

Add 282 and 5 to get 287.

$$\frac{161}{24}+\frac{287}{6}-\frac{32\times 12+5}{12}-\left(\frac{12\times 2+1}{2}-\frac{5\times 4+3}{4}\right)$$

Least common multiple of 24 and 6 is 24. Convert \frac{161}{24} and \frac{287}{6} to fractions with denominator 24.

$$\frac{161}{24}+\frac{1148}{24}-\frac{32\times 12+5}{12}-\left(\frac{12\times 2+1}{2}-\frac{5\times 4+3}{4}\right)$$

Since \frac{161}{24} and \frac{1148}{24} have the same denominator, add them by adding their numerators.

$$\frac{161+1148}{24}-\frac{32\times 12+5}{12}-\left(\frac{12\times 2+1}{2}-\frac{5\times 4+3}{4}\right)$$

Add 161 and 1148 to get 1309.

$$\frac{1309}{24}-\frac{32\times 12+5}{12}-\left(\frac{12\times 2+1}{2}-\frac{5\times 4+3}{4}\right)$$

Multiply 32 and 12 to get 384.

$$\frac{1309}{24}-\frac{384+5}{12}-\left(\frac{12\times 2+1}{2}-\frac{5\times 4+3}{4}\right)$$

Add 384 and 5 to get 389.

$$\frac{1309}{24}-\frac{389}{12}-\left(\frac{12\times 2+1}{2}-\frac{5\times 4+3}{4}\right)$$

Least common multiple of 24 and 12 is 24. Convert \frac{1309}{24} and \frac{389}{12} to fractions with denominator 24.

$$\frac{1309}{24}-\frac{778}{24}-\left(\frac{12\times 2+1}{2}-\frac{5\times 4+3}{4}\right)$$

Since \frac{1309}{24} and \frac{778}{24} have the same denominator, subtract them by subtracting their numerators.

$$\frac{1309-778}{24}-\left(\frac{12\times 2+1}{2}-\frac{5\times 4+3}{4}\right)$$

Subtract 778 from 1309 to get 531.

$$\frac{531}{24}-\left(\frac{12\times 2+1}{2}-\frac{5\times 4+3}{4}\right)$$

Reduce the fraction \frac{531}{24} to lowest terms by extracting and canceling out 3.

$$\frac{177}{8}-\left(\frac{12\times 2+1}{2}-\frac{5\times 4+3}{4}\right)$$

Multiply 12 and 2 to get 24.

$$\frac{177}{8}-\left(\frac{24+1}{2}-\frac{5\times 4+3}{4}\right)$$

Add 24 and 1 to get 25.

$$\frac{177}{8}-\left(\frac{25}{2}-\frac{5\times 4+3}{4}\right)$$

Multiply 5 and 4 to get 20.

$$\frac{177}{8}-\left(\frac{25}{2}-\frac{20+3}{4}\right)$$

Add 20 and 3 to get 23.

$$\frac{177}{8}-\left(\frac{25}{2}-\frac{23}{4}\right)$$

Least common multiple of 2 and 4 is 4. Convert \frac{25}{2} and \frac{23}{4} to fractions with denominator 4.

$$\frac{177}{8}-\left(\frac{50}{4}-\frac{23}{4}\right)$$

Since \frac{50}{4} and \frac{23}{4} have the same denominator, subtract them by subtracting their numerators.

$$\frac{177}{8}-\frac{50-23}{4}$$

Subtract 23 from 50 to get 27.

$$\frac{177}{8}-\frac{27}{4}$$

Least common multiple of 8 and 4 is 8. Convert \frac{177}{8} and \frac{27}{4} to fractions with denominator 8.

$$\frac{177}{8}-\frac{54}{8}$$

Since \frac{177}{8} and \frac{54}{8} have the same denominator, subtract them by subtracting their numerators.

$$\frac{177-54}{8}$$

Subtract 54 from 177 to get 123.

$$\frac{123}{8}$$

Factor

$$\frac{3 \cdot 41}{2 ^ {3}} = 15\frac{3}{8} = 15.375$$