Solve 151/2-23/8-53/6+63/4+10frac{2}{3}-5frac{3}{8}=

$$15 \frac{ 1 }{ 2 } -2 \frac{ 3 }{ 8 } -5 \frac{ 3 }{ 6 } +6 \frac{ 3 }{ 4 } +10 \frac{ 2 }{ 3 } -5 \frac{ 3 }{ 8 } =$$

Evaluate

$$\frac{59}{3}\approx 19.666666667$$

Solution Steps

Multiply 15 and 2 to get 30.

$$\frac{30+1}{2}-\frac{2\times 8+3}{8}-\frac{5\times 6+3}{6}+\frac{6\times 4+3}{4}+\frac{10\times 3+2}{3}-\frac{5\times 8+3}{8}$$

Add 30 and 1 to get 31.

$$\frac{31}{2}-\frac{2\times 8+3}{8}-\frac{5\times 6+3}{6}+\frac{6\times 4+3}{4}+\frac{10\times 3+2}{3}-\frac{5\times 8+3}{8}$$

Multiply 2 and 8 to get 16.

$$\frac{31}{2}-\frac{16+3}{8}-\frac{5\times 6+3}{6}+\frac{6\times 4+3}{4}+\frac{10\times 3+2}{3}-\frac{5\times 8+3}{8}$$

Add 16 and 3 to get 19.

$$\frac{31}{2}-\frac{19}{8}-\frac{5\times 6+3}{6}+\frac{6\times 4+3}{4}+\frac{10\times 3+2}{3}-\frac{5\times 8+3}{8}$$

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

$$\frac{124}{8}-\frac{19}{8}-\frac{5\times 6+3}{6}+\frac{6\times 4+3}{4}+\frac{10\times 3+2}{3}-\frac{5\times 8+3}{8}$$

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

$$\frac{124-19}{8}-\frac{5\times 6+3}{6}+\frac{6\times 4+3}{4}+\frac{10\times 3+2}{3}-\frac{5\times 8+3}{8}$$

Subtract 19 from 124 to get 105.

$$\frac{105}{8}-\frac{5\times 6+3}{6}+\frac{6\times 4+3}{4}+\frac{10\times 3+2}{3}-\frac{5\times 8+3}{8}$$

Multiply 5 and 6 to get 30.

$$\frac{105}{8}-\frac{30+3}{6}+\frac{6\times 4+3}{4}+\frac{10\times 3+2}{3}-\frac{5\times 8+3}{8}$$

Add 30 and 3 to get 33.

$$\frac{105}{8}-\frac{33}{6}+\frac{6\times 4+3}{4}+\frac{10\times 3+2}{3}-\frac{5\times 8+3}{8}$$

Reduce the fraction \frac{33}{6} to lowest terms by extracting and canceling out 3.

$$\frac{105}{8}-\frac{11}{2}+\frac{6\times 4+3}{4}+\frac{10\times 3+2}{3}-\frac{5\times 8+3}{8}$$

Least common multiple of 8 and 2 is 8. Convert \frac{105}{8} and \frac{11}{2} to fractions with denominator 8.

$$\frac{105}{8}-\frac{44}{8}+\frac{6\times 4+3}{4}+\frac{10\times 3+2}{3}-\frac{5\times 8+3}{8}$$

Since \frac{105}{8} and \frac{44}{8} have the same denominator, subtract them by subtracting their numerators.

$$\frac{105-44}{8}+\frac{6\times 4+3}{4}+\frac{10\times 3+2}{3}-\frac{5\times 8+3}{8}$$

Subtract 44 from 105 to get 61.

$$\frac{61}{8}+\frac{6\times 4+3}{4}+\frac{10\times 3+2}{3}-\frac{5\times 8+3}{8}$$

Multiply 6 and 4 to get 24.

$$\frac{61}{8}+\frac{24+3}{4}+\frac{10\times 3+2}{3}-\frac{5\times 8+3}{8}$$

Add 24 and 3 to get 27.

$$\frac{61}{8}+\frac{27}{4}+\frac{10\times 3+2}{3}-\frac{5\times 8+3}{8}$$

Least common multiple of 8 and 4 is 8. Convert \frac{61}{8} and \frac{27}{4} to fractions with denominator 8.

$$\frac{61}{8}+\frac{54}{8}+\frac{10\times 3+2}{3}-\frac{5\times 8+3}{8}$$

Since \frac{61}{8} and \frac{54}{8} have the same denominator, add them by adding their numerators.

$$\frac{61+54}{8}+\frac{10\times 3+2}{3}-\frac{5\times 8+3}{8}$$

Add 61 and 54 to get 115.

$$\frac{115}{8}+\frac{10\times 3+2}{3}-\frac{5\times 8+3}{8}$$

Multiply 10 and 3 to get 30.

$$\frac{115}{8}+\frac{30+2}{3}-\frac{5\times 8+3}{8}$$

Add 30 and 2 to get 32.

$$\frac{115}{8}+\frac{32}{3}-\frac{5\times 8+3}{8}$$

Least common multiple of 8 and 3 is 24. Convert \frac{115}{8} and \frac{32}{3} to fractions with denominator 24.

$$\frac{345}{24}+\frac{256}{24}-\frac{5\times 8+3}{8}$$

Since \frac{345}{24} and \frac{256}{24} have the same denominator, add them by adding their numerators.

$$\frac{345+256}{24}-\frac{5\times 8+3}{8}$$

Add 345 and 256 to get 601.

$$\frac{601}{24}-\frac{5\times 8+3}{8}$$

Multiply 5 and 8 to get 40.

$$\frac{601}{24}-\frac{40+3}{8}$$

Add 40 and 3 to get 43.

$$\frac{601}{24}-\frac{43}{8}$$

Least common multiple of 24 and 8 is 24. Convert \frac{601}{24} and \frac{43}{8} to fractions with denominator 24.

$$\frac{601}{24}-\frac{129}{24}$$

Since \frac{601}{24} and \frac{129}{24} have the same denominator, subtract them by subtracting their numerators.

$$\frac{601-129}{24}$$

Subtract 129 from 601 to get 472.

$$\frac{472}{24}$$

Reduce the fraction \frac{472}{24} to lowest terms by extracting and canceling out 8.

$$\frac{59}{3}$$

Factor

$$\frac{59}{3} = 19\frac{2}{3} = 19.666666666666668$$