Solve 23/4+13/8+23/10-35/24+1frac{8}{15}

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

Evaluate

$$5$$

Solution Steps

Multiply 2 and 4 to get 8.

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

Add 8 and 3 to get 11.

$$\frac{11}{4}+\frac{13}{8}+\frac{23}{10}-\frac{3\times 24+5}{24}+\frac{1\times 15+8}{15}$$

Least common multiple of 4 and 8 is 8. Convert \frac{11}{4} and \frac{13}{8} to fractions with denominator 8.

$$\frac{22}{8}+\frac{13}{8}+\frac{23}{10}-\frac{3\times 24+5}{24}+\frac{1\times 15+8}{15}$$

Since \frac{22}{8} and \frac{13}{8} have the same denominator, add them by adding their numerators.

$$\frac{22+13}{8}+\frac{23}{10}-\frac{3\times 24+5}{24}+\frac{1\times 15+8}{15}$$

Add 22 and 13 to get 35.

$$\frac{35}{8}+\frac{23}{10}-\frac{3\times 24+5}{24}+\frac{1\times 15+8}{15}$$

Least common multiple of 8 and 10 is 40. Convert \frac{35}{8} and \frac{23}{10} to fractions with denominator 40.

$$\frac{175}{40}+\frac{92}{40}-\frac{3\times 24+5}{24}+\frac{1\times 15+8}{15}$$

Since \frac{175}{40} and \frac{92}{40} have the same denominator, add them by adding their numerators.

$$\frac{175+92}{40}-\frac{3\times 24+5}{24}+\frac{1\times 15+8}{15}$$

Add 175 and 92 to get 267.

$$\frac{267}{40}-\frac{3\times 24+5}{24}+\frac{1\times 15+8}{15}$$

Multiply 3 and 24 to get 72.

$$\frac{267}{40}-\frac{72+5}{24}+\frac{1\times 15+8}{15}$$

Add 72 and 5 to get 77.

$$\frac{267}{40}-\frac{77}{24}+\frac{1\times 15+8}{15}$$

Least common multiple of 40 and 24 is 120. Convert \frac{267}{40} and \frac{77}{24} to fractions with denominator 120.

$$\frac{801}{120}-\frac{385}{120}+\frac{1\times 15+8}{15}$$

Since \frac{801}{120} and \frac{385}{120} have the same denominator, subtract them by subtracting their numerators.

$$\frac{801-385}{120}+\frac{1\times 15+8}{15}$$

Subtract 385 from 801 to get 416.

$$\frac{416}{120}+\frac{1\times 15+8}{15}$$

Reduce the fraction \frac{416}{120} to lowest terms by extracting and canceling out 8.

$$\frac{52}{15}+\frac{1\times 15+8}{15}$$

Multiply 1 and 15 to get 15.

$$\frac{52}{15}+\frac{15+8}{15}$$

Add 15 and 8 to get 23.

$$\frac{52}{15}+\frac{23}{15}$$

Since \frac{52}{15} and \frac{23}{15} have the same denominator, add them by adding their numerators.

$$\frac{52+23}{15}$$

Add 52 and 23 to get 75.

$$\frac{75}{15}$$

Divide 75 by 15 to get 5.

$$5$$

Factor

$$5$$