Solve 2(3/4)+13/8+23/10-3(5/24)+1(frac{8}{15})

$$2( \frac{ 3 }{ 4 } )+ \frac{ 13 }{ 8 } + \frac{ 23 }{ 10 } -3( \frac{ 5 }{ 24 } )+1( \frac{ 8 }{ 15 } )$$

Evaluate

$$\frac{16}{3}\approx 5.333333333$$

Solution Steps

Express 2\times \frac{3}{4} as a single fraction.

$$\frac{2\times 3}{4}+\frac{13}{8}+\frac{23}{10}-3\times \frac{5}{24}+1\times \frac{8}{15}$$

Multiply 2 and 3 to get 6.

$$\frac{6}{4}+\frac{13}{8}+\frac{23}{10}-3\times \frac{5}{24}+1\times \frac{8}{15}$$

Reduce the fraction \frac{6}{4} to lowest terms by extracting and canceling out 2.

$$\frac{3}{2}+\frac{13}{8}+\frac{23}{10}-3\times \frac{5}{24}+1\times \frac{8}{15}$$

Least common multiple of 2 and 8 is 8. Convert \frac{3}{2} and \frac{13}{8} to fractions with denominator 8.

$$\frac{12}{8}+\frac{13}{8}+\frac{23}{10}-3\times \frac{5}{24}+1\times \frac{8}{15}$$

Since \frac{12}{8} and \frac{13}{8} have the same denominator, add them by adding their numerators.

$$\frac{12+13}{8}+\frac{23}{10}-3\times \frac{5}{24}+1\times \frac{8}{15}$$

Add 12 and 13 to get 25.

$$\frac{25}{8}+\frac{23}{10}-3\times \frac{5}{24}+1\times \frac{8}{15}$$

Least common multiple of 8 and 10 is 40. Convert \frac{25}{8} and \frac{23}{10} to fractions with denominator 40.

$$\frac{125}{40}+\frac{92}{40}-3\times \frac{5}{24}+1\times \frac{8}{15}$$

Since \frac{125}{40} and \frac{92}{40} have the same denominator, add them by adding their numerators.

$$\frac{125+92}{40}-3\times \frac{5}{24}+1\times \frac{8}{15}$$

Add 125 and 92 to get 217.

$$\frac{217}{40}-3\times \frac{5}{24}+1\times \frac{8}{15}$$

Express 3\times \frac{5}{24} as a single fraction.

$$\frac{217}{40}-\frac{3\times 5}{24}+1\times \frac{8}{15}$$

Multiply 3 and 5 to get 15.

$$\frac{217}{40}-\frac{15}{24}+1\times \frac{8}{15}$$

Reduce the fraction \frac{15}{24} to lowest terms by extracting and canceling out 3.

$$\frac{217}{40}-\frac{5}{8}+1\times \frac{8}{15}$$

Least common multiple of 40 and 8 is 40. Convert \frac{217}{40} and \frac{5}{8} to fractions with denominator 40.

$$\frac{217}{40}-\frac{25}{40}+1\times \frac{8}{15}$$

Since \frac{217}{40} and \frac{25}{40} have the same denominator, subtract them by subtracting their numerators.

$$\frac{217-25}{40}+1\times \frac{8}{15}$$

Subtract 25 from 217 to get 192.

$$\frac{192}{40}+1\times \frac{8}{15}$$

Reduce the fraction \frac{192}{40} to lowest terms by extracting and canceling out 8.

$$\frac{24}{5}+1\times \frac{8}{15}$$

Multiply 1 and \frac{8}{15} to get \frac{8}{15}.

$$\frac{24}{5}+\frac{8}{15}$$

Least common multiple of 5 and 15 is 15. Convert \frac{24}{5} and \frac{8}{15} to fractions with denominator 15.

$$\frac{72}{15}+\frac{8}{15}$$

Since \frac{72}{15} and \frac{8}{15} have the same denominator, add them by adding their numerators.

$$\frac{72+8}{15}$$

Add 72 and 8 to get 80.

$$\frac{80}{15}$$

Reduce the fraction \frac{80}{15} to lowest terms by extracting and canceling out 5.

$$\frac{16}{3}$$

Factor

$$\frac{2 ^ {4}}{3} = 5\frac{1}{3} = 5.333333333333333$$