Solve 71/3/2frac{1{2}13/5}-3/8+frac{1}{7}1frac{3}{4}-frac{5}{24}

$$\frac{ 7 \frac{ 1 }{ 3 } }{ 2 \frac{ 1 }{ 2 } 1 \frac{ 3 }{ 5 } } - \frac{ 3 }{ 8 } + \frac{ 1 }{ 7 } 1 \frac{ 3 }{ 4 } - \frac{ 5 }{ 24 }$$

Evaluate

$$\frac{3}{2}=1.5$$

Solution Steps

Multiply 7 and 3 to get 21.

$$\frac{\frac{21+1}{3}}{\frac{2\times 2+1}{2}\times \frac{1\times 5+3}{5}}-\frac{3}{8}+\frac{1}{7}\times \frac{1\times 4+3}{4}-\frac{5}{24}$$

Add 21 and 1 to get 22.

$$\frac{\frac{22}{3}}{\frac{2\times 2+1}{2}\times \frac{1\times 5+3}{5}}-\frac{3}{8}+\frac{1}{7}\times \frac{1\times 4+3}{4}-\frac{5}{24}$$

Multiply 2 and 2 to get 4.

$$\frac{\frac{22}{3}}{\frac{4+1}{2}\times \frac{1\times 5+3}{5}}-\frac{3}{8}+\frac{1}{7}\times \frac{1\times 4+3}{4}-\frac{5}{24}$$

Add 4 and 1 to get 5.

$$\frac{\frac{22}{3}}{\frac{5}{2}\times \frac{1\times 5+3}{5}}-\frac{3}{8}+\frac{1}{7}\times \frac{1\times 4+3}{4}-\frac{5}{24}$$

Multiply 1 and 5 to get 5.

$$\frac{\frac{22}{3}}{\frac{5}{2}\times \frac{5+3}{5}}-\frac{3}{8}+\frac{1}{7}\times \frac{1\times 4+3}{4}-\frac{5}{24}$$

Add 5 and 3 to get 8.

$$\frac{\frac{22}{3}}{\frac{5}{2}\times \frac{8}{5}}-\frac{3}{8}+\frac{1}{7}\times \frac{1\times 4+3}{4}-\frac{5}{24}$$

Multiply \frac{5}{2} times \frac{8}{5} by multiplying numerator times numerator and denominator times denominator.

$$\frac{\frac{22}{3}}{\frac{5\times 8}{2\times 5}}-\frac{3}{8}+\frac{1}{7}\times \frac{1\times 4+3}{4}-\frac{5}{24}$$

Cancel out 5 in both numerator and denominator.

$$\frac{\frac{22}{3}}{\frac{8}{2}}-\frac{3}{8}+\frac{1}{7}\times \frac{1\times 4+3}{4}-\frac{5}{24}$$

Divide 8 by 2 to get 4.

$$\frac{\frac{22}{3}}{4}-\frac{3}{8}+\frac{1}{7}\times \frac{1\times 4+3}{4}-\frac{5}{24}$$

Express \frac{\frac{22}{3}}{4} as a single fraction.

$$\frac{22}{3\times 4}-\frac{3}{8}+\frac{1}{7}\times \frac{1\times 4+3}{4}-\frac{5}{24}$$

Multiply 3 and 4 to get 12.

$$\frac{22}{12}-\frac{3}{8}+\frac{1}{7}\times \frac{1\times 4+3}{4}-\frac{5}{24}$$

Reduce the fraction \frac{22}{12} to lowest terms by extracting and canceling out 2.

$$\frac{11}{6}-\frac{3}{8}+\frac{1}{7}\times \frac{1\times 4+3}{4}-\frac{5}{24}$$

Least common multiple of 6 and 8 is 24. Convert \frac{11}{6} and \frac{3}{8} to fractions with denominator 24.

$$\frac{44}{24}-\frac{9}{24}+\frac{1}{7}\times \frac{1\times 4+3}{4}-\frac{5}{24}$$

Since \frac{44}{24} and \frac{9}{24} have the same denominator, subtract them by subtracting their numerators.

$$\frac{44-9}{24}+\frac{1}{7}\times \frac{1\times 4+3}{4}-\frac{5}{24}$$

Subtract 9 from 44 to get 35.

$$\frac{35}{24}+\frac{1}{7}\times \frac{1\times 4+3}{4}-\frac{5}{24}$$

Multiply 1 and 4 to get 4.

$$\frac{35}{24}+\frac{1}{7}\times \frac{4+3}{4}-\frac{5}{24}$$

Add 4 and 3 to get 7.

$$\frac{35}{24}+\frac{1}{7}\times \frac{7}{4}-\frac{5}{24}$$

Multiply \frac{1}{7} times \frac{7}{4} by multiplying numerator times numerator and denominator times denominator.

$$\frac{35}{24}+\frac{1\times 7}{7\times 4}-\frac{5}{24}$$

Cancel out 7 in both numerator and denominator.

$$\frac{35}{24}+\frac{1}{4}-\frac{5}{24}$$

Least common multiple of 24 and 4 is 24. Convert \frac{35}{24} and \frac{1}{4} to fractions with denominator 24.

$$\frac{35}{24}+\frac{6}{24}-\frac{5}{24}$$

Since \frac{35}{24} and \frac{6}{24} have the same denominator, add them by adding their numerators.

$$\frac{35+6}{24}-\frac{5}{24}$$

Add 35 and 6 to get 41.

$$\frac{41}{24}-\frac{5}{24}$$

Since \frac{41}{24} and \frac{5}{24} have the same denominator, subtract them by subtracting their numerators.

$$\frac{41-5}{24}$$

Subtract 5 from 41 to get 36.

$$\frac{36}{24}$$

Reduce the fraction \frac{36}{24} to lowest terms by extracting and canceling out 12.

$$\frac{3}{2}$$

Factor

$$\frac{3}{2} = 1\frac{1}{2} = 1.5$$